add `box2d` as builtin modules (WIP)

3rd/box2d/CHANGELOG.md

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+# Changes for version 2.4.1
+
+## API Changes
+- Extended distance joint to have a minimum and maximum limit.
+- Removed rope joint. Use the distance joint instead.
+- B2_USER_SETTINGS and b2_user_settings.h can control user data, length units, and maximum polygon vertices.
+- Default user data is now uintptr_t instead of void*
+- b2FixtureDef::restitutionThreshold lets you set the restitution velocity threshold per fixture.
+
+## BREAKING Changes
+- BREAKING: distance joint 0 stiffness now means the spring is turned off rather than making the joint rigid.
+- BREAKING: distance joint minimum and maximum must be set correctly to get old behavior.
+
+## Infrastructure
+- Library installation function available in CMake.
+- Shared library (DLL) option available.
+- Bug fixes
+
+# Changes for version 2.4.0
+
+## Infrastructure
+- Documentation in Doxygen format
+- CMake build system
+- Unit test support
+- Continuous integration testing using Travis CI
+- Limited use of C++11 (nullptr and override)
+- Restructured folders and renamed files to better match open-source standards
+- MIT License
+- Removed float32 and float64
+- Linked the Box2D project to GitHub Sponsors
+
+## Collision
+- Chain and edge shape must now be one-sided to eliminate ghost collisions
+- Broad-phase optimizations
+- Added b2ShapeCast for linear shape casting
+
+## Dynamics
+- Joint limits are now predictive and not stateful
+- Experimental 2D cloth (rope)
+- b2Body::SetActive -> b2Body::SetEnabled
+- Better support for running multiple worlds
+- Handle zero density better
+  - The body behaves like a static body
+  - The body is drawn with a red color
+- Added translation limit to wheel joint
+- World dump now writes to box2d_dump.inl
+- Static bodies are never awake
+- All joints with spring-dampers now use stiffness and damping
+- Added utility functions to convert frequency and damping ratio to stiffness and damping
+
+## Testbed
+- Testbed uses dear imgui
+- glad OpenGL loader
+- OpenGL 3.3 required
+
+# Changes for version 2.3.0
+- Polygon creation now computes the convex hull. Vertices no longer need to be ordered.
+- The convex hull code will merge vertices closer than dm_linearSlop. This may lead to failure on very small polygons.
+- Added b2MotorJoint.
+- Bug fixes.

3rd/box2d/CMakeLists.txt

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+cmake_minimum_required(VERSION 3.10)
+
+project(box2d)
+
+set(CMAKE_CXX_STANDARD 17)
+
+include_directories(${CMAKE_CURRENT_LIST_DIR}/include)
+include_directories(${CMAKE_CURRENT_LIST_DIR}/../pocketpy/include)
+
+aux_source_directory(${CMAKE_CURRENT_LIST_DIR}/src/collision BOX2D_SRC_0)
+aux_source_directory(${CMAKE_CURRENT_LIST_DIR}/src/common BOX2D_SRC_1)
+aux_source_directory(${CMAKE_CURRENT_LIST_DIR}/src/dynamics BOX2D_SRC_2)
+aux_source_directory(${CMAKE_CURRENT_LIST_DIR}/src/rope BOX2D_SRC_3)
+
+set(CMAKE_CXX_FLAGS_RELEASE "-O2")
+
+add_library(
+    box2d
+    STATIC
+    ${BOX2D_SRC_0} ${BOX2D_SRC_1} ${BOX2D_SRC_2} ${BOX2D_SRC_3}
+    ${CMAKE_CURRENT_LIST_DIR}/src/box2d_bindings.cpp
+)

3rd/box2d/LICENSE

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+MIT License
+
+Copyright (c) 2019 Erin Catto
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.

3rd/box2d/README.md

@@ -0,0 +1,109 @@
+![Box2D Logo](https://box2d.org/images/logo.svg)
+
+# Build Status
+[![Build Status](https://github.com/erincatto/box2d/actions/workflows/build.yml/badge.svg)](https://github.com/erincatto/box2d/actions)
+
+# Box2D 
+
+Box2D is a 2D physics engine for games.
+
+## Contributing
+
+Please do not submit pull requests with new features or core library changes. Instead, please file an issue first for discussion. For bugs, I prefer detailed bug reports over pull requests.
+
+## Features
+
+### Collision
+- Continuous collision detection
+- Contact callbacks: begin, end, pre-solve, post-solve
+- Convex polygons and circles
+- Multiple shapes per body
+- One-shot contact manifolds
+- Dynamic tree broadphase
+- Efficient pair management
+- Fast broadphase AABB queries
+- Collision groups and categories
+
+### Physics
+- Continuous physics with time of impact solver
+- Persistent body-joint-contact graph
+- Island solution and sleep management
+- Contact, friction, and restitution
+- Stable stacking with a linear-time solver
+- Revolute, prismatic, distance, pulley, gear, mouse joint, and other joint types
+- Joint limits, motors, and friction
+- Momentum decoupled position correction
+- Fairly accurate reaction forces/impulses
+
+### System
+- Small block and stack allocators
+- Centralized tuning parameters
+- Highly portable C++ with no use of STL containers
+
+### Testbed
+- OpenGL with GLFW
+- Graphical user interface with imgui
+- Extensible test framework
+- Support for loading world dumps
+
+## Building
+- Install [CMake](https://cmake.org/)
+- Ensure CMake is in the user `PATH`
+- Visual Studio: run `build.bat` from the command prompt
+- Otherwise: run `build.sh` from a bash shell
+- Results are in the build sub-folder
+- On Windows you can open box2d.sln
+
+## Building Box2D - Using vcpkg
+You can download and install Box2D using the [vcpkg](https://github.com/Microsoft/vcpkg) dependency manager:
+
+- git clone https://github.com/Microsoft/vcpkg.git
+- cd vcpkg
+- ./bootstrap-vcpkg.sh
+- ./vcpkg integrate install
+- ./vcpkg install box2d
+
+The Box2D port in vcpkg is kept up to date by Microsoft team members and community contributors. If the version is out of date, please [create an issue or pull request](https://github.com/Microsoft/vcpkg) on the vcpkg repository.
+
+Note: vcpkg support is not provided by the Box2D project
+
+## Building for Xcode
+- Install [CMake](https://cmake.org)
+- Add Cmake to the path in .zprofile (the default Terminal shell is zsh)
+    - export PATH="/Applications/CMake.app/Contents/bin:$PATH"
+- mkdir build
+- cd build
+- cmake -G Xcode ..
+- open box2d.xcodeproj
+- Select the testbed scheme
+- Edit the scheme to set a custom working directory, make this be in box2d/testbed
+- You can now build and run the testbed
+
+## Installing using CMake
+You can build and install the library and docs using this command sequence (requires Doxygen):
+```
+mkdir build
+cd build
+cmake -DBOX2D_BUILD_DOCS=ON ..
+cmake --build .
+cmake --build . --target INSTALL
+```
+On Windows this tries to install in `Program Files` and thus requires admin privileges. Alternatively you can target another directory using something like this:
+```
+mkdir build
+cd build
+cmake -DBOX2D_BUILD_DOCS=ON -DCMAKE_INSTALL_PREFIX="C:/packages" ..
+cmake --build .
+cmake --build . --target INSTALL
+```
+
+## Documentation
+- [Manual](https://box2d.org/documentation/)
+- [reddit](https://www.reddit.com/r/box2d/)
+- [Discord](https://discord.gg/NKYgCBP)
+
+## License
+Box2D is developed by Erin Catto, and uses the [MIT license](https://en.wikipedia.org/wiki/MIT_License).
+
+## Sponsorship
+Support development of Box2D through [Github Sponsors](https://github.com/sponsors/erincatto)

3rd/box2d/include/box2d/b2_api.h

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+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#ifndef B2_API_H
+#define B2_API_H
+
+#ifdef B2_SHARED
+  #if defined _WIN32 || defined __CYGWIN__
+    #ifdef box2d_EXPORTS
+      #ifdef __GNUC__
+        #define B2_API __attribute__ ((dllexport))
+      #else
+        #define B2_API __declspec(dllexport)
+      #endif
+    #else
+      #ifdef __GNUC__
+        #define B2_API __attribute__ ((dllimport))
+      #else
+        #define B2_API __declspec(dllimport)
+      #endif
+    #endif
+  #else
+    #if __GNUC__ >= 4
+      #define B2_API __attribute__ ((visibility ("default")))
+    #else
+      #define B2_API
+    #endif
+  #endif
+#else
+  #define B2_API
+#endif
+
+#endif

3rd/box2d/include/box2d/b2_block_allocator.h

@@ -0,0 +1,60 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#ifndef B2_BLOCK_ALLOCATOR_H
+#define B2_BLOCK_ALLOCATOR_H
+
+#include "b2_api.h"
+#include "b2_settings.h"
+
+const int32 b2_blockSizeCount = 14;
+
+struct b2Block;
+struct b2Chunk;
+
+/// This is a small object allocator used for allocating small
+/// objects that persist for more than one time step.
+/// See: http://www.codeproject.com/useritems/Small_Block_Allocator.asp
+class B2_API b2BlockAllocator
+{
+public:
+	b2BlockAllocator();
+	~b2BlockAllocator();
+
+	/// Allocate memory. This will use b2Alloc if the size is larger than b2_maxBlockSize.
+	void* Allocate(int32 size);
+
+	/// Free memory. This will use b2Free if the size is larger than b2_maxBlockSize.
+	void Free(void* p, int32 size);
+
+	void Clear();
+
+private:
+
+	b2Chunk* m_chunks;
+	int32 m_chunkCount;
+	int32 m_chunkSpace;
+
+	b2Block* m_freeLists[b2_blockSizeCount];
+};
+
+#endif

3rd/box2d/include/box2d/b2_body.h

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+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#ifndef B2_BODY_H
+#define B2_BODY_H
+
+#include "b2_api.h"
+#include "b2_math.h"
+#include "b2_shape.h"
+
+class b2Fixture;
+class b2Joint;
+class b2Contact;
+class b2Controller;
+class b2World;
+struct b2FixtureDef;
+struct b2JointEdge;
+struct b2ContactEdge;
+
+/// The body type.
+/// static: zero mass, zero velocity, may be manually moved
+/// kinematic: zero mass, non-zero velocity set by user, moved by solver
+/// dynamic: positive mass, non-zero velocity determined by forces, moved by solver
+enum b2BodyType
+{
+	b2_staticBody = 0,
+	b2_kinematicBody,
+	b2_dynamicBody
+};
+
+/// A body definition holds all the data needed to construct a rigid body.
+/// You can safely re-use body definitions. Shapes are added to a body after construction.
+struct B2_API b2BodyDef
+{
+	/// This constructor sets the body definition default values.
+	b2BodyDef()
+	{
+		position.Set(0.0f, 0.0f);
+		angle = 0.0f;
+		linearVelocity.Set(0.0f, 0.0f);
+		angularVelocity = 0.0f;
+		linearDamping = 0.0f;
+		angularDamping = 0.0f;
+		allowSleep = true;
+		awake = true;
+		fixedRotation = false;
+		bullet = false;
+		type = b2_staticBody;
+		enabled = true;
+		gravityScale = 1.0f;
+	}
+
+	/// The body type: static, kinematic, or dynamic.
+	/// Note: if a dynamic body would have zero mass, the mass is set to one.
+	b2BodyType type;
+
+	/// The world position of the body. Avoid creating bodies at the origin
+	/// since this can lead to many overlapping shapes.
+	b2Vec2 position;
+
+	/// The world angle of the body in radians.
+	float angle;
+
+	/// The linear velocity of the body's origin in world co-ordinates.
+	b2Vec2 linearVelocity;
+
+	/// The angular velocity of the body.
+	float angularVelocity;
+
+	/// Linear damping is use to reduce the linear velocity. The damping parameter
+	/// can be larger than 1.0f but the damping effect becomes sensitive to the
+	/// time step when the damping parameter is large.
+	/// Units are 1/time
+	float linearDamping;
+
+	/// Angular damping is use to reduce the angular velocity. The damping parameter
+	/// can be larger than 1.0f but the damping effect becomes sensitive to the
+	/// time step when the damping parameter is large.
+	/// Units are 1/time
+	float angularDamping;
+
+	/// Set this flag to false if this body should never fall asleep. Note that
+	/// this increases CPU usage.
+	bool allowSleep;
+
+	/// Is this body initially awake or sleeping?
+	bool awake;
+
+	/// Should this body be prevented from rotating? Useful for characters.
+	bool fixedRotation;
+
+	/// Is this a fast moving body that should be prevented from tunneling through
+	/// other moving bodies? Note that all bodies are prevented from tunneling through
+	/// kinematic and static bodies. This setting is only considered on dynamic bodies.
+	/// @warning You should use this flag sparingly since it increases processing time.
+	bool bullet;
+
+	/// Does this body start out enabled?
+	bool enabled;
+
+	/// Use this to store application specific body data.
+	b2BodyUserData userData;
+
+	/// Scale the gravity applied to this body.
+	float gravityScale;
+};
+
+/// A rigid body. These are created via b2World::CreateBody.
+class B2_API b2Body
+{
+public:
+	/// Creates a fixture and attach it to this body. Use this function if you need
+	/// to set some fixture parameters, like friction. Otherwise you can create the
+	/// fixture directly from a shape.
+	/// If the density is non-zero, this function automatically updates the mass of the body.
+	/// Contacts are not created until the next time step.
+	/// @param def the fixture definition.
+	/// @warning This function is locked during callbacks.
+	b2Fixture* CreateFixture(const b2FixtureDef* def);
+
+	/// Creates a fixture from a shape and attach it to this body.
+	/// This is a convenience function. Use b2FixtureDef if you need to set parameters
+	/// like friction, restitution, user data, or filtering.
+	/// If the density is non-zero, this function automatically updates the mass of the body.
+	/// @param shape the shape to be cloned.
+	/// @param density the shape density (set to zero for static bodies).
+	/// @warning This function is locked during callbacks.
+	b2Fixture* CreateFixture(const b2Shape* shape, float density);
+
+	/// Destroy a fixture. This removes the fixture from the broad-phase and
+	/// destroys all contacts associated with this fixture. This will
+	/// automatically adjust the mass of the body if the body is dynamic and the
+	/// fixture has positive density.
+	/// All fixtures attached to a body are implicitly destroyed when the body is destroyed.
+	/// @param fixture the fixture to be removed.
+	/// @warning This function is locked during callbacks.
+	void DestroyFixture(b2Fixture* fixture);
+
+	/// Set the position of the body's origin and rotation.
+	/// Manipulating a body's transform may cause non-physical behavior.
+	/// Note: contacts are updated on the next call to b2World::Step.
+	/// @param position the world position of the body's local origin.
+	/// @param angle the world rotation in radians.
+	void SetTransform(const b2Vec2& position, float angle);
+
+	/// Get the body transform for the body's origin.
+	/// @return the world transform of the body's origin.
+	const b2Transform& GetTransform() const;
+
+	/// Get the world body origin position.
+	/// @return the world position of the body's origin.
+	const b2Vec2& GetPosition() const;
+
+	/// Get the angle in radians.
+	/// @return the current world rotation angle in radians.
+	float GetAngle() const;
+
+	/// Get the world position of the center of mass.
+	const b2Vec2& GetWorldCenter() const;
+
+	/// Get the local position of the center of mass.
+	const b2Vec2& GetLocalCenter() const;
+
+	/// Set the linear velocity of the center of mass.
+	/// @param v the new linear velocity of the center of mass.
+	void SetLinearVelocity(const b2Vec2& v);
+
+	/// Get the linear velocity of the center of mass.
+	/// @return the linear velocity of the center of mass.
+	const b2Vec2& GetLinearVelocity() const;
+
+	/// Set the angular velocity.
+	/// @param omega the new angular velocity in radians/second.
+	void SetAngularVelocity(float omega);
+
+	/// Get the angular velocity.
+	/// @return the angular velocity in radians/second.
+	float GetAngularVelocity() const;
+
+	/// Apply a force at a world point. If the force is not
+	/// applied at the center of mass, it will generate a torque and
+	/// affect the angular velocity. This wakes up the body.
+	/// @param force the world force vector, usually in Newtons (N).
+	/// @param point the world position of the point of application.
+	/// @param wake also wake up the body
+	void ApplyForce(const b2Vec2& force, const b2Vec2& point, bool wake);
+
+	/// Apply a force to the center of mass. This wakes up the body.
+	/// @param force the world force vector, usually in Newtons (N).
+	/// @param wake also wake up the body
+	void ApplyForceToCenter(const b2Vec2& force, bool wake);
+
+	/// Apply a torque. This affects the angular velocity
+	/// without affecting the linear velocity of the center of mass.
+	/// @param torque about the z-axis (out of the screen), usually in N-m.
+	/// @param wake also wake up the body
+	void ApplyTorque(float torque, bool wake);
+
+	/// Apply an impulse at a point. This immediately modifies the velocity.
+	/// It also modifies the angular velocity if the point of application
+	/// is not at the center of mass. This wakes up the body.
+	/// @param impulse the world impulse vector, usually in N-seconds or kg-m/s.
+	/// @param point the world position of the point of application.
+	/// @param wake also wake up the body
+	void ApplyLinearImpulse(const b2Vec2& impulse, const b2Vec2& point, bool wake);
+
+	/// Apply an impulse to the center of mass. This immediately modifies the velocity.
+	/// @param impulse the world impulse vector, usually in N-seconds or kg-m/s.
+	/// @param wake also wake up the body
+	void ApplyLinearImpulseToCenter(const b2Vec2& impulse, bool wake);
+
+	/// Apply an angular impulse.
+	/// @param impulse the angular impulse in units of kg*m*m/s
+	/// @param wake also wake up the body
+	void ApplyAngularImpulse(float impulse, bool wake);
+
+	/// Get the total mass of the body.
+	/// @return the mass, usually in kilograms (kg).
+	float GetMass() const;
+
+	/// Get the rotational inertia of the body about the local origin.
+	/// @return the rotational inertia, usually in kg-m^2.
+	float GetInertia() const;
+
+	/// Get the mass data of the body.
+	/// @return a struct containing the mass, inertia and center of the body.
+	b2MassData GetMassData() const;
+
+	/// Set the mass properties to override the mass properties of the fixtures.
+	/// Note that this changes the center of mass position.
+	/// Note that creating or destroying fixtures can also alter the mass.
+	/// This function has no effect if the body isn't dynamic.
+	/// @param data the mass properties.
+	void SetMassData(const b2MassData* data);
+
+	/// This resets the mass properties to the sum of the mass properties of the fixtures.
+	/// This normally does not need to be called unless you called SetMassData to override
+	/// the mass and you later want to reset the mass.
+	void ResetMassData();
+
+	/// Get the world coordinates of a point given the local coordinates.
+	/// @param localPoint a point on the body measured relative the the body's origin.
+	/// @return the same point expressed in world coordinates.
+	b2Vec2 GetWorldPoint(const b2Vec2& localPoint) const;
+
+	/// Get the world coordinates of a vector given the local coordinates.
+	/// @param localVector a vector fixed in the body.
+	/// @return the same vector expressed in world coordinates.
+	b2Vec2 GetWorldVector(const b2Vec2& localVector) const;
+
+	/// Gets a local point relative to the body's origin given a world point.
+	/// @param worldPoint a point in world coordinates.
+	/// @return the corresponding local point relative to the body's origin.
+	b2Vec2 GetLocalPoint(const b2Vec2& worldPoint) const;
+
+	/// Gets a local vector given a world vector.
+	/// @param worldVector a vector in world coordinates.
+	/// @return the corresponding local vector.
+	b2Vec2 GetLocalVector(const b2Vec2& worldVector) const;
+
+	/// Get the world linear velocity of a world point attached to this body.
+	/// @param worldPoint a point in world coordinates.
+	/// @return the world velocity of a point.
+	b2Vec2 GetLinearVelocityFromWorldPoint(const b2Vec2& worldPoint) const;
+
+	/// Get the world velocity of a local point.
+	/// @param localPoint a point in local coordinates.
+	/// @return the world velocity of a point.
+	b2Vec2 GetLinearVelocityFromLocalPoint(const b2Vec2& localPoint) const;
+
+	/// Get the linear damping of the body.
+	float GetLinearDamping() const;
+
+	/// Set the linear damping of the body.
+	void SetLinearDamping(float linearDamping);
+
+	/// Get the angular damping of the body.
+	float GetAngularDamping() const;
+
+	/// Set the angular damping of the body.
+	void SetAngularDamping(float angularDamping);
+
+	/// Get the gravity scale of the body.
+	float GetGravityScale() const;
+
+	/// Set the gravity scale of the body.
+	void SetGravityScale(float scale);
+
+	/// Set the type of this body. This may alter the mass and velocity.
+	void SetType(b2BodyType type);
+
+	/// Get the type of this body.
+	b2BodyType GetType() const;
+
+	/// Should this body be treated like a bullet for continuous collision detection?
+	void SetBullet(bool flag);
+
+	/// Is this body treated like a bullet for continuous collision detection?
+	bool IsBullet() const;
+
+	/// You can disable sleeping on this body. If you disable sleeping, the
+	/// body will be woken.
+	void SetSleepingAllowed(bool flag);
+
+	/// Is this body allowed to sleep
+	bool IsSleepingAllowed() const;
+
+	/// Set the sleep state of the body. A sleeping body has very
+	/// low CPU cost.
+	/// @param flag set to true to wake the body, false to put it to sleep.
+	void SetAwake(bool flag);
+
+	/// Get the sleeping state of this body.
+	/// @return true if the body is awake.
+	bool IsAwake() const;
+
+	/// Allow a body to be disabled. A disabled body is not simulated and cannot
+	/// be collided with or woken up.
+	/// If you pass a flag of true, all fixtures will be added to the broad-phase.
+	/// If you pass a flag of false, all fixtures will be removed from the
+	/// broad-phase and all contacts will be destroyed.
+	/// Fixtures and joints are otherwise unaffected. You may continue
+	/// to create/destroy fixtures and joints on disabled bodies.
+	/// Fixtures on a disabled body are implicitly disabled and will
+	/// not participate in collisions, ray-casts, or queries.
+	/// Joints connected to a disabled body are implicitly disabled.
+	/// An diabled body is still owned by a b2World object and remains
+	/// in the body list.
+	void SetEnabled(bool flag);
+
+	/// Get the active state of the body.
+	bool IsEnabled() const;
+
+	/// Set this body to have fixed rotation. This causes the mass
+	/// to be reset.
+	void SetFixedRotation(bool flag);
+
+	/// Does this body have fixed rotation?
+	bool IsFixedRotation() const;
+
+	/// Get the list of all fixtures attached to this body.
+	b2Fixture* GetFixtureList();
+	const b2Fixture* GetFixtureList() const;
+
+	/// Get the list of all joints attached to this body.
+	b2JointEdge* GetJointList();
+	const b2JointEdge* GetJointList() const;
+
+	/// Get the list of all contacts attached to this body.
+	/// @warning this list changes during the time step and you may
+	/// miss some collisions if you don't use b2ContactListener.
+	b2ContactEdge* GetContactList();
+	const b2ContactEdge* GetContactList() const;
+
+	/// Get the next body in the world's body list.
+	b2Body* GetNext();
+	const b2Body* GetNext() const;
+
+	/// Get the user data pointer that was provided in the body definition.
+	b2BodyUserData& GetUserData();
+	const b2BodyUserData& GetUserData() const;
+
+	/// Get the parent world of this body.
+	b2World* GetWorld();
+	const b2World* GetWorld() const;
+
+	/// Dump this body to a file
+	void Dump();
+
+private:
+
+	friend class b2World;
+	friend class b2Island;
+	friend class b2ContactManager;
+	friend class b2ContactSolver;
+	friend class b2Contact;
+
+	friend class b2DistanceJoint;
+	friend class b2FrictionJoint;
+	friend class b2GearJoint;
+	friend class b2MotorJoint;
+	friend class b2MouseJoint;
+	friend class b2PrismaticJoint;
+	friend class b2PulleyJoint;
+	friend class b2RevoluteJoint;
+	friend class b2WeldJoint;
+	friend class b2WheelJoint;
+
+	// m_flags
+	enum
+	{
+		e_islandFlag		= 0x0001,
+		e_awakeFlag			= 0x0002,
+		e_autoSleepFlag		= 0x0004,
+		e_bulletFlag		= 0x0008,
+		e_fixedRotationFlag	= 0x0010,
+		e_enabledFlag		= 0x0020,
+		e_toiFlag			= 0x0040
+	};
+
+	b2Body(const b2BodyDef* bd, b2World* world);
+	~b2Body();
+
+	void SynchronizeFixtures();
+	void SynchronizeTransform();
+
+	// This is used to prevent connected bodies from colliding.
+	// It may lie, depending on the collideConnected flag.
+	bool ShouldCollide(const b2Body* other) const;
+
+	void Advance(float t);
+
+	b2BodyType m_type;
+
+	uint16 m_flags;
+
+	int32 m_islandIndex;
+
+	b2Transform m_xf;		// the body origin transform
+	b2Sweep m_sweep;		// the swept motion for CCD
+
+	b2Vec2 m_linearVelocity;
+	float m_angularVelocity;
+
+	b2Vec2 m_force;
+	float m_torque;
+
+	b2World* m_world;
+	b2Body* m_prev;
+	b2Body* m_next;
+
+	b2Fixture* m_fixtureList;
+	int32 m_fixtureCount;
+
+	b2JointEdge* m_jointList;
+	b2ContactEdge* m_contactList;
+
+	float m_mass, m_invMass;
+
+	// Rotational inertia about the center of mass.
+	float m_I, m_invI;
+
+	float m_linearDamping;
+	float m_angularDamping;
+	float m_gravityScale;
+
+	float m_sleepTime;
+
+	b2BodyUserData m_userData;
+};
+
+inline b2BodyType b2Body::GetType() const
+{
+	return m_type;
+}
+
+inline const b2Transform& b2Body::GetTransform() const
+{
+	return m_xf;
+}
+
+inline const b2Vec2& b2Body::GetPosition() const
+{
+	return m_xf.p;
+}
+
+inline float b2Body::GetAngle() const
+{
+	return m_sweep.a;
+}
+
+inline const b2Vec2& b2Body::GetWorldCenter() const
+{
+	return m_sweep.c;
+}
+
+inline const b2Vec2& b2Body::GetLocalCenter() const
+{
+	return m_sweep.localCenter;
+}
+
+inline void b2Body::SetLinearVelocity(const b2Vec2& v)
+{
+	if (m_type == b2_staticBody)
+	{
+		return;
+	}
+
+	if (b2Dot(v,v) > 0.0f)
+	{
+		SetAwake(true);
+	}
+
+	m_linearVelocity = v;
+}
+
+inline const b2Vec2& b2Body::GetLinearVelocity() const
+{
+	return m_linearVelocity;
+}
+
+inline void b2Body::SetAngularVelocity(float w)
+{
+	if (m_type == b2_staticBody)
+	{
+		return;
+	}
+
+	if (w * w > 0.0f)
+	{
+		SetAwake(true);
+	}
+
+	m_angularVelocity = w;
+}
+
+inline float b2Body::GetAngularVelocity() const
+{
+	return m_angularVelocity;
+}
+
+inline float b2Body::GetMass() const
+{
+	return m_mass;
+}
+
+inline float b2Body::GetInertia() const
+{
+	return m_I + m_mass * b2Dot(m_sweep.localCenter, m_sweep.localCenter);
+}
+
+inline b2MassData b2Body::GetMassData() const
+{
+	b2MassData data;
+	data.mass = m_mass;
+	data.I = m_I + m_mass * b2Dot(m_sweep.localCenter, m_sweep.localCenter);
+	data.center = m_sweep.localCenter;
+	return data;
+}
+
+inline b2Vec2 b2Body::GetWorldPoint(const b2Vec2& localPoint) const
+{
+	return b2Mul(m_xf, localPoint);
+}
+
+inline b2Vec2 b2Body::GetWorldVector(const b2Vec2& localVector) const
+{
+	return b2Mul(m_xf.q, localVector);
+}
+
+inline b2Vec2 b2Body::GetLocalPoint(const b2Vec2& worldPoint) const
+{
+	return b2MulT(m_xf, worldPoint);
+}
+
+inline b2Vec2 b2Body::GetLocalVector(const b2Vec2& worldVector) const
+{
+	return b2MulT(m_xf.q, worldVector);
+}
+
+inline b2Vec2 b2Body::GetLinearVelocityFromWorldPoint(const b2Vec2& worldPoint) const
+{
+	return m_linearVelocity + b2Cross(m_angularVelocity, worldPoint - m_sweep.c);
+}
+
+inline b2Vec2 b2Body::GetLinearVelocityFromLocalPoint(const b2Vec2& localPoint) const
+{
+	return GetLinearVelocityFromWorldPoint(GetWorldPoint(localPoint));
+}
+
+inline float b2Body::GetLinearDamping() const
+{
+	return m_linearDamping;
+}
+
+inline void b2Body::SetLinearDamping(float linearDamping)
+{
+	m_linearDamping = linearDamping;
+}
+
+inline float b2Body::GetAngularDamping() const
+{
+	return m_angularDamping;
+}
+
+inline void b2Body::SetAngularDamping(float angularDamping)
+{
+	m_angularDamping = angularDamping;
+}
+
+inline float b2Body::GetGravityScale() const
+{
+	return m_gravityScale;
+}
+
+inline void b2Body::SetGravityScale(float scale)
+{
+	m_gravityScale = scale;
+}
+
+inline void b2Body::SetBullet(bool flag)
+{
+	if (flag)
+	{
+		m_flags |= e_bulletFlag;
+	}
+	else
+	{
+		m_flags &= ~e_bulletFlag;
+	}
+}
+
+inline bool b2Body::IsBullet() const
+{
+	return (m_flags & e_bulletFlag) == e_bulletFlag;
+}
+
+inline void b2Body::SetAwake(bool flag)
+{
+	if (m_type == b2_staticBody)
+	{
+		return;
+	}
+
+	if (flag)
+	{
+		m_flags |= e_awakeFlag;
+		m_sleepTime = 0.0f;
+	}
+	else
+	{
+		m_flags &= ~e_awakeFlag;
+		m_sleepTime = 0.0f;
+		m_linearVelocity.SetZero();
+		m_angularVelocity = 0.0f;
+		m_force.SetZero();
+		m_torque = 0.0f;
+	}
+}
+
+inline bool b2Body::IsAwake() const
+{
+	return (m_flags & e_awakeFlag) == e_awakeFlag;
+}
+
+inline bool b2Body::IsEnabled() const
+{
+	return (m_flags & e_enabledFlag) == e_enabledFlag;
+}
+
+inline bool b2Body::IsFixedRotation() const
+{
+	return (m_flags & e_fixedRotationFlag) == e_fixedRotationFlag;
+}
+
+inline void b2Body::SetSleepingAllowed(bool flag)
+{
+	if (flag)
+	{
+		m_flags |= e_autoSleepFlag;
+	}
+	else
+	{
+		m_flags &= ~e_autoSleepFlag;
+		SetAwake(true);
+	}
+}
+
+inline bool b2Body::IsSleepingAllowed() const
+{
+	return (m_flags & e_autoSleepFlag) == e_autoSleepFlag;
+}
+
+inline b2Fixture* b2Body::GetFixtureList()
+{
+	return m_fixtureList;
+}
+
+inline const b2Fixture* b2Body::GetFixtureList() const
+{
+	return m_fixtureList;
+}
+
+inline b2JointEdge* b2Body::GetJointList()
+{
+	return m_jointList;
+}
+
+inline const b2JointEdge* b2Body::GetJointList() const
+{
+	return m_jointList;
+}
+
+inline b2ContactEdge* b2Body::GetContactList()
+{
+	return m_contactList;
+}
+
+inline const b2ContactEdge* b2Body::GetContactList() const
+{
+	return m_contactList;
+}
+
+inline b2Body* b2Body::GetNext()
+{
+	return m_next;
+}
+
+inline const b2Body* b2Body::GetNext() const
+{
+	return m_next;
+}
+
+inline b2BodyUserData& b2Body::GetUserData()
+{
+	return m_userData;
+}
+
+inline const b2BodyUserData& b2Body::GetUserData() const
+{
+	return m_userData;
+}
+
+inline void b2Body::ApplyForce(const b2Vec2& force, const b2Vec2& point, bool wake)
+{
+	if (m_type != b2_dynamicBody)
+	{
+		return;
+	}
+
+	if (wake && (m_flags & e_awakeFlag) == 0)
+	{
+		SetAwake(true);
+	}
+
+	// Don't accumulate a force if the body is sleeping.
+	if (m_flags & e_awakeFlag)
+	{
+		m_force += force;
+		m_torque += b2Cross(point - m_sweep.c, force);
+	}
+}
+
+inline void b2Body::ApplyForceToCenter(const b2Vec2& force, bool wake)
+{
+	if (m_type != b2_dynamicBody)
+	{
+		return;
+	}
+
+	if (wake && (m_flags & e_awakeFlag) == 0)
+	{
+		SetAwake(true);
+	}
+
+	// Don't accumulate a force if the body is sleeping
+	if (m_flags & e_awakeFlag)
+	{
+		m_force += force;
+	}
+}
+
+inline void b2Body::ApplyTorque(float torque, bool wake)
+{
+	if (m_type != b2_dynamicBody)
+	{
+		return;
+	}
+
+	if (wake && (m_flags & e_awakeFlag) == 0)
+	{
+		SetAwake(true);
+	}
+
+	// Don't accumulate a force if the body is sleeping
+	if (m_flags & e_awakeFlag)
+	{
+		m_torque += torque;
+	}
+}
+
+inline void b2Body::ApplyLinearImpulse(const b2Vec2& impulse, const b2Vec2& point, bool wake)
+{
+	if (m_type != b2_dynamicBody)
+	{
+		return;
+	}
+
+	if (wake && (m_flags & e_awakeFlag) == 0)
+	{
+		SetAwake(true);
+	}
+
+	// Don't accumulate velocity if the body is sleeping
+	if (m_flags & e_awakeFlag)
+	{
+		m_linearVelocity += m_invMass * impulse;
+		m_angularVelocity += m_invI * b2Cross(point - m_sweep.c, impulse);
+	}
+}
+
+inline void b2Body::ApplyLinearImpulseToCenter(const b2Vec2& impulse, bool wake)
+{
+	if (m_type != b2_dynamicBody)
+	{
+		return;
+	}
+
+	if (wake && (m_flags & e_awakeFlag) == 0)
+	{
+		SetAwake(true);
+	}
+
+	// Don't accumulate velocity if the body is sleeping
+	if (m_flags & e_awakeFlag)
+	{
+		m_linearVelocity += m_invMass * impulse;
+	}
+}
+
+inline void b2Body::ApplyAngularImpulse(float impulse, bool wake)
+{
+	if (m_type != b2_dynamicBody)
+	{
+		return;
+	}
+
+	if (wake && (m_flags & e_awakeFlag) == 0)
+	{
+		SetAwake(true);
+	}
+
+	// Don't accumulate velocity if the body is sleeping
+	if (m_flags & e_awakeFlag)
+	{
+		m_angularVelocity += m_invI * impulse;
+	}
+}
+
+inline void b2Body::SynchronizeTransform()
+{
+	m_xf.q.Set(m_sweep.a);
+	m_xf.p = m_sweep.c - b2Mul(m_xf.q, m_sweep.localCenter);
+}
+
+inline void b2Body::Advance(float alpha)
+{
+	// Advance to the new safe time. This doesn't sync the broad-phase.
+	m_sweep.Advance(alpha);
+	m_sweep.c = m_sweep.c0;
+	m_sweep.a = m_sweep.a0;
+	m_xf.q.Set(m_sweep.a);
+	m_xf.p = m_sweep.c - b2Mul(m_xf.q, m_sweep.localCenter);
+}
+
+inline b2World* b2Body::GetWorld()
+{
+	return m_world;
+}
+
+inline const b2World* b2Body::GetWorld() const
+{
+	return m_world;
+}
+
+#endif

3rd/box2d/include/box2d/b2_broad_phase.h

@@ -0,0 +1,238 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#ifndef B2_BROAD_PHASE_H
+#define B2_BROAD_PHASE_H
+
+#include "b2_api.h"
+#include "b2_settings.h"
+#include "b2_collision.h"
+#include "b2_dynamic_tree.h"
+
+struct B2_API b2Pair
+{
+	int32 proxyIdA;
+	int32 proxyIdB;
+};
+
+/// The broad-phase is used for computing pairs and performing volume queries and ray casts.
+/// This broad-phase does not persist pairs. Instead, this reports potentially new pairs.
+/// It is up to the client to consume the new pairs and to track subsequent overlap.
+class B2_API b2BroadPhase
+{
+public:
+
+	enum
+	{
+		e_nullProxy = -1
+	};
+
+	b2BroadPhase();
+	~b2BroadPhase();
+
+	/// Create a proxy with an initial AABB. Pairs are not reported until
+	/// UpdatePairs is called.
+	int32 CreateProxy(const b2AABB& aabb, void* userData);
+
+	/// Destroy a proxy. It is up to the client to remove any pairs.
+	void DestroyProxy(int32 proxyId);
+
+	/// Call MoveProxy as many times as you like, then when you are done
+	/// call UpdatePairs to finalized the proxy pairs (for your time step).
+	void MoveProxy(int32 proxyId, const b2AABB& aabb, const b2Vec2& displacement);
+
+	/// Call to trigger a re-processing of it's pairs on the next call to UpdatePairs.
+	void TouchProxy(int32 proxyId);
+
+	/// Get the fat AABB for a proxy.
+	const b2AABB& GetFatAABB(int32 proxyId) const;
+
+	/// Get user data from a proxy. Returns nullptr if the id is invalid.
+	void* GetUserData(int32 proxyId) const;
+
+	/// Test overlap of fat AABBs.
+	bool TestOverlap(int32 proxyIdA, int32 proxyIdB) const;
+
+	/// Get the number of proxies.
+	int32 GetProxyCount() const;
+
+	/// Update the pairs. This results in pair callbacks. This can only add pairs.
+	template <typename T>
+	void UpdatePairs(T* callback);
+
+	/// Query an AABB for overlapping proxies. The callback class
+	/// is called for each proxy that overlaps the supplied AABB.
+	template <typename T>
+	void Query(T* callback, const b2AABB& aabb) const;
+
+	/// Ray-cast against the proxies in the tree. This relies on the callback
+	/// to perform a exact ray-cast in the case were the proxy contains a shape.
+	/// The callback also performs the any collision filtering. This has performance
+	/// roughly equal to k * log(n), where k is the number of collisions and n is the
+	/// number of proxies in the tree.
+	/// @param input the ray-cast input data. The ray extends from p1 to p1 + maxFraction * (p2 - p1).
+	/// @param callback a callback class that is called for each proxy that is hit by the ray.
+	template <typename T>
+	void RayCast(T* callback, const b2RayCastInput& input) const;
+
+	/// Get the height of the embedded tree.
+	int32 GetTreeHeight() const;
+
+	/// Get the balance of the embedded tree.
+	int32 GetTreeBalance() const;
+
+	/// Get the quality metric of the embedded tree.
+	float GetTreeQuality() const;
+
+	/// Shift the world origin. Useful for large worlds.
+	/// The shift formula is: position -= newOrigin
+	/// @param newOrigin the new origin with respect to the old origin
+	void ShiftOrigin(const b2Vec2& newOrigin);
+
+private:
+
+	friend class b2DynamicTree;
+
+	void BufferMove(int32 proxyId);
+	void UnBufferMove(int32 proxyId);
+
+	bool QueryCallback(int32 proxyId);
+
+	b2DynamicTree m_tree;
+
+	int32 m_proxyCount;
+
+	int32* m_moveBuffer;
+	int32 m_moveCapacity;
+	int32 m_moveCount;
+
+	b2Pair* m_pairBuffer;
+	int32 m_pairCapacity;
+	int32 m_pairCount;
+
+	int32 m_queryProxyId;
+};
+
+inline void* b2BroadPhase::GetUserData(int32 proxyId) const
+{
+	return m_tree.GetUserData(proxyId);
+}
+
+inline bool b2BroadPhase::TestOverlap(int32 proxyIdA, int32 proxyIdB) const
+{
+	const b2AABB& aabbA = m_tree.GetFatAABB(proxyIdA);
+	const b2AABB& aabbB = m_tree.GetFatAABB(proxyIdB);
+	return b2TestOverlap(aabbA, aabbB);
+}
+
+inline const b2AABB& b2BroadPhase::GetFatAABB(int32 proxyId) const
+{
+	return m_tree.GetFatAABB(proxyId);
+}
+
+inline int32 b2BroadPhase::GetProxyCount() const
+{
+	return m_proxyCount;
+}
+
+inline int32 b2BroadPhase::GetTreeHeight() const
+{
+	return m_tree.GetHeight();
+}
+
+inline int32 b2BroadPhase::GetTreeBalance() const
+{
+	return m_tree.GetMaxBalance();
+}
+
+inline float b2BroadPhase::GetTreeQuality() const
+{
+	return m_tree.GetAreaRatio();
+}
+
+template <typename T>
+void b2BroadPhase::UpdatePairs(T* callback)
+{
+	// Reset pair buffer
+	m_pairCount = 0;
+
+	// Perform tree queries for all moving proxies.
+	for (int32 i = 0; i < m_moveCount; ++i)
+	{
+		m_queryProxyId = m_moveBuffer[i];
+		if (m_queryProxyId == e_nullProxy)
+		{
+			continue;
+		}
+
+		// We have to query the tree with the fat AABB so that
+		// we don't fail to create a pair that may touch later.
+		const b2AABB& fatAABB = m_tree.GetFatAABB(m_queryProxyId);
+
+		// Query tree, create pairs and add them pair buffer.
+		m_tree.Query(this, fatAABB);
+	}
+
+	// Send pairs to caller
+	for (int32 i = 0; i < m_pairCount; ++i)
+	{
+		b2Pair* primaryPair = m_pairBuffer + i;
+		void* userDataA = m_tree.GetUserData(primaryPair->proxyIdA);
+		void* userDataB = m_tree.GetUserData(primaryPair->proxyIdB);
+
+		callback->AddPair(userDataA, userDataB);
+	}
+
+	// Clear move flags
+	for (int32 i = 0; i < m_moveCount; ++i)
+	{
+		int32 proxyId = m_moveBuffer[i];
+		if (proxyId == e_nullProxy)
+		{
+			continue;
+		}
+
+		m_tree.ClearMoved(proxyId);
+	}
+
+	// Reset move buffer
+	m_moveCount = 0;
+}
+
+template <typename T>
+inline void b2BroadPhase::Query(T* callback, const b2AABB& aabb) const
+{
+	m_tree.Query(callback, aabb);
+}
+
+template <typename T>
+inline void b2BroadPhase::RayCast(T* callback, const b2RayCastInput& input) const
+{
+	m_tree.RayCast(callback, input);
+}
+
+inline void b2BroadPhase::ShiftOrigin(const b2Vec2& newOrigin)
+{
+	m_tree.ShiftOrigin(newOrigin);
+}
+
+#endif

3rd/box2d/include/box2d/b2_chain_shape.h

@@ -0,0 +1,101 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#ifndef B2_CHAIN_SHAPE_H
+#define B2_CHAIN_SHAPE_H
+
+#include "b2_api.h"
+#include "b2_shape.h"
+
+class b2EdgeShape;
+
+/// A chain shape is a free form sequence of line segments.
+/// The chain has one-sided collision, with the surface normal pointing to the right of the edge.
+/// This provides a counter-clockwise winding like the polygon shape.
+/// Connectivity information is used to create smooth collisions.
+/// @warning the chain will not collide properly if there are self-intersections.
+class B2_API b2ChainShape : public b2Shape
+{
+public:
+	b2ChainShape();
+
+	/// The destructor frees the vertices using b2Free.
+	~b2ChainShape();
+
+	/// Clear all data.
+	void Clear();
+
+	/// Create a loop. This automatically adjusts connectivity.
+	/// @param vertices an array of vertices, these are copied
+	/// @param count the vertex count
+	void CreateLoop(const b2Vec2* vertices, int32 count);
+
+	/// Create a chain with ghost vertices to connect multiple chains together.
+	/// @param vertices an array of vertices, these are copied
+	/// @param count the vertex count
+	/// @param prevVertex previous vertex from chain that connects to the start
+	/// @param nextVertex next vertex from chain that connects to the end
+	void CreateChain(const b2Vec2* vertices, int32 count,
+		const b2Vec2& prevVertex, const b2Vec2& nextVertex);
+
+	/// Implement b2Shape. Vertices are cloned using b2Alloc.
+	b2Shape* Clone(b2BlockAllocator* allocator) const override;
+
+	/// @see b2Shape::GetChildCount
+	int32 GetChildCount() const override;
+
+	/// Get a child edge.
+	void GetChildEdge(b2EdgeShape* edge, int32 index) const;
+
+	/// This always return false.
+	/// @see b2Shape::TestPoint
+	bool TestPoint(const b2Transform& transform, const b2Vec2& p) const override;
+
+	/// Implement b2Shape.
+	bool RayCast(b2RayCastOutput* output, const b2RayCastInput& input,
+					const b2Transform& transform, int32 childIndex) const override;
+
+	/// @see b2Shape::ComputeAABB
+	void ComputeAABB(b2AABB* aabb, const b2Transform& transform, int32 childIndex) const override;
+
+	/// Chains have zero mass.
+	/// @see b2Shape::ComputeMass
+	void ComputeMass(b2MassData* massData, float density) const override;
+
+	/// The vertices. Owned by this class.
+	b2Vec2* m_vertices;
+
+	/// The vertex count.
+	int32 m_count;
+
+	b2Vec2 m_prevVertex, m_nextVertex;
+};
+
+inline b2ChainShape::b2ChainShape()
+{
+	m_type = e_chain;
+	m_radius = b2_polygonRadius;
+	m_vertices = nullptr;
+	m_count = 0;
+}
+
+#endif

3rd/box2d/include/box2d/b2_circle_shape.h

@@ -0,0 +1,67 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#ifndef B2_CIRCLE_SHAPE_H
+#define B2_CIRCLE_SHAPE_H
+
+#include "b2_api.h"
+#include "b2_shape.h"
+
+/// A solid circle shape
+class B2_API b2CircleShape : public b2Shape
+{
+public:
+	b2CircleShape();
+
+	/// Implement b2Shape.
+	b2Shape* Clone(b2BlockAllocator* allocator) const override;
+
+	/// @see b2Shape::GetChildCount
+	int32 GetChildCount() const override;
+
+	/// Implement b2Shape.
+	bool TestPoint(const b2Transform& transform, const b2Vec2& p) const override;
+
+	/// Implement b2Shape.
+	/// @note because the circle is solid, rays that start inside do not hit because the normal is
+	/// not defined.
+	bool RayCast(b2RayCastOutput* output, const b2RayCastInput& input,
+				const b2Transform& transform, int32 childIndex) const override;
+
+	/// @see b2Shape::ComputeAABB
+	void ComputeAABB(b2AABB* aabb, const b2Transform& transform, int32 childIndex) const override;
+
+	/// @see b2Shape::ComputeMass
+	void ComputeMass(b2MassData* massData, float density) const override;
+
+	/// Position
+	b2Vec2 m_p;
+};
+
+inline b2CircleShape::b2CircleShape()
+{
+	m_type = e_circle;
+	m_radius = 0.0f;
+	m_p.SetZero();
+}
+
+#endif

3rd/box2d/include/box2d/b2_collision.h

@@ -0,0 +1,306 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#ifndef B2_COLLISION_H
+#define B2_COLLISION_H
+
+#include <limits.h>
+
+#include "b2_api.h"
+#include "b2_math.h"
+
+/// @file
+/// Structures and functions used for computing contact points, distance
+/// queries, and TOI queries.
+
+class b2Shape;
+class b2CircleShape;
+class b2EdgeShape;
+class b2PolygonShape;
+
+const uint8 b2_nullFeature = UCHAR_MAX;
+
+/// The features that intersect to form the contact point
+/// This must be 4 bytes or less.
+struct B2_API b2ContactFeature
+{
+	enum Type
+	{
+		e_vertex = 0,
+		e_face = 1
+	};
+
+	uint8 indexA;		///< Feature index on shapeA
+	uint8 indexB;		///< Feature index on shapeB
+	uint8 typeA;		///< The feature type on shapeA
+	uint8 typeB;		///< The feature type on shapeB
+};
+
+/// Contact ids to facilitate warm starting.
+union B2_API b2ContactID
+{
+	b2ContactFeature cf;
+	uint32 key;					///< Used to quickly compare contact ids.
+};
+
+/// A manifold point is a contact point belonging to a contact
+/// manifold. It holds details related to the geometry and dynamics
+/// of the contact points.
+/// The local point usage depends on the manifold type:
+/// -e_circles: the local center of circleB
+/// -e_faceA: the local center of cirlceB or the clip point of polygonB
+/// -e_faceB: the clip point of polygonA
+/// This structure is stored across time steps, so we keep it small.
+/// Note: the impulses are used for internal caching and may not
+/// provide reliable contact forces, especially for high speed collisions.
+struct B2_API b2ManifoldPoint
+{
+	b2Vec2 localPoint;		///< usage depends on manifold type
+	float normalImpulse;	///< the non-penetration impulse
+	float tangentImpulse;	///< the friction impulse
+	b2ContactID id;			///< uniquely identifies a contact point between two shapes
+};
+
+/// A manifold for two touching convex shapes.
+/// Box2D supports multiple types of contact:
+/// - clip point versus plane with radius
+/// - point versus point with radius (circles)
+/// The local point usage depends on the manifold type:
+/// -e_circles: the local center of circleA
+/// -e_faceA: the center of faceA
+/// -e_faceB: the center of faceB
+/// Similarly the local normal usage:
+/// -e_circles: not used
+/// -e_faceA: the normal on polygonA
+/// -e_faceB: the normal on polygonB
+/// We store contacts in this way so that position correction can
+/// account for movement, which is critical for continuous physics.
+/// All contact scenarios must be expressed in one of these types.
+/// This structure is stored across time steps, so we keep it small.
+struct B2_API b2Manifold
+{
+	enum Type
+	{
+		e_circles,
+		e_faceA,
+		e_faceB
+	};
+
+	b2ManifoldPoint points[b2_maxManifoldPoints];	///< the points of contact
+	b2Vec2 localNormal;								///< not use for Type::e_points
+	b2Vec2 localPoint;								///< usage depends on manifold type
+	Type type;
+	int32 pointCount;								///< the number of manifold points
+};
+
+/// This is used to compute the current state of a contact manifold.
+struct B2_API b2WorldManifold
+{
+	/// Evaluate the manifold with supplied transforms. This assumes
+	/// modest motion from the original state. This does not change the
+	/// point count, impulses, etc. The radii must come from the shapes
+	/// that generated the manifold.
+	void Initialize(const b2Manifold* manifold,
+					const b2Transform& xfA, float radiusA,
+					const b2Transform& xfB, float radiusB);
+
+	b2Vec2 normal;								///< world vector pointing from A to B
+	b2Vec2 points[b2_maxManifoldPoints];		///< world contact point (point of intersection)
+	float separations[b2_maxManifoldPoints];	///< a negative value indicates overlap, in meters
+};
+
+/// This is used for determining the state of contact points.
+enum b2PointState
+{
+	b2_nullState,		///< point does not exist
+	b2_addState,		///< point was added in the update
+	b2_persistState,	///< point persisted across the update
+	b2_removeState		///< point was removed in the update
+};
+
+/// Compute the point states given two manifolds. The states pertain to the transition from manifold1
+/// to manifold2. So state1 is either persist or remove while state2 is either add or persist.
+B2_API void b2GetPointStates(b2PointState state1[b2_maxManifoldPoints], b2PointState state2[b2_maxManifoldPoints],
+					  const b2Manifold* manifold1, const b2Manifold* manifold2);
+
+/// Used for computing contact manifolds.
+struct B2_API b2ClipVertex
+{
+	b2Vec2 v;
+	b2ContactID id;
+};
+
+/// Ray-cast input data. The ray extends from p1 to p1 + maxFraction * (p2 - p1).
+struct B2_API b2RayCastInput
+{
+	b2Vec2 p1, p2;
+	float maxFraction;
+};
+
+/// Ray-cast output data. The ray hits at p1 + fraction * (p2 - p1), where p1 and p2
+/// come from b2RayCastInput.
+struct B2_API b2RayCastOutput
+{
+	b2Vec2 normal;
+	float fraction;
+};
+
+/// An axis aligned bounding box.
+struct B2_API b2AABB
+{
+	/// Verify that the bounds are sorted.
+	bool IsValid() const;
+
+	/// Get the center of the AABB.
+	b2Vec2 GetCenter() const
+	{
+		return 0.5f * (lowerBound + upperBound);
+	}
+
+	/// Get the extents of the AABB (half-widths).
+	b2Vec2 GetExtents() const
+	{
+		return 0.5f * (upperBound - lowerBound);
+	}
+
+	/// Get the perimeter length
+	float GetPerimeter() const
+	{
+		float wx = upperBound.x - lowerBound.x;
+		float wy = upperBound.y - lowerBound.y;
+		return 2.0f * (wx + wy);
+	}
+
+	/// Combine an AABB into this one.
+	void Combine(const b2AABB& aabb)
+	{
+		lowerBound = b2Min(lowerBound, aabb.lowerBound);
+		upperBound = b2Max(upperBound, aabb.upperBound);
+	}
+
+	/// Combine two AABBs into this one.
+	void Combine(const b2AABB& aabb1, const b2AABB& aabb2)
+	{
+		lowerBound = b2Min(aabb1.lowerBound, aabb2.lowerBound);
+		upperBound = b2Max(aabb1.upperBound, aabb2.upperBound);
+	}
+
+	/// Does this aabb contain the provided AABB.
+	bool Contains(const b2AABB& aabb) const
+	{
+		bool result = true;
+		result = result && lowerBound.x <= aabb.lowerBound.x;
+		result = result && lowerBound.y <= aabb.lowerBound.y;
+		result = result && aabb.upperBound.x <= upperBound.x;
+		result = result && aabb.upperBound.y <= upperBound.y;
+		return result;
+	}
+
+	bool RayCast(b2RayCastOutput* output, const b2RayCastInput& input) const;
+
+	b2Vec2 lowerBound;	///< the lower vertex
+	b2Vec2 upperBound;	///< the upper vertex
+};
+
+/// Compute the collision manifold between two circles.
+B2_API void b2CollideCircles(b2Manifold* manifold,
+					  const b2CircleShape* circleA, const b2Transform& xfA,
+					  const b2CircleShape* circleB, const b2Transform& xfB);
+
+/// Compute the collision manifold between a polygon and a circle.
+B2_API void b2CollidePolygonAndCircle(b2Manifold* manifold,
+							   const b2PolygonShape* polygonA, const b2Transform& xfA,
+							   const b2CircleShape* circleB, const b2Transform& xfB);
+
+/// Compute the collision manifold between two polygons.
+B2_API void b2CollidePolygons(b2Manifold* manifold,
+					   const b2PolygonShape* polygonA, const b2Transform& xfA,
+					   const b2PolygonShape* polygonB, const b2Transform& xfB);
+
+/// Compute the collision manifold between an edge and a circle.
+B2_API void b2CollideEdgeAndCircle(b2Manifold* manifold,
+							   const b2EdgeShape* polygonA, const b2Transform& xfA,
+							   const b2CircleShape* circleB, const b2Transform& xfB);
+
+/// Compute the collision manifold between an edge and a polygon.
+B2_API void b2CollideEdgeAndPolygon(b2Manifold* manifold,
+							   const b2EdgeShape* edgeA, const b2Transform& xfA,
+							   const b2PolygonShape* polygonB, const b2Transform& xfB);
+
+/// Clipping for contact manifolds.
+B2_API int32 b2ClipSegmentToLine(b2ClipVertex vOut[2], const b2ClipVertex vIn[2],
+							const b2Vec2& normal, float offset, int32 vertexIndexA);
+
+/// Determine if two generic shapes overlap.
+B2_API bool b2TestOverlap(	const b2Shape* shapeA, int32 indexA,
+					const b2Shape* shapeB, int32 indexB,
+					const b2Transform& xfA, const b2Transform& xfB);
+
+/// Convex hull used for polygon collision
+struct b2Hull
+{
+	b2Vec2 points[b2_maxPolygonVertices];
+	int32 count;
+};
+
+/// Compute the convex hull of a set of points. Returns an empty hull if it fails.
+/// Some failure cases:
+/// - all points very close together
+/// - all points on a line
+/// - less than 3 points
+/// - more than b2_maxPolygonVertices points
+/// This welds close points and removes collinear points.
+b2Hull b2ComputeHull(const b2Vec2* points, int32 count);
+
+/// This determines if a hull is valid. Checks for:
+/// - convexity
+/// - collinear points
+/// This is expensive and should not be called at runtime.
+bool b2ValidateHull(const b2Hull& hull);
+
+
+// ---------------- Inline Functions ------------------------------------------
+
+inline bool b2AABB::IsValid() const
+{
+	b2Vec2 d = upperBound - lowerBound;
+	bool valid = d.x >= 0.0f && d.y >= 0.0f;
+	valid = valid && lowerBound.IsValid() && upperBound.IsValid();
+	return valid;
+}
+
+inline bool b2TestOverlap(const b2AABB& a, const b2AABB& b)
+{
+	b2Vec2 d1, d2;
+	d1 = b.lowerBound - a.upperBound;
+	d2 = a.lowerBound - b.upperBound;
+
+	if (d1.x > 0.0f || d1.y > 0.0f)
+		return false;
+
+	if (d2.x > 0.0f || d2.y > 0.0f)
+		return false;
+
+	return true;
+}
+
+#endif

3rd/box2d/include/box2d/b2_common.h

@@ -0,0 +1,138 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#ifndef B2_COMMON_H
+#define B2_COMMON_H
+
+#include "b2_settings.h"
+
+#include <stddef.h>
+#include <assert.h>
+#include <float.h>
+
+#if !defined(NDEBUG)
+	#define b2DEBUG
+#endif
+
+#define B2_NOT_USED(x) ((void)(x))
+#define b2Assert(A) assert(A)
+
+#define	b2_maxFloat		FLT_MAX
+#define	b2_epsilon		FLT_EPSILON
+#define b2_pi			3.14159265359f
+
+/// @file
+/// Global tuning constants based on meters-kilograms-seconds (MKS) units.
+///
+
+// Collision
+
+/// The maximum number of contact points between two convex shapes. Do
+/// not change this value.
+#define b2_maxManifoldPoints	2
+
+/// This is used to fatten AABBs in the dynamic tree. This allows proxies
+/// to move by a small amount without triggering a tree adjustment.
+/// This is in meters.
+#define b2_aabbExtension		(0.1f * b2_lengthUnitsPerMeter)
+
+/// This is used to fatten AABBs in the dynamic tree. This is used to predict
+/// the future position based on the current displacement.
+/// This is a dimensionless multiplier.
+#define b2_aabbMultiplier		4.0f
+
+/// A small length used as a collision and constraint tolerance. Usually it is
+/// chosen to be numerically significant, but visually insignificant. In meters.
+#define b2_linearSlop			(0.005f * b2_lengthUnitsPerMeter)
+
+/// A small angle used as a collision and constraint tolerance. Usually it is
+/// chosen to be numerically significant, but visually insignificant.
+#define b2_angularSlop			(2.0f / 180.0f * b2_pi)
+
+/// The radius of the polygon/edge shape skin. This should not be modified. Making
+/// this smaller means polygons will have an insufficient buffer for continuous collision.
+/// Making it larger may create artifacts for vertex collision.
+#define b2_polygonRadius		(2.0f * b2_linearSlop)
+
+/// Maximum number of sub-steps per contact in continuous physics simulation.
+#define b2_maxSubSteps			8
+
+
+// Dynamics
+
+/// Maximum number of contacts to be handled to solve a TOI impact.
+#define b2_maxTOIContacts			32
+
+/// The maximum linear position correction used when solving constraints. This helps to
+/// prevent overshoot. Meters.
+#define b2_maxLinearCorrection		(0.2f * b2_lengthUnitsPerMeter)
+
+/// The maximum angular position correction used when solving constraints. This helps to
+/// prevent overshoot.
+#define b2_maxAngularCorrection		(8.0f / 180.0f * b2_pi)
+
+/// The maximum linear translation of a body per step. This limit is very large and is used
+/// to prevent numerical problems. You shouldn't need to adjust this. Meters.
+#define b2_maxTranslation			(2.0f * b2_lengthUnitsPerMeter)
+#define b2_maxTranslationSquared	(b2_maxTranslation * b2_maxTranslation)
+
+/// The maximum angular velocity of a body. This limit is very large and is used
+/// to prevent numerical problems. You shouldn't need to adjust this.
+#define b2_maxRotation				(0.5f * b2_pi)
+#define b2_maxRotationSquared		(b2_maxRotation * b2_maxRotation)
+
+/// This scale factor controls how fast overlap is resolved. Ideally this would be 1 so
+/// that overlap is removed in one time step. However using values close to 1 often lead
+/// to overshoot.
+#define b2_baumgarte				0.2f
+#define b2_toiBaumgarte				0.75f
+
+
+// Sleep
+
+/// The time that a body must be still before it will go to sleep.
+#define b2_timeToSleep				0.5f
+
+/// A body cannot sleep if its linear velocity is above this tolerance.
+#define b2_linearSleepTolerance		(0.01f * b2_lengthUnitsPerMeter)
+
+/// A body cannot sleep if its angular velocity is above this tolerance.
+#define b2_angularSleepTolerance	(2.0f / 180.0f * b2_pi)
+
+/// Dump to a file. Only one dump file allowed at a time.
+void b2OpenDump(const char* fileName);
+void b2Dump(const char* string, ...);
+void b2CloseDump();
+
+/// Version numbering scheme.
+/// See http://en.wikipedia.org/wiki/Software_versioning
+struct b2Version
+{
+	int32 major;		///< significant changes
+	int32 minor;		///< incremental changes
+	int32 revision;		///< bug fixes
+};
+
+/// Current version.
+extern B2_API b2Version b2_version;
+
+#endif

3rd/box2d/include/box2d/b2_contact.h

@@ -0,0 +1,386 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#ifndef B2_CONTACT_H
+#define B2_CONTACT_H
+
+#include "b2_api.h"
+#include "b2_collision.h"
+#include "b2_fixture.h"
+#include "b2_math.h"
+#include "b2_shape.h"
+
+class b2Body;
+class b2Contact;
+class b2Fixture;
+class b2World;
+class b2BlockAllocator;
+class b2StackAllocator;
+class b2ContactListener;
+
+/// Friction mixing law. The idea is to allow either fixture to drive the friction to zero.
+/// For example, anything slides on ice.
+inline float b2MixFriction(float friction1, float friction2)
+{
+	return b2Sqrt(friction1 * friction2);
+}
+
+/// Restitution mixing law. The idea is allow for anything to bounce off an inelastic surface.
+/// For example, a superball bounces on anything.
+inline float b2MixRestitution(float restitution1, float restitution2)
+{
+	return restitution1 > restitution2 ? restitution1 : restitution2;
+}
+
+/// Restitution mixing law. This picks the lowest value.
+inline float b2MixRestitutionThreshold(float threshold1, float threshold2)
+{
+	return threshold1 < threshold2 ? threshold1 : threshold2;
+}
+
+typedef b2Contact* b2ContactCreateFcn(	b2Fixture* fixtureA, int32 indexA,
+										b2Fixture* fixtureB, int32 indexB,
+										b2BlockAllocator* allocator);
+typedef void b2ContactDestroyFcn(b2Contact* contact, b2BlockAllocator* allocator);
+
+struct B2_API b2ContactRegister
+{
+	b2ContactCreateFcn* createFcn;
+	b2ContactDestroyFcn* destroyFcn;
+	bool primary;
+};
+
+/// A contact edge is used to connect bodies and contacts together
+/// in a contact graph where each body is a node and each contact
+/// is an edge. A contact edge belongs to a doubly linked list
+/// maintained in each attached body. Each contact has two contact
+/// nodes, one for each attached body.
+struct B2_API b2ContactEdge
+{
+	b2Body* other;			///< provides quick access to the other body attached.
+	b2Contact* contact;		///< the contact
+	b2ContactEdge* prev;	///< the previous contact edge in the body's contact list
+	b2ContactEdge* next;	///< the next contact edge in the body's contact list
+};
+
+/// The class manages contact between two shapes. A contact exists for each overlapping
+/// AABB in the broad-phase (except if filtered). Therefore a contact object may exist
+/// that has no contact points.
+class B2_API b2Contact
+{
+public:
+
+	/// Get the contact manifold. Do not modify the manifold unless you understand the
+	/// internals of Box2D.
+	b2Manifold* GetManifold();
+	const b2Manifold* GetManifold() const;
+
+	/// Get the world manifold.
+	void GetWorldManifold(b2WorldManifold* worldManifold) const;
+
+	/// Is this contact touching?
+	bool IsTouching() const;
+
+	/// Enable/disable this contact. This can be used inside the pre-solve
+	/// contact listener. The contact is only disabled for the current
+	/// time step (or sub-step in continuous collisions).
+	void SetEnabled(bool flag);
+
+	/// Has this contact been disabled?
+	bool IsEnabled() const;
+
+	/// Get the next contact in the world's contact list.
+	b2Contact* GetNext();
+	const b2Contact* GetNext() const;
+
+	/// Get fixture A in this contact.
+	b2Fixture* GetFixtureA();
+	const b2Fixture* GetFixtureA() const;
+
+	/// Get the child primitive index for fixture A.
+	int32 GetChildIndexA() const;
+
+	/// Get fixture B in this contact.
+	b2Fixture* GetFixtureB();
+	const b2Fixture* GetFixtureB() const;
+
+	/// Get the child primitive index for fixture B.
+	int32 GetChildIndexB() const;
+
+	/// Override the default friction mixture. You can call this in b2ContactListener::PreSolve.
+	/// This value persists until set or reset.
+	void SetFriction(float friction);
+
+	/// Get the friction.
+	float GetFriction() const;
+
+	/// Reset the friction mixture to the default value.
+	void ResetFriction();
+
+	/// Override the default restitution mixture. You can call this in b2ContactListener::PreSolve.
+	/// The value persists until you set or reset.
+	void SetRestitution(float restitution);
+
+	/// Get the restitution.
+	float GetRestitution() const;
+
+	/// Reset the restitution to the default value.
+	void ResetRestitution();
+
+	/// Override the default restitution velocity threshold mixture. You can call this in b2ContactListener::PreSolve.
+	/// The value persists until you set or reset.
+	void SetRestitutionThreshold(float threshold);
+
+	/// Get the restitution threshold.
+	float GetRestitutionThreshold() const;
+
+	/// Reset the restitution threshold to the default value.
+	void ResetRestitutionThreshold();
+
+	/// Set the desired tangent speed for a conveyor belt behavior. In meters per second.
+	void SetTangentSpeed(float speed);
+
+	/// Get the desired tangent speed. In meters per second.
+	float GetTangentSpeed() const;
+
+	/// Evaluate this contact with your own manifold and transforms.
+	virtual void Evaluate(b2Manifold* manifold, const b2Transform& xfA, const b2Transform& xfB) = 0;
+
+protected:
+	friend class b2ContactManager;
+	friend class b2World;
+	friend class b2ContactSolver;
+	friend class b2Body;
+	friend class b2Fixture;
+
+	// Flags stored in m_flags
+	enum
+	{
+		// Used when crawling contact graph when forming islands.
+		e_islandFlag		= 0x0001,
+
+		// Set when the shapes are touching.
+		e_touchingFlag		= 0x0002,
+
+		// This contact can be disabled (by user)
+		e_enabledFlag		= 0x0004,
+
+		// This contact needs filtering because a fixture filter was changed.
+		e_filterFlag		= 0x0008,
+
+		// This bullet contact had a TOI event
+		e_bulletHitFlag		= 0x0010,
+
+		// This contact has a valid TOI in m_toi
+		e_toiFlag			= 0x0020
+	};
+
+	/// Flag this contact for filtering. Filtering will occur the next time step.
+	void FlagForFiltering();
+
+	static void AddType(b2ContactCreateFcn* createFcn, b2ContactDestroyFcn* destroyFcn,
+						b2Shape::Type typeA, b2Shape::Type typeB);
+	static void InitializeRegisters();
+	static b2Contact* Create(b2Fixture* fixtureA, int32 indexA, b2Fixture* fixtureB, int32 indexB, b2BlockAllocator* allocator);
+	static void Destroy(b2Contact* contact, b2Shape::Type typeA, b2Shape::Type typeB, b2BlockAllocator* allocator);
+	static void Destroy(b2Contact* contact, b2BlockAllocator* allocator);
+
+	b2Contact() : m_fixtureA(nullptr), m_fixtureB(nullptr) {}
+	b2Contact(b2Fixture* fixtureA, int32 indexA, b2Fixture* fixtureB, int32 indexB);
+	virtual ~b2Contact() {}
+
+	void Update(b2ContactListener* listener);
+
+	static b2ContactRegister s_registers[b2Shape::e_typeCount][b2Shape::e_typeCount];
+	static bool s_initialized;
+
+	uint32 m_flags;
+
+	// World pool and list pointers.
+	b2Contact* m_prev;
+	b2Contact* m_next;
+
+	// Nodes for connecting bodies.
+	b2ContactEdge m_nodeA;
+	b2ContactEdge m_nodeB;
+
+	b2Fixture* m_fixtureA;
+	b2Fixture* m_fixtureB;
+
+	int32 m_indexA;
+	int32 m_indexB;
+
+	b2Manifold m_manifold;
+
+	int32 m_toiCount;
+	float m_toi;
+
+	float m_friction;
+	float m_restitution;
+	float m_restitutionThreshold;
+
+	float m_tangentSpeed;
+};
+
+inline b2Manifold* b2Contact::GetManifold()
+{
+	return &m_manifold;
+}
+
+inline const b2Manifold* b2Contact::GetManifold() const
+{
+	return &m_manifold;
+}
+
+inline void b2Contact::GetWorldManifold(b2WorldManifold* worldManifold) const
+{
+	const b2Body* bodyA = m_fixtureA->GetBody();
+	const b2Body* bodyB = m_fixtureB->GetBody();
+	const b2Shape* shapeA = m_fixtureA->GetShape();
+	const b2Shape* shapeB = m_fixtureB->GetShape();
+
+	worldManifold->Initialize(&m_manifold, bodyA->GetTransform(), shapeA->m_radius, bodyB->GetTransform(), shapeB->m_radius);
+}
+
+inline void b2Contact::SetEnabled(bool flag)
+{
+	if (flag)
+	{
+		m_flags |= e_enabledFlag;
+	}
+	else
+	{
+		m_flags &= ~e_enabledFlag;
+	}
+}
+
+inline bool b2Contact::IsEnabled() const
+{
+	return (m_flags & e_enabledFlag) == e_enabledFlag;
+}
+
+inline bool b2Contact::IsTouching() const
+{
+	return (m_flags & e_touchingFlag) == e_touchingFlag;
+}
+
+inline b2Contact* b2Contact::GetNext()
+{
+	return m_next;
+}
+
+inline const b2Contact* b2Contact::GetNext() const
+{
+	return m_next;
+}
+
+inline b2Fixture* b2Contact::GetFixtureA()
+{
+	return m_fixtureA;
+}
+
+inline const b2Fixture* b2Contact::GetFixtureA() const
+{
+	return m_fixtureA;
+}
+
+inline b2Fixture* b2Contact::GetFixtureB()
+{
+	return m_fixtureB;
+}
+
+inline int32 b2Contact::GetChildIndexA() const
+{
+	return m_indexA;
+}
+
+inline const b2Fixture* b2Contact::GetFixtureB() const
+{
+	return m_fixtureB;
+}
+
+inline int32 b2Contact::GetChildIndexB() const
+{
+	return m_indexB;
+}
+
+inline void b2Contact::FlagForFiltering()
+{
+	m_flags |= e_filterFlag;
+}
+
+inline void b2Contact::SetFriction(float friction)
+{
+	m_friction = friction;
+}
+
+inline float b2Contact::GetFriction() const
+{
+	return m_friction;
+}
+
+inline void b2Contact::ResetFriction()
+{
+	m_friction = b2MixFriction(m_fixtureA->m_friction, m_fixtureB->m_friction);
+}
+
+inline void b2Contact::SetRestitution(float restitution)
+{
+	m_restitution = restitution;
+}
+
+inline float b2Contact::GetRestitution() const
+{
+	return m_restitution;
+}
+
+inline void b2Contact::ResetRestitution()
+{
+	m_restitution = b2MixRestitution(m_fixtureA->m_restitution, m_fixtureB->m_restitution);
+}
+
+inline void b2Contact::SetRestitutionThreshold(float threshold)
+{
+	m_restitutionThreshold = threshold;
+}
+
+inline float b2Contact::GetRestitutionThreshold() const
+{
+	return m_restitutionThreshold;
+}
+
+inline void b2Contact::ResetRestitutionThreshold()
+{
+	m_restitutionThreshold = b2MixRestitutionThreshold(m_fixtureA->m_restitutionThreshold, m_fixtureB->m_restitutionThreshold);
+}
+
+inline void b2Contact::SetTangentSpeed(float speed)
+{
+	m_tangentSpeed = speed;
+}
+
+inline float b2Contact::GetTangentSpeed() const
+{
+	return m_tangentSpeed;
+}
+
+#endif

3rd/box2d/include/box2d/b2_contact_manager.h

@@ -0,0 +1,57 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#ifndef B2_CONTACT_MANAGER_H
+#define B2_CONTACT_MANAGER_H
+
+#include "b2_api.h"
+#include "b2_broad_phase.h"
+
+class b2Contact;
+class b2ContactFilter;
+class b2ContactListener;
+class b2BlockAllocator;
+
+// Delegate of b2World.
+class B2_API b2ContactManager
+{
+public:
+	b2ContactManager();
+
+	// Broad-phase callback.
+	void AddPair(void* proxyUserDataA, void* proxyUserDataB);
+
+	void FindNewContacts();
+
+	void Destroy(b2Contact* c);
+
+	void Collide();
+
+	b2BroadPhase m_broadPhase;
+	b2Contact* m_contactList;
+	int32 m_contactCount;
+	b2ContactFilter* m_contactFilter;
+	b2ContactListener* m_contactListener;
+	b2BlockAllocator* m_allocator;
+};
+
+#endif

3rd/box2d/include/box2d/b2_distance.h

@@ -0,0 +1,171 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#ifndef B2_DISTANCE_H
+#define B2_DISTANCE_H
+
+#include "b2_api.h"
+#include "b2_math.h"
+
+class b2Shape;
+
+/// A distance proxy is used by the GJK algorithm.
+/// It encapsulates any shape.
+struct B2_API b2DistanceProxy
+{
+	b2DistanceProxy() : m_vertices(nullptr), m_count(0), m_radius(0.0f) {}
+
+	/// Initialize the proxy using the given shape. The shape
+	/// must remain in scope while the proxy is in use.
+	void Set(const b2Shape* shape, int32 index);
+
+    /// Initialize the proxy using a vertex cloud and radius. The vertices
+    /// must remain in scope while the proxy is in use.
+    void Set(const b2Vec2* vertices, int32 count, float radius);
+
+	/// Get the supporting vertex index in the given direction.
+	int32 GetSupport(const b2Vec2& d) const;
+
+	/// Get the supporting vertex in the given direction.
+	const b2Vec2& GetSupportVertex(const b2Vec2& d) const;
+
+	/// Get the vertex count.
+	int32 GetVertexCount() const;
+
+	/// Get a vertex by index. Used by b2Distance.
+	const b2Vec2& GetVertex(int32 index) const;
+
+	b2Vec2 m_buffer[2];
+	const b2Vec2* m_vertices;
+	int32 m_count;
+	float m_radius;
+};
+
+/// Used to warm start b2Distance.
+/// Set count to zero on first call.
+struct B2_API b2SimplexCache
+{
+	float metric;		///< length or area
+	uint16 count;
+	uint8 indexA[3];	///< vertices on shape A
+	uint8 indexB[3];	///< vertices on shape B
+};
+
+/// Input for b2Distance.
+/// You have to option to use the shape radii
+/// in the computation. Even
+struct B2_API b2DistanceInput
+{
+	b2DistanceProxy proxyA;
+	b2DistanceProxy proxyB;
+	b2Transform transformA;
+	b2Transform transformB;
+	bool useRadii;
+};
+
+/// Output for b2Distance.
+struct B2_API b2DistanceOutput
+{
+	b2Vec2 pointA;		///< closest point on shapeA
+	b2Vec2 pointB;		///< closest point on shapeB
+	float distance;
+	int32 iterations;	///< number of GJK iterations used
+};
+
+/// Compute the closest points between two shapes. Supports any combination of:
+/// b2CircleShape, b2PolygonShape, b2EdgeShape. The simplex cache is input/output.
+/// On the first call set b2SimplexCache.count to zero.
+B2_API void b2Distance(b2DistanceOutput* output,
+				b2SimplexCache* cache,
+				const b2DistanceInput* input);
+
+/// Input parameters for b2ShapeCast
+struct B2_API b2ShapeCastInput
+{
+	b2DistanceProxy proxyA;
+	b2DistanceProxy proxyB;
+	b2Transform transformA;
+	b2Transform transformB;
+	b2Vec2 translationB;
+};
+
+/// Output results for b2ShapeCast
+struct B2_API b2ShapeCastOutput
+{
+	b2Vec2 point;
+	b2Vec2 normal;
+	float lambda;
+	int32 iterations;
+};
+
+/// Perform a linear shape cast of shape B moving and shape A fixed. Determines the hit point, normal, and translation fraction.
+/// @returns true if hit, false if there is no hit or an initial overlap
+B2_API bool b2ShapeCast(b2ShapeCastOutput* output, const b2ShapeCastInput* input);
+
+//////////////////////////////////////////////////////////////////////////
+
+inline int32 b2DistanceProxy::GetVertexCount() const
+{
+	return m_count;
+}
+
+inline const b2Vec2& b2DistanceProxy::GetVertex(int32 index) const
+{
+	b2Assert(0 <= index && index < m_count);
+	return m_vertices[index];
+}
+
+inline int32 b2DistanceProxy::GetSupport(const b2Vec2& d) const
+{
+	int32 bestIndex = 0;
+	float bestValue = b2Dot(m_vertices[0], d);
+	for (int32 i = 1; i < m_count; ++i)
+	{
+		float value = b2Dot(m_vertices[i], d);
+		if (value > bestValue)
+		{
+			bestIndex = i;
+			bestValue = value;
+		}
+	}
+
+	return bestIndex;
+}
+
+inline const b2Vec2& b2DistanceProxy::GetSupportVertex(const b2Vec2& d) const
+{
+	int32 bestIndex = 0;
+	float bestValue = b2Dot(m_vertices[0], d);
+	for (int32 i = 1; i < m_count; ++i)
+	{
+		float value = b2Dot(m_vertices[i], d);
+		if (value > bestValue)
+		{
+			bestIndex = i;
+			bestValue = value;
+		}
+	}
+
+	return m_vertices[bestIndex];
+}
+
+#endif

3rd/box2d/include/box2d/b2_distance_joint.h

@@ -0,0 +1,176 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#ifndef B2_DISTANCE_JOINT_H
+#define B2_DISTANCE_JOINT_H
+
+#include "b2_api.h"
+#include "b2_joint.h"
+
+/// Distance joint definition. This requires defining an anchor point on both
+/// bodies and the non-zero distance of the distance joint. The definition uses
+/// local anchor points so that the initial configuration can violate the
+/// constraint slightly. This helps when saving and loading a game.
+struct B2_API b2DistanceJointDef : public b2JointDef
+{
+	b2DistanceJointDef()
+	{
+		type = e_distanceJoint;
+		localAnchorA.Set(0.0f, 0.0f);
+		localAnchorB.Set(0.0f, 0.0f);
+		length = 1.0f;
+		minLength = 0.0f;
+		maxLength = FLT_MAX;
+		stiffness = 0.0f;
+		damping = 0.0f;
+	}
+
+	/// Initialize the bodies, anchors, and rest length using world space anchors.
+	/// The minimum and maximum lengths are set to the rest length.
+	void Initialize(b2Body* bodyA, b2Body* bodyB,
+					const b2Vec2& anchorA, const b2Vec2& anchorB);
+
+	/// The local anchor point relative to bodyA's origin.
+	b2Vec2 localAnchorA;
+
+	/// The local anchor point relative to bodyB's origin.
+	b2Vec2 localAnchorB;
+
+	/// The rest length of this joint. Clamped to a stable minimum value.
+	float length;
+
+	/// Minimum length. Clamped to a stable minimum value.
+	float minLength;
+
+	/// Maximum length. Must be greater than or equal to the minimum length.
+	float maxLength;
+
+	/// The linear stiffness in N/m.
+	float stiffness;
+
+	/// The linear damping in N*s/m.
+	float damping;
+};
+
+/// A distance joint constrains two points on two bodies to remain at a fixed
+/// distance from each other. You can view this as a massless, rigid rod.
+class B2_API b2DistanceJoint : public b2Joint
+{
+public:
+
+	b2Vec2 GetAnchorA() const override;
+	b2Vec2 GetAnchorB() const override;
+
+	/// Get the reaction force given the inverse time step.
+	/// Unit is N.
+	b2Vec2 GetReactionForce(float inv_dt) const override;
+
+	/// Get the reaction torque given the inverse time step.
+	/// Unit is N*m. This is always zero for a distance joint.
+	float GetReactionTorque(float inv_dt) const override;
+
+	/// The local anchor point relative to bodyA's origin.
+	const b2Vec2& GetLocalAnchorA() const { return m_localAnchorA; }
+
+	/// The local anchor point relative to bodyB's origin.
+	const b2Vec2& GetLocalAnchorB() const  { return m_localAnchorB; }
+
+	/// Get the rest length
+	float GetLength() const { return m_length; }
+
+	/// Set the rest length
+	/// @returns clamped rest length
+	float SetLength(float length);
+
+	/// Get the minimum length
+	float GetMinLength() const { return m_minLength; }
+
+	/// Set the minimum length
+	/// @returns the clamped minimum length
+	float SetMinLength(float minLength);
+
+	/// Get the maximum length
+	float GetMaxLength() const { return m_maxLength; }
+
+	/// Set the maximum length
+	/// @returns the clamped maximum length
+	float SetMaxLength(float maxLength);
+
+	/// Get the current length
+	float GetCurrentLength() const;
+
+	/// Set/get the linear stiffness in N/m
+	void SetStiffness(float stiffness) { m_stiffness = stiffness; }
+	float GetStiffness() const { return m_stiffness; }
+
+	/// Set/get linear damping in N*s/m
+	void SetDamping(float damping) { m_damping = damping; }
+	float GetDamping() const { return m_damping; }
+
+	/// Dump joint to dmLog
+	void Dump() override;
+
+	///
+	void Draw(b2Draw* draw) const override;
+
+protected:
+
+	friend class b2Joint;
+	b2DistanceJoint(const b2DistanceJointDef* data);
+
+	void InitVelocityConstraints(const b2SolverData& data) override;
+	void SolveVelocityConstraints(const b2SolverData& data) override;
+	bool SolvePositionConstraints(const b2SolverData& data) override;
+
+	float m_stiffness;
+	float m_damping;
+	float m_bias;
+	float m_length;
+	float m_minLength;
+	float m_maxLength;
+
+	// Solver shared
+	b2Vec2 m_localAnchorA;
+	b2Vec2 m_localAnchorB;
+	float m_gamma;
+	float m_impulse;
+	float m_lowerImpulse;
+	float m_upperImpulse;
+
+	// Solver temp
+	int32 m_indexA;
+	int32 m_indexB;
+	b2Vec2 m_u;
+	b2Vec2 m_rA;
+	b2Vec2 m_rB;
+	b2Vec2 m_localCenterA;
+	b2Vec2 m_localCenterB;
+	float m_currentLength;
+	float m_invMassA;
+	float m_invMassB;
+	float m_invIA;
+	float m_invIB;
+	float m_softMass;
+	float m_mass;
+};
+
+#endif

3rd/box2d/include/box2d/b2_draw.h

@@ -0,0 +1,102 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#ifndef B2_DRAW_H
+#define B2_DRAW_H
+
+#include "b2_api.h"
+#include "b2_math.h"
+
+/// Color for debug drawing. Each value has the range [0,1].
+struct B2_API b2Color
+{
+	b2Color() {}
+	b2Color(float rIn, float gIn, float bIn, float aIn = 1.0f)
+	{
+		r = rIn; g = gIn; b = bIn; a = aIn;
+	}
+
+	void Set(float rIn, float gIn, float bIn, float aIn = 1.0f)
+	{
+		r = rIn; g = gIn; b = bIn; a = aIn;
+	}
+
+	float r, g, b, a;
+};
+
+/// Implement and register this class with a b2World to provide debug drawing of physics
+/// entities in your game.
+class B2_API b2Draw
+{
+public:
+	b2Draw();
+
+	virtual ~b2Draw() {}
+
+	enum
+	{
+		e_shapeBit				= 0x0001,	///< draw shapes
+		e_jointBit				= 0x0002,	///< draw joint connections
+		e_aabbBit				= 0x0004,	///< draw axis aligned bounding boxes
+		e_pairBit				= 0x0008,	///< draw broad-phase pairs
+		e_centerOfMassBit		= 0x0010	///< draw center of mass frame
+	};
+
+	/// Set the drawing flags.
+	void SetFlags(uint32 flags);
+
+	/// Get the drawing flags.
+	uint32 GetFlags() const;
+
+	/// Append flags to the current flags.
+	void AppendFlags(uint32 flags);
+
+	/// Clear flags from the current flags.
+	void ClearFlags(uint32 flags);
+
+	/// Draw a closed polygon provided in CCW order.
+	virtual void DrawPolygon(const b2Vec2* vertices, int32 vertexCount, const b2Color& color) = 0;
+
+	/// Draw a solid closed polygon provided in CCW order.
+	virtual void DrawSolidPolygon(const b2Vec2* vertices, int32 vertexCount, const b2Color& color) = 0;
+
+	/// Draw a circle.
+	virtual void DrawCircle(const b2Vec2& center, float radius, const b2Color& color) = 0;
+
+	/// Draw a solid circle.
+	virtual void DrawSolidCircle(const b2Vec2& center, float radius, const b2Vec2& axis, const b2Color& color) = 0;
+
+	/// Draw a line segment.
+	virtual void DrawSegment(const b2Vec2& p1, const b2Vec2& p2, const b2Color& color) = 0;
+
+	/// Draw a transform. Choose your own length scale.
+	/// @param xf a transform.
+	virtual void DrawTransform(const b2Transform& xf) = 0;
+
+	/// Draw a point.
+	virtual void DrawPoint(const b2Vec2& p, float size, const b2Color& color) = 0;
+
+protected:
+	uint32 m_drawFlags;
+};
+
+#endif

3rd/box2d/include/box2d/b2_dynamic_tree.h

@@ -0,0 +1,308 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#ifndef B2_DYNAMIC_TREE_H
+#define B2_DYNAMIC_TREE_H
+
+#include "b2_api.h"
+#include "b2_collision.h"
+#include "b2_growable_stack.h"
+
+#define b2_nullNode (-1)
+
+/// A node in the dynamic tree. The client does not interact with this directly.
+struct B2_API b2TreeNode
+{
+	bool IsLeaf() const
+	{
+		return child1 == b2_nullNode;
+	}
+
+	/// Enlarged AABB
+	b2AABB aabb;
+
+	void* userData;
+
+	union
+	{
+		int32 parent;
+		int32 next;
+	};
+
+	int32 child1;
+	int32 child2;
+
+	// leaf = 0, free node = -1
+	int32 height;
+
+	bool moved;
+};
+
+/// A dynamic AABB tree broad-phase, inspired by Nathanael Presson's btDbvt.
+/// A dynamic tree arranges data in a binary tree to accelerate
+/// queries such as volume queries and ray casts. Leafs are proxies
+/// with an AABB. In the tree we expand the proxy AABB by b2_fatAABBFactor
+/// so that the proxy AABB is bigger than the client object. This allows the client
+/// object to move by small amounts without triggering a tree update.
+///
+/// Nodes are pooled and relocatable, so we use node indices rather than pointers.
+class B2_API b2DynamicTree
+{
+public:
+	/// Constructing the tree initializes the node pool.
+	b2DynamicTree();
+
+	/// Destroy the tree, freeing the node pool.
+	~b2DynamicTree();
+
+	/// Create a proxy. Provide a tight fitting AABB and a userData pointer.
+	int32 CreateProxy(const b2AABB& aabb, void* userData);
+
+	/// Destroy a proxy. This asserts if the id is invalid.
+	void DestroyProxy(int32 proxyId);
+
+	/// Move a proxy with a swepted AABB. If the proxy has moved outside of its fattened AABB,
+	/// then the proxy is removed from the tree and re-inserted. Otherwise
+	/// the function returns immediately.
+	/// @return true if the proxy was re-inserted.
+	bool MoveProxy(int32 proxyId, const b2AABB& aabb1, const b2Vec2& displacement);
+
+	/// Get proxy user data.
+	/// @return the proxy user data or 0 if the id is invalid.
+	void* GetUserData(int32 proxyId) const;
+
+	bool WasMoved(int32 proxyId) const;
+	void ClearMoved(int32 proxyId);
+
+	/// Get the fat AABB for a proxy.
+	const b2AABB& GetFatAABB(int32 proxyId) const;
+
+	/// Query an AABB for overlapping proxies. The callback class
+	/// is called for each proxy that overlaps the supplied AABB.
+	template <typename T>
+	void Query(T* callback, const b2AABB& aabb) const;
+
+	/// Ray-cast against the proxies in the tree. This relies on the callback
+	/// to perform a exact ray-cast in the case were the proxy contains a shape.
+	/// The callback also performs the any collision filtering. This has performance
+	/// roughly equal to k * log(n), where k is the number of collisions and n is the
+	/// number of proxies in the tree.
+	/// @param input the ray-cast input data. The ray extends from p1 to p1 + maxFraction * (p2 - p1).
+	/// @param callback a callback class that is called for each proxy that is hit by the ray.
+	template <typename T>
+	void RayCast(T* callback, const b2RayCastInput& input) const;
+
+	/// Validate this tree. For testing.
+	void Validate() const;
+
+	/// Compute the height of the binary tree in O(N) time. Should not be
+	/// called often.
+	int32 GetHeight() const;
+
+	/// Get the maximum balance of an node in the tree. The balance is the difference
+	/// in height of the two children of a node.
+	int32 GetMaxBalance() const;
+
+	/// Get the ratio of the sum of the node areas to the root area.
+	float GetAreaRatio() const;
+
+	/// Build an optimal tree. Very expensive. For testing.
+	void RebuildBottomUp();
+
+	/// Shift the world origin. Useful for large worlds.
+	/// The shift formula is: position -= newOrigin
+	/// @param newOrigin the new origin with respect to the old origin
+	void ShiftOrigin(const b2Vec2& newOrigin);
+
+private:
+
+	int32 AllocateNode();
+	void FreeNode(int32 node);
+
+	void InsertLeaf(int32 node);
+	void RemoveLeaf(int32 node);
+
+	int32 Balance(int32 index);
+
+	int32 ComputeHeight() const;
+	int32 ComputeHeight(int32 nodeId) const;
+
+	void ValidateStructure(int32 index) const;
+	void ValidateMetrics(int32 index) const;
+
+	int32 m_root;
+
+	b2TreeNode* m_nodes;
+	int32 m_nodeCount;
+	int32 m_nodeCapacity;
+
+	int32 m_freeList;
+
+	int32 m_insertionCount;
+};
+
+inline void* b2DynamicTree::GetUserData(int32 proxyId) const
+{
+	b2Assert(0 <= proxyId && proxyId < m_nodeCapacity);
+	return m_nodes[proxyId].userData;
+}
+
+inline bool b2DynamicTree::WasMoved(int32 proxyId) const
+{
+	b2Assert(0 <= proxyId && proxyId < m_nodeCapacity);
+	return m_nodes[proxyId].moved;
+}
+
+inline void b2DynamicTree::ClearMoved(int32 proxyId)
+{
+	b2Assert(0 <= proxyId && proxyId < m_nodeCapacity);
+	m_nodes[proxyId].moved = false;
+}
+
+inline const b2AABB& b2DynamicTree::GetFatAABB(int32 proxyId) const
+{
+	b2Assert(0 <= proxyId && proxyId < m_nodeCapacity);
+	return m_nodes[proxyId].aabb;
+}
+
+template <typename T>
+inline void b2DynamicTree::Query(T* callback, const b2AABB& aabb) const
+{
+	b2GrowableStack<int32, 256> stack;
+	stack.Push(m_root);
+
+	while (stack.GetCount() > 0)
+	{
+		int32 nodeId = stack.Pop();
+		if (nodeId == b2_nullNode)
+		{
+			continue;
+		}
+
+		const b2TreeNode* node = m_nodes + nodeId;
+
+		if (b2TestOverlap(node->aabb, aabb))
+		{
+			if (node->IsLeaf())
+			{
+				bool proceed = callback->QueryCallback(nodeId);
+				if (proceed == false)
+				{
+					return;
+				}
+			}
+			else
+			{
+				stack.Push(node->child1);
+				stack.Push(node->child2);
+			}
+		}
+	}
+}
+
+template <typename T>
+inline void b2DynamicTree::RayCast(T* callback, const b2RayCastInput& input) const
+{
+	b2Vec2 p1 = input.p1;
+	b2Vec2 p2 = input.p2;
+	b2Vec2 r = p2 - p1;
+	b2Assert(r.LengthSquared() > 0.0f);
+	r.Normalize();
+
+	// v is perpendicular to the segment.
+	b2Vec2 v = b2Cross(1.0f, r);
+	b2Vec2 abs_v = b2Abs(v);
+
+	// Separating axis for segment (Gino, p80).
+	// |dot(v, p1 - c)| > dot(|v|, h)
+
+	float maxFraction = input.maxFraction;
+
+	// Build a bounding box for the segment.
+	b2AABB segmentAABB;
+	{
+		b2Vec2 t = p1 + maxFraction * (p2 - p1);
+		segmentAABB.lowerBound = b2Min(p1, t);
+		segmentAABB.upperBound = b2Max(p1, t);
+	}
+
+	b2GrowableStack<int32, 256> stack;
+	stack.Push(m_root);
+
+	while (stack.GetCount() > 0)
+	{
+		int32 nodeId = stack.Pop();
+		if (nodeId == b2_nullNode)
+		{
+			continue;
+		}
+
+		const b2TreeNode* node = m_nodes + nodeId;
+
+		if (b2TestOverlap(node->aabb, segmentAABB) == false)
+		{
+			continue;
+		}
+
+		// Separating axis for segment (Gino, p80).
+		// |dot(v, p1 - c)| > dot(|v|, h)
+		b2Vec2 c = node->aabb.GetCenter();
+		b2Vec2 h = node->aabb.GetExtents();
+		float separation = b2Abs(b2Dot(v, p1 - c)) - b2Dot(abs_v, h);
+		if (separation > 0.0f)
+		{
+			continue;
+		}
+
+		if (node->IsLeaf())
+		{
+			b2RayCastInput subInput;
+			subInput.p1 = input.p1;
+			subInput.p2 = input.p2;
+			subInput.maxFraction = maxFraction;
+
+			float value = callback->RayCastCallback(subInput, nodeId);
+
+			if (value == 0.0f)
+			{
+				// The client has terminated the ray cast.
+				return;
+			}
+
+			if (value > 0.0f)
+			{
+				// Update segment bounding box.
+				maxFraction = value;
+				b2Vec2 t = p1 + maxFraction * (p2 - p1);
+				segmentAABB.lowerBound = b2Min(p1, t);
+				segmentAABB.upperBound = b2Max(p1, t);
+			}
+		}
+		else
+		{
+			stack.Push(node->child1);
+			stack.Push(node->child2);
+		}
+	}
+}
+
+#endif

3rd/box2d/include/box2d/b2_edge_shape.h

@@ -0,0 +1,86 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#ifndef B2_EDGE_SHAPE_H
+#define B2_EDGE_SHAPE_H
+
+#include "b2_api.h"
+#include "b2_shape.h"
+
+/// A line segment (edge) shape. These can be connected in chains or loops
+/// to other edge shapes. Edges created independently are two-sided and do
+/// no provide smooth movement across junctions.
+class B2_API b2EdgeShape : public b2Shape
+{
+public:
+	b2EdgeShape();
+
+	/// Set this as a part of a sequence. Vertex v0 precedes the edge and vertex v3
+	/// follows. These extra vertices are used to provide smooth movement
+	/// across junctions. This also makes the collision one-sided. The edge
+	/// normal points to the right looking from v1 to v2.
+	void SetOneSided(const b2Vec2& v0, const b2Vec2& v1,const b2Vec2& v2, const b2Vec2& v3);
+
+	/// Set this as an isolated edge. Collision is two-sided.
+	void SetTwoSided(const b2Vec2& v1, const b2Vec2& v2);
+
+	/// Implement b2Shape.
+	b2Shape* Clone(b2BlockAllocator* allocator) const override;
+
+	/// @see b2Shape::GetChildCount
+	int32 GetChildCount() const override;
+
+	/// @see b2Shape::TestPoint
+	bool TestPoint(const b2Transform& transform, const b2Vec2& p) const override;
+
+	/// Implement b2Shape.
+	bool RayCast(b2RayCastOutput* output, const b2RayCastInput& input,
+				const b2Transform& transform, int32 childIndex) const override;
+
+	/// @see b2Shape::ComputeAABB
+	void ComputeAABB(b2AABB* aabb, const b2Transform& transform, int32 childIndex) const override;
+
+	/// @see b2Shape::ComputeMass
+	void ComputeMass(b2MassData* massData, float density) const override;
+
+	/// These are the edge vertices
+	b2Vec2 m_vertex1, m_vertex2;
+
+	/// Optional adjacent vertices. These are used for smooth collision.
+	b2Vec2 m_vertex0, m_vertex3;
+
+	/// Uses m_vertex0 and m_vertex3 to create smooth collision.
+	bool m_oneSided;
+};
+
+inline b2EdgeShape::b2EdgeShape()
+{
+	m_type = e_edge;
+	m_radius = b2_polygonRadius;
+	m_vertex0.x = 0.0f;
+	m_vertex0.y = 0.0f;
+	m_vertex3.x = 0.0f;
+	m_vertex3.y = 0.0f;
+	m_oneSided = false;
+}
+
+#endif

3rd/box2d/include/box2d/b2_fixture.h

@@ -0,0 +1,371 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#ifndef B2_FIXTURE_H
+#define B2_FIXTURE_H
+
+#include "b2_api.h"
+#include "b2_body.h"
+#include "b2_collision.h"
+#include "b2_shape.h"
+
+class b2BlockAllocator;
+class b2Body;
+class b2BroadPhase;
+class b2Fixture;
+
+/// This holds contact filtering data.
+struct B2_API b2Filter
+{
+	b2Filter()
+	{
+		categoryBits = 0x0001;
+		maskBits = 0xFFFF;
+		groupIndex = 0;
+	}
+
+	/// The collision category bits. Normally you would just set one bit.
+	uint16 categoryBits;
+
+	/// The collision mask bits. This states the categories that this
+	/// shape would accept for collision.
+	uint16 maskBits;
+
+	/// Collision groups allow a certain group of objects to never collide (negative)
+	/// or always collide (positive). Zero means no collision group. Non-zero group
+	/// filtering always wins against the mask bits.
+	int16 groupIndex;
+};
+
+/// A fixture definition is used to create a fixture. This class defines an
+/// abstract fixture definition. You can reuse fixture definitions safely.
+struct B2_API b2FixtureDef
+{
+	/// The constructor sets the default fixture definition values.
+	b2FixtureDef()
+	{
+		shape = nullptr;
+		friction = 0.2f;
+		restitution = 0.0f;
+		restitutionThreshold = 1.0f * b2_lengthUnitsPerMeter;
+		density = 0.0f;
+		isSensor = false;
+	}
+
+	/// The shape, this must be set. The shape will be cloned, so you
+	/// can create the shape on the stack.
+	const b2Shape* shape;
+
+	/// Use this to store application specific fixture data.
+	b2FixtureUserData userData;
+
+	/// The friction coefficient, usually in the range [0,1].
+	float friction;
+
+	/// The restitution (elasticity) usually in the range [0,1].
+	float restitution;
+
+	/// Restitution velocity threshold, usually in m/s. Collisions above this
+	/// speed have restitution applied (will bounce).
+	float restitutionThreshold;
+
+	/// The density, usually in kg/m^2.
+	float density;
+
+	/// A sensor shape collects contact information but never generates a collision
+	/// response.
+	bool isSensor;
+
+	/// Contact filtering data.
+	b2Filter filter;
+};
+
+/// This proxy is used internally to connect fixtures to the broad-phase.
+struct B2_API b2FixtureProxy
+{
+	b2AABB aabb;
+	b2Fixture* fixture;
+	int32 childIndex;
+	int32 proxyId;
+};
+
+/// A fixture is used to attach a shape to a body for collision detection. A fixture
+/// inherits its transform from its parent. Fixtures hold additional non-geometric data
+/// such as friction, collision filters, etc.
+/// Fixtures are created via b2Body::CreateFixture.
+/// @warning you cannot reuse fixtures.
+class B2_API b2Fixture
+{
+public:
+	/// Get the type of the child shape. You can use this to down cast to the concrete shape.
+	/// @return the shape type.
+	b2Shape::Type GetType() const;
+
+	/// Get the child shape. You can modify the child shape, however you should not change the
+	/// number of vertices because this will crash some collision caching mechanisms.
+	/// Manipulating the shape may lead to non-physical behavior.
+	b2Shape* GetShape();
+	const b2Shape* GetShape() const;
+
+	/// Set if this fixture is a sensor.
+	void SetSensor(bool sensor);
+
+	/// Is this fixture a sensor (non-solid)?
+	/// @return the true if the shape is a sensor.
+	bool IsSensor() const;
+
+	/// Set the contact filtering data. This will not update contacts until the next time
+	/// step when either parent body is active and awake.
+	/// This automatically calls Refilter.
+	void SetFilterData(const b2Filter& filter);
+
+	/// Get the contact filtering data.
+	const b2Filter& GetFilterData() const;
+
+	/// Call this if you want to establish collision that was previously disabled by b2ContactFilter::ShouldCollide.
+	void Refilter();
+
+	/// Get the parent body of this fixture. This is nullptr if the fixture is not attached.
+	/// @return the parent body.
+	b2Body* GetBody();
+	const b2Body* GetBody() const;
+
+	/// Get the next fixture in the parent body's fixture list.
+	/// @return the next shape.
+	b2Fixture* GetNext();
+	const b2Fixture* GetNext() const;
+
+	/// Get the user data that was assigned in the fixture definition. Use this to
+	/// store your application specific data.
+	b2FixtureUserData& GetUserData();
+	const b2FixtureUserData& GetUserData() const;
+
+	/// Test a point for containment in this fixture.
+	/// @param p a point in world coordinates.
+	bool TestPoint(const b2Vec2& p) const;
+
+	/// Cast a ray against this shape.
+	/// @param output the ray-cast results.
+	/// @param input the ray-cast input parameters.
+	/// @param childIndex the child shape index (e.g. edge index)
+	bool RayCast(b2RayCastOutput* output, const b2RayCastInput& input, int32 childIndex) const;
+
+	/// Get the mass data for this fixture. The mass data is based on the density and
+	/// the shape. The rotational inertia is about the shape's origin. This operation
+	/// may be expensive.
+	void GetMassData(b2MassData* massData) const;
+
+	/// Set the density of this fixture. This will _not_ automatically adjust the mass
+	/// of the body. You must call b2Body::ResetMassData to update the body's mass.
+	void SetDensity(float density);
+
+	/// Get the density of this fixture.
+	float GetDensity() const;
+
+	/// Get the coefficient of friction.
+	float GetFriction() const;
+
+	/// Set the coefficient of friction. This will _not_ change the friction of
+	/// existing contacts.
+	void SetFriction(float friction);
+
+	/// Get the coefficient of restitution.
+	float GetRestitution() const;
+
+	/// Set the coefficient of restitution. This will _not_ change the restitution of
+	/// existing contacts.
+	void SetRestitution(float restitution);
+
+	/// Get the restitution velocity threshold.
+	float GetRestitutionThreshold() const;
+
+	/// Set the restitution threshold. This will _not_ change the restitution threshold of
+	/// existing contacts.
+	void SetRestitutionThreshold(float threshold);
+
+	/// Get the fixture's AABB. This AABB may be enlarge and/or stale.
+	/// If you need a more accurate AABB, compute it using the shape and
+	/// the body transform.
+	const b2AABB& GetAABB(int32 childIndex) const;
+
+	/// Dump this fixture to the log file.
+	void Dump(int32 bodyIndex);
+
+protected:
+
+	friend class b2Body;
+	friend class b2World;
+	friend class b2Contact;
+	friend class b2ContactManager;
+
+	b2Fixture();
+
+	// We need separation create/destroy functions from the constructor/destructor because
+	// the destructor cannot access the allocator (no destructor arguments allowed by C++).
+	void Create(b2BlockAllocator* allocator, b2Body* body, const b2FixtureDef* def);
+	void Destroy(b2BlockAllocator* allocator);
+
+	// These support body activation/deactivation.
+	void CreateProxies(b2BroadPhase* broadPhase, const b2Transform& xf);
+	void DestroyProxies(b2BroadPhase* broadPhase);
+
+	void Synchronize(b2BroadPhase* broadPhase, const b2Transform& xf1, const b2Transform& xf2);
+
+	float m_density;
+
+	b2Fixture* m_next;
+	b2Body* m_body;
+
+	b2Shape* m_shape;
+
+	float m_friction;
+	float m_restitution;
+	float m_restitutionThreshold;
+
+	b2FixtureProxy* m_proxies;
+	int32 m_proxyCount;
+
+	b2Filter m_filter;
+
+	bool m_isSensor;
+
+	b2FixtureUserData m_userData;
+};
+
+inline b2Shape::Type b2Fixture::GetType() const
+{
+	return m_shape->GetType();
+}
+
+inline b2Shape* b2Fixture::GetShape()
+{
+	return m_shape;
+}
+
+inline const b2Shape* b2Fixture::GetShape() const
+{
+	return m_shape;
+}
+
+inline bool b2Fixture::IsSensor() const
+{
+	return m_isSensor;
+}
+
+inline const b2Filter& b2Fixture::GetFilterData() const
+{
+	return m_filter;
+}
+
+inline b2FixtureUserData& b2Fixture::GetUserData()
+{
+	return m_userData;
+}
+
+inline const b2FixtureUserData& b2Fixture::GetUserData() const
+{
+	return m_userData;
+}
+
+inline b2Body* b2Fixture::GetBody()
+{
+	return m_body;
+}
+
+inline const b2Body* b2Fixture::GetBody() const
+{
+	return m_body;
+}
+
+inline b2Fixture* b2Fixture::GetNext()
+{
+	return m_next;
+}
+
+inline const b2Fixture* b2Fixture::GetNext() const
+{
+	return m_next;
+}
+
+inline void b2Fixture::SetDensity(float density)
+{
+	b2Assert(b2IsValid(density) && density >= 0.0f);
+	m_density = density;
+}
+
+inline float b2Fixture::GetDensity() const
+{
+	return m_density;
+}
+
+inline float b2Fixture::GetFriction() const
+{
+	return m_friction;
+}
+
+inline void b2Fixture::SetFriction(float friction)
+{
+	m_friction = friction;
+}
+
+inline float b2Fixture::GetRestitution() const
+{
+	return m_restitution;
+}
+
+inline void b2Fixture::SetRestitution(float restitution)
+{
+	m_restitution = restitution;
+}
+
+inline float b2Fixture::GetRestitutionThreshold() const
+{
+	return m_restitutionThreshold;
+}
+
+inline void b2Fixture::SetRestitutionThreshold(float threshold)
+{
+	m_restitutionThreshold = threshold;
+}
+
+inline bool b2Fixture::TestPoint(const b2Vec2& p) const
+{
+	return m_shape->TestPoint(m_body->GetTransform(), p);
+}
+
+inline bool b2Fixture::RayCast(b2RayCastOutput* output, const b2RayCastInput& input, int32 childIndex) const
+{
+	return m_shape->RayCast(output, input, m_body->GetTransform(), childIndex);
+}
+
+inline void b2Fixture::GetMassData(b2MassData* massData) const
+{
+	m_shape->ComputeMass(massData, m_density);
+}
+
+inline const b2AABB& b2Fixture::GetAABB(int32 childIndex) const
+{
+	b2Assert(0 <= childIndex && childIndex < m_proxyCount);
+	return m_proxies[childIndex].aabb;
+}
+
+#endif

3rd/box2d/include/box2d/b2_friction_joint.h

@@ -0,0 +1,124 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#ifndef B2_FRICTION_JOINT_H
+#define B2_FRICTION_JOINT_H
+
+#include "b2_api.h"
+#include "b2_joint.h"
+
+/// Friction joint definition.
+struct B2_API b2FrictionJointDef : public b2JointDef
+{
+	b2FrictionJointDef()
+	{
+		type = e_frictionJoint;
+		localAnchorA.SetZero();
+		localAnchorB.SetZero();
+		maxForce = 0.0f;
+		maxTorque = 0.0f;
+	}
+
+	/// Initialize the bodies, anchors, axis, and reference angle using the world
+	/// anchor and world axis.
+	void Initialize(b2Body* bodyA, b2Body* bodyB, const b2Vec2& anchor);
+
+	/// The local anchor point relative to bodyA's origin.
+	b2Vec2 localAnchorA;
+
+	/// The local anchor point relative to bodyB's origin.
+	b2Vec2 localAnchorB;
+
+	/// The maximum friction force in N.
+	float maxForce;
+
+	/// The maximum friction torque in N-m.
+	float maxTorque;
+};
+
+/// Friction joint. This is used for top-down friction.
+/// It provides 2D translational friction and angular friction.
+class B2_API b2FrictionJoint : public b2Joint
+{
+public:
+	b2Vec2 GetAnchorA() const override;
+	b2Vec2 GetAnchorB() const override;
+
+	b2Vec2 GetReactionForce(float inv_dt) const override;
+	float GetReactionTorque(float inv_dt) const override;
+
+	/// The local anchor point relative to bodyA's origin.
+	const b2Vec2& GetLocalAnchorA() const { return m_localAnchorA; }
+
+	/// The local anchor point relative to bodyB's origin.
+	const b2Vec2& GetLocalAnchorB() const  { return m_localAnchorB; }
+
+	/// Set the maximum friction force in N.
+	void SetMaxForce(float force);
+
+	/// Get the maximum friction force in N.
+	float GetMaxForce() const;
+
+	/// Set the maximum friction torque in N*m.
+	void SetMaxTorque(float torque);
+
+	/// Get the maximum friction torque in N*m.
+	float GetMaxTorque() const;
+
+	/// Dump joint to dmLog
+	void Dump() override;
+
+protected:
+
+	friend class b2Joint;
+
+	b2FrictionJoint(const b2FrictionJointDef* def);
+
+	void InitVelocityConstraints(const b2SolverData& data) override;
+	void SolveVelocityConstraints(const b2SolverData& data) override;
+	bool SolvePositionConstraints(const b2SolverData& data) override;
+
+	b2Vec2 m_localAnchorA;
+	b2Vec2 m_localAnchorB;
+
+	// Solver shared
+	b2Vec2 m_linearImpulse;
+	float m_angularImpulse;
+	float m_maxForce;
+	float m_maxTorque;
+
+	// Solver temp
+	int32 m_indexA;
+	int32 m_indexB;
+	b2Vec2 m_rA;
+	b2Vec2 m_rB;
+	b2Vec2 m_localCenterA;
+	b2Vec2 m_localCenterB;
+	float m_invMassA;
+	float m_invMassB;
+	float m_invIA;
+	float m_invIB;
+	b2Mat22 m_linearMass;
+	float m_angularMass;
+};
+
+#endif

3rd/box2d/include/box2d/b2_gear_joint.h

@@ -0,0 +1,131 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#ifndef B2_GEAR_JOINT_H
+#define B2_GEAR_JOINT_H
+
+#include "b2_joint.h"
+
+/// Gear joint definition. This definition requires two existing
+/// revolute or prismatic joints (any combination will work).
+/// @warning bodyB on the input joints must both be dynamic
+struct B2_API b2GearJointDef : public b2JointDef
+{
+	b2GearJointDef()
+	{
+		type = e_gearJoint;
+		joint1 = nullptr;
+		joint2 = nullptr;
+		ratio = 1.0f;
+	}
+
+	/// The first revolute/prismatic joint attached to the gear joint.
+	b2Joint* joint1;
+
+	/// The second revolute/prismatic joint attached to the gear joint.
+	b2Joint* joint2;
+
+	/// The gear ratio.
+	/// @see b2GearJoint for explanation.
+	float ratio;
+};
+
+/// A gear joint is used to connect two joints together. Either joint
+/// can be a revolute or prismatic joint. You specify a gear ratio
+/// to bind the motions together:
+/// coordinate1 + ratio * coordinate2 = constant
+/// The ratio can be negative or positive. If one joint is a revolute joint
+/// and the other joint is a prismatic joint, then the ratio will have units
+/// of length or units of 1/length.
+/// @warning You have to manually destroy the gear joint if joint1 or joint2
+/// is destroyed.
+class B2_API b2GearJoint : public b2Joint
+{
+public:
+	b2Vec2 GetAnchorA() const override;
+	b2Vec2 GetAnchorB() const override;
+
+	b2Vec2 GetReactionForce(float inv_dt) const override;
+	float GetReactionTorque(float inv_dt) const override;
+
+	/// Get the first joint.
+	b2Joint* GetJoint1() { return m_joint1; }
+
+	/// Get the second joint.
+	b2Joint* GetJoint2() { return m_joint2; }
+
+	/// Set/Get the gear ratio.
+	void SetRatio(float ratio);
+	float GetRatio() const;
+
+	/// Dump joint to dmLog
+	void Dump() override;
+
+protected:
+
+	friend class b2Joint;
+	b2GearJoint(const b2GearJointDef* data);
+
+	void InitVelocityConstraints(const b2SolverData& data) override;
+	void SolveVelocityConstraints(const b2SolverData& data) override;
+	bool SolvePositionConstraints(const b2SolverData& data) override;
+
+	b2Joint* m_joint1;
+	b2Joint* m_joint2;
+
+	b2JointType m_typeA;
+	b2JointType m_typeB;
+
+	// Body A is connected to body C
+	// Body B is connected to body D
+	b2Body* m_bodyC;
+	b2Body* m_bodyD;
+
+	// Solver shared
+	b2Vec2 m_localAnchorA;
+	b2Vec2 m_localAnchorB;
+	b2Vec2 m_localAnchorC;
+	b2Vec2 m_localAnchorD;
+
+	b2Vec2 m_localAxisC;
+	b2Vec2 m_localAxisD;
+
+	float m_referenceAngleA;
+	float m_referenceAngleB;
+
+	float m_constant;
+	float m_ratio;
+	float m_tolerance;
+
+	float m_impulse;
+
+	// Solver temp
+	int32 m_indexA, m_indexB, m_indexC, m_indexD;
+	b2Vec2 m_lcA, m_lcB, m_lcC, m_lcD;
+	float m_mA, m_mB, m_mC, m_mD;
+	float m_iA, m_iB, m_iC, m_iD;
+	b2Vec2 m_JvAC, m_JvBD;
+	float m_JwA, m_JwB, m_JwC, m_JwD;
+	float m_mass;
+};
+
+#endif

3rd/box2d/include/box2d/b2_growable_stack.h

@@ -0,0 +1,91 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#ifndef B2_GROWABLE_STACK_H
+#define B2_GROWABLE_STACK_H
+
+#include <string.h>
+
+#include "b2_settings.h"
+
+/// This is a growable LIFO stack with an initial capacity of N.
+/// If the stack size exceeds the initial capacity, the heap is used
+/// to increase the size of the stack.
+template <typename T, int32 N>
+class b2GrowableStack
+{
+public:
+	b2GrowableStack()
+	{
+		m_stack = m_array;
+		m_count = 0;
+		m_capacity = N;
+	}
+
+	~b2GrowableStack()
+	{
+		if (m_stack != m_array)
+		{
+			b2Free(m_stack);
+			m_stack = nullptr;
+		}
+	}
+
+	void Push(const T& element)
+	{
+		if (m_count == m_capacity)
+		{
+			T* old = m_stack;
+			m_capacity *= 2;
+			m_stack = (T*)b2Alloc(m_capacity * sizeof(T));
+			memcpy(m_stack, old, m_count * sizeof(T));
+			if (old != m_array)
+			{
+				b2Free(old);
+			}
+		}
+
+		m_stack[m_count] = element;
+		++m_count;
+	}
+
+	T Pop()
+	{
+		b2Assert(m_count > 0);
+		--m_count;
+		return m_stack[m_count];
+	}
+
+	int32 GetCount()
+	{
+		return m_count;
+	}
+
+private:
+	T* m_stack;
+	T m_array[N];
+	int32 m_count;
+	int32 m_capacity;
+};
+
+
+#endif

3rd/box2d/include/box2d/b2_joint.h

@@ -0,0 +1,233 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#ifndef B2_JOINT_H
+#define B2_JOINT_H
+
+#include "b2_api.h"
+#include "b2_math.h"
+
+class b2Body;
+class b2Draw;
+class b2Joint;
+struct b2SolverData;
+class b2BlockAllocator;
+
+enum b2JointType
+{
+	e_unknownJoint,
+	e_revoluteJoint,
+	e_prismaticJoint,
+	e_distanceJoint,
+	e_pulleyJoint,
+	e_mouseJoint,
+	e_gearJoint,
+	e_wheelJoint,
+    e_weldJoint,
+	e_frictionJoint,
+	e_motorJoint
+};
+
+struct B2_API b2Jacobian
+{
+	b2Vec2 linear;
+	float angularA;
+	float angularB;
+};
+
+/// A joint edge is used to connect bodies and joints together
+/// in a joint graph where each body is a node and each joint
+/// is an edge. A joint edge belongs to a doubly linked list
+/// maintained in each attached body. Each joint has two joint
+/// nodes, one for each attached body.
+struct B2_API b2JointEdge
+{
+	b2Body* other;			///< provides quick access to the other body attached.
+	b2Joint* joint;			///< the joint
+	b2JointEdge* prev;		///< the previous joint edge in the body's joint list
+	b2JointEdge* next;		///< the next joint edge in the body's joint list
+};
+
+/// Joint definitions are used to construct joints.
+struct B2_API b2JointDef
+{
+	b2JointDef()
+	{
+		type = e_unknownJoint;
+		bodyA = nullptr;
+		bodyB = nullptr;
+		collideConnected = false;
+	}
+
+	/// The joint type is set automatically for concrete joint types.
+	b2JointType type;
+
+	/// Use this to attach application specific data to your joints.
+	b2JointUserData userData;
+
+	/// The first attached body.
+	b2Body* bodyA;
+
+	/// The second attached body.
+	b2Body* bodyB;
+
+	/// Set this flag to true if the attached bodies should collide.
+	bool collideConnected;
+};
+
+/// Utility to compute linear stiffness values from frequency and damping ratio
+B2_API void b2LinearStiffness(float& stiffness, float& damping,
+	float frequencyHertz, float dampingRatio,
+	const b2Body* bodyA, const b2Body* bodyB);
+
+/// Utility to compute rotational stiffness values frequency and damping ratio
+B2_API void b2AngularStiffness(float& stiffness, float& damping,
+	float frequencyHertz, float dampingRatio,
+	const b2Body* bodyA, const b2Body* bodyB);
+
+/// The base joint class. Joints are used to constraint two bodies together in
+/// various fashions. Some joints also feature limits and motors.
+class B2_API b2Joint
+{
+public:
+
+	/// Get the type of the concrete joint.
+	b2JointType GetType() const;
+
+	/// Get the first body attached to this joint.
+	b2Body* GetBodyA();
+
+	/// Get the second body attached to this joint.
+	b2Body* GetBodyB();
+
+	/// Get the anchor point on bodyA in world coordinates.
+	virtual b2Vec2 GetAnchorA() const = 0;
+
+	/// Get the anchor point on bodyB in world coordinates.
+	virtual b2Vec2 GetAnchorB() const = 0;
+
+	/// Get the reaction force on bodyB at the joint anchor in Newtons.
+	virtual b2Vec2 GetReactionForce(float inv_dt) const = 0;
+
+	/// Get the reaction torque on bodyB in N*m.
+	virtual float GetReactionTorque(float inv_dt) const = 0;
+
+	/// Get the next joint the world joint list.
+	b2Joint* GetNext();
+	const b2Joint* GetNext() const;
+
+	/// Get the user data pointer.
+	b2JointUserData& GetUserData();
+	const b2JointUserData& GetUserData() const;
+
+	/// Short-cut function to determine if either body is enabled.
+	bool IsEnabled() const;
+
+	/// Get collide connected.
+	/// Note: modifying the collide connect flag won't work correctly because
+	/// the flag is only checked when fixture AABBs begin to overlap.
+	bool GetCollideConnected() const;
+
+	/// Dump this joint to the log file.
+	virtual void Dump() { b2Dump("// Dump is not supported for this joint type.\n"); }
+
+	/// Shift the origin for any points stored in world coordinates.
+	virtual void ShiftOrigin(const b2Vec2& newOrigin) { B2_NOT_USED(newOrigin);  }
+
+	/// Debug draw this joint
+	virtual void Draw(b2Draw* draw) const;
+
+protected:
+	friend class b2World;
+	friend class b2Body;
+	friend class b2Island;
+	friend class b2GearJoint;
+
+	static b2Joint* Create(const b2JointDef* def, b2BlockAllocator* allocator);
+	static void Destroy(b2Joint* joint, b2BlockAllocator* allocator);
+
+	b2Joint(const b2JointDef* def);
+	virtual ~b2Joint() {}
+
+	virtual void InitVelocityConstraints(const b2SolverData& data) = 0;
+	virtual void SolveVelocityConstraints(const b2SolverData& data) = 0;
+
+	// This returns true if the position errors are within tolerance.
+	virtual bool SolvePositionConstraints(const b2SolverData& data) = 0;
+
+	b2JointType m_type;
+	b2Joint* m_prev;
+	b2Joint* m_next;
+	b2JointEdge m_edgeA;
+	b2JointEdge m_edgeB;
+	b2Body* m_bodyA;
+	b2Body* m_bodyB;
+
+	int32 m_index;
+
+	bool m_islandFlag;
+	bool m_collideConnected;
+
+	b2JointUserData m_userData;
+};
+
+inline b2JointType b2Joint::GetType() const
+{
+	return m_type;
+}
+
+inline b2Body* b2Joint::GetBodyA()
+{
+	return m_bodyA;
+}
+
+inline b2Body* b2Joint::GetBodyB()
+{
+	return m_bodyB;
+}
+
+inline b2Joint* b2Joint::GetNext()
+{
+	return m_next;
+}
+
+inline const b2Joint* b2Joint::GetNext() const
+{
+	return m_next;
+}
+
+inline b2JointUserData& b2Joint::GetUserData()
+{
+	return m_userData;
+}
+
+inline const b2JointUserData& b2Joint::GetUserData() const
+{
+	return m_userData;
+}
+
+inline bool b2Joint::GetCollideConnected() const
+{
+	return m_collideConnected;
+}
+
+#endif

3rd/box2d/include/box2d/b2_math.h

@@ -0,0 +1,717 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#ifndef B2_MATH_H
+#define B2_MATH_H
+
+#include <math.h>
+
+#include "b2_api.h"
+#include "b2_settings.h"
+
+/// This function is used to ensure that a floating point number is not a NaN or infinity.
+inline bool b2IsValid(float x)
+{
+	return isfinite(x);
+}
+
+#define	b2Sqrt(x)	sqrtf(x)
+#define	b2Atan2(y, x)	atan2f(y, x)
+
+/// A 2D column vector.
+struct B2_API b2Vec2
+{
+	/// Default constructor does nothing (for performance).
+	b2Vec2() = default;
+
+	/// Construct using coordinates.
+	b2Vec2(float xIn, float yIn) : x(xIn), y(yIn) {}
+
+	/// Set this vector to all zeros.
+	void SetZero() { x = 0.0f; y = 0.0f; }
+
+	/// Set this vector to some specified coordinates.
+	void Set(float x_, float y_) { x = x_; y = y_; }
+
+	/// Negate this vector.
+	b2Vec2 operator -() const { b2Vec2 v; v.Set(-x, -y); return v; }
+
+	/// Read from and indexed element.
+	float operator () (int32 i) const
+	{
+		return (&x)[i];
+	}
+
+	/// Write to an indexed element.
+	float& operator () (int32 i)
+	{
+		return (&x)[i];
+	}
+
+	/// Add a vector to this vector.
+	void operator += (const b2Vec2& v)
+	{
+		x += v.x; y += v.y;
+	}
+
+	/// Subtract a vector from this vector.
+	void operator -= (const b2Vec2& v)
+	{
+		x -= v.x; y -= v.y;
+	}
+
+	/// Multiply this vector by a scalar.
+	void operator *= (float a)
+	{
+		x *= a; y *= a;
+	}
+
+	/// Get the length of this vector (the norm).
+	float Length() const
+	{
+		return b2Sqrt(x * x + y * y);
+	}
+
+	/// Get the length squared. For performance, use this instead of
+	/// b2Vec2::Length (if possible).
+	float LengthSquared() const
+	{
+		return x * x + y * y;
+	}
+
+	/// Convert this vector into a unit vector. Returns the length.
+	float Normalize()
+	{
+		float length = Length();
+		if (length < b2_epsilon)
+		{
+			return 0.0f;
+		}
+		float invLength = 1.0f / length;
+		x *= invLength;
+		y *= invLength;
+
+		return length;
+	}
+
+	/// Does this vector contain finite coordinates?
+	bool IsValid() const
+	{
+		return b2IsValid(x) && b2IsValid(y);
+	}
+
+	/// Get the skew vector such that dot(skew_vec, other) == cross(vec, other)
+	b2Vec2 Skew() const
+	{
+		return b2Vec2(-y, x);
+	}
+
+	float x, y;
+};
+
+/// A 2D column vector with 3 elements.
+struct B2_API b2Vec3
+{
+	/// Default constructor does nothing (for performance).
+	b2Vec3() = default;
+
+	/// Construct using coordinates.
+	b2Vec3(float xIn, float yIn, float zIn) : x(xIn), y(yIn), z(zIn) {}
+
+	/// Set this vector to all zeros.
+	void SetZero() { x = 0.0f; y = 0.0f; z = 0.0f; }
+
+	/// Set this vector to some specified coordinates.
+	void Set(float x_, float y_, float z_) { x = x_; y = y_; z = z_; }
+
+	/// Negate this vector.
+	b2Vec3 operator -() const { b2Vec3 v; v.Set(-x, -y, -z); return v; }
+
+	/// Add a vector to this vector.
+	void operator += (const b2Vec3& v)
+	{
+		x += v.x; y += v.y; z += v.z;
+	}
+
+	/// Subtract a vector from this vector.
+	void operator -= (const b2Vec3& v)
+	{
+		x -= v.x; y -= v.y; z -= v.z;
+	}
+
+	/// Multiply this vector by a scalar.
+	void operator *= (float s)
+	{
+		x *= s; y *= s; z *= s;
+	}
+
+	float x, y, z;
+};
+
+/// A 2-by-2 matrix. Stored in column-major order.
+struct B2_API b2Mat22
+{
+	/// The default constructor does nothing (for performance).
+	b2Mat22() = default;
+
+	/// Construct this matrix using columns.
+	b2Mat22(const b2Vec2& c1, const b2Vec2& c2)
+	{
+		ex = c1;
+		ey = c2;
+	}
+
+	/// Construct this matrix using scalars.
+	b2Mat22(float a11, float a12, float a21, float a22)
+	{
+		ex.x = a11; ex.y = a21;
+		ey.x = a12; ey.y = a22;
+	}
+
+	/// Initialize this matrix using columns.
+	void Set(const b2Vec2& c1, const b2Vec2& c2)
+	{
+		ex = c1;
+		ey = c2;
+	}
+
+	/// Set this to the identity matrix.
+	void SetIdentity()
+	{
+		ex.x = 1.0f; ey.x = 0.0f;
+		ex.y = 0.0f; ey.y = 1.0f;
+	}
+
+	/// Set this matrix to all zeros.
+	void SetZero()
+	{
+		ex.x = 0.0f; ey.x = 0.0f;
+		ex.y = 0.0f; ey.y = 0.0f;
+	}
+
+	b2Mat22 GetInverse() const
+	{
+		float a = ex.x, b = ey.x, c = ex.y, d = ey.y;
+		b2Mat22 B;
+		float det = a * d - b * c;
+		if (det != 0.0f)
+		{
+			det = 1.0f / det;
+		}
+		B.ex.x =  det * d;	B.ey.x = -det * b;
+		B.ex.y = -det * c;	B.ey.y =  det * a;
+		return B;
+	}
+
+	/// Solve A * x = b, where b is a column vector. This is more efficient
+	/// than computing the inverse in one-shot cases.
+	b2Vec2 Solve(const b2Vec2& b) const
+	{
+		float a11 = ex.x, a12 = ey.x, a21 = ex.y, a22 = ey.y;
+		float det = a11 * a22 - a12 * a21;
+		if (det != 0.0f)
+		{
+			det = 1.0f / det;
+		}
+		b2Vec2 x;
+		x.x = det * (a22 * b.x - a12 * b.y);
+		x.y = det * (a11 * b.y - a21 * b.x);
+		return x;
+	}
+
+	b2Vec2 ex, ey;
+};
+
+/// A 3-by-3 matrix. Stored in column-major order.
+struct B2_API b2Mat33
+{
+	/// The default constructor does nothing (for performance).
+	b2Mat33() = default;
+
+	/// Construct this matrix using columns.
+	b2Mat33(const b2Vec3& c1, const b2Vec3& c2, const b2Vec3& c3)
+	{
+		ex = c1;
+		ey = c2;
+		ez = c3;
+	}
+
+	/// Set this matrix to all zeros.
+	void SetZero()
+	{
+		ex.SetZero();
+		ey.SetZero();
+		ez.SetZero();
+	}
+
+	/// Solve A * x = b, where b is a column vector. This is more efficient
+	/// than computing the inverse in one-shot cases.
+	b2Vec3 Solve33(const b2Vec3& b) const;
+
+	/// Solve A * x = b, where b is a column vector. This is more efficient
+	/// than computing the inverse in one-shot cases. Solve only the upper
+	/// 2-by-2 matrix equation.
+	b2Vec2 Solve22(const b2Vec2& b) const;
+
+	/// Get the inverse of this matrix as a 2-by-2.
+	/// Returns the zero matrix if singular.
+	void GetInverse22(b2Mat33* M) const;
+
+	/// Get the symmetric inverse of this matrix as a 3-by-3.
+	/// Returns the zero matrix if singular.
+	void GetSymInverse33(b2Mat33* M) const;
+
+	b2Vec3 ex, ey, ez;
+};
+
+/// Rotation
+struct B2_API b2Rot
+{
+	b2Rot() = default;
+
+	/// Initialize from an angle in radians
+	explicit b2Rot(float angle)
+	{
+		/// TODO_ERIN optimize
+		s = sinf(angle);
+		c = cosf(angle);
+	}
+
+	/// Set using an angle in radians.
+	void Set(float angle)
+	{
+		/// TODO_ERIN optimize
+		s = sinf(angle);
+		c = cosf(angle);
+	}
+
+	/// Set to the identity rotation
+	void SetIdentity()
+	{
+		s = 0.0f;
+		c = 1.0f;
+	}
+
+	/// Get the angle in radians
+	float GetAngle() const
+	{
+		return b2Atan2(s, c);
+	}
+
+	/// Get the x-axis
+	b2Vec2 GetXAxis() const
+	{
+		return b2Vec2(c, s);
+	}
+
+	/// Get the u-axis
+	b2Vec2 GetYAxis() const
+	{
+		return b2Vec2(-s, c);
+	}
+
+	/// Sine and cosine
+	float s, c;
+};
+
+/// A transform contains translation and rotation. It is used to represent
+/// the position and orientation of rigid frames.
+struct B2_API b2Transform
+{
+	/// The default constructor does nothing.
+	b2Transform() = default;
+
+	/// Initialize using a position vector and a rotation.
+	b2Transform(const b2Vec2& position, const b2Rot& rotation) : p(position), q(rotation) {}
+
+	/// Set this to the identity transform.
+	void SetIdentity()
+	{
+		p.SetZero();
+		q.SetIdentity();
+	}
+
+	/// Set this based on the position and angle.
+	void Set(const b2Vec2& position, float angle)
+	{
+		p = position;
+		q.Set(angle);
+	}
+
+	b2Vec2 p;
+	b2Rot q;
+};
+
+/// This describes the motion of a body/shape for TOI computation.
+/// Shapes are defined with respect to the body origin, which may
+/// no coincide with the center of mass. However, to support dynamics
+/// we must interpolate the center of mass position.
+struct B2_API b2Sweep
+{
+	b2Sweep() = default;
+
+	/// Get the interpolated transform at a specific time.
+	/// @param transform the output transform
+	/// @param beta is a factor in [0,1], where 0 indicates alpha0.
+	void GetTransform(b2Transform* transform, float beta) const;
+
+	/// Advance the sweep forward, yielding a new initial state.
+	/// @param alpha the new initial time.
+	void Advance(float alpha);
+
+	/// Normalize the angles.
+	void Normalize();
+
+	b2Vec2 localCenter;	///< local center of mass position
+	b2Vec2 c0, c;		///< center world positions
+	float a0, a;		///< world angles
+
+	/// Fraction of the current time step in the range [0,1]
+	/// c0 and a0 are the positions at alpha0.
+	float alpha0;
+};
+
+/// Useful constant
+extern B2_API const b2Vec2 b2Vec2_zero;
+
+/// Perform the dot product on two vectors.
+inline float b2Dot(const b2Vec2& a, const b2Vec2& b)
+{
+	return a.x * b.x + a.y * b.y;
+}
+
+/// Perform the cross product on two vectors. In 2D this produces a scalar.
+inline float b2Cross(const b2Vec2& a, const b2Vec2& b)
+{
+	return a.x * b.y - a.y * b.x;
+}
+
+/// Perform the cross product on a vector and a scalar. In 2D this produces
+/// a vector.
+inline b2Vec2 b2Cross(const b2Vec2& a, float s)
+{
+	return b2Vec2(s * a.y, -s * a.x);
+}
+
+/// Perform the cross product on a scalar and a vector. In 2D this produces
+/// a vector.
+inline b2Vec2 b2Cross(float s, const b2Vec2& a)
+{
+	return b2Vec2(-s * a.y, s * a.x);
+}
+
+/// Multiply a matrix times a vector. If a rotation matrix is provided,
+/// then this transforms the vector from one frame to another.
+inline b2Vec2 b2Mul(const b2Mat22& A, const b2Vec2& v)
+{
+	return b2Vec2(A.ex.x * v.x + A.ey.x * v.y, A.ex.y * v.x + A.ey.y * v.y);
+}
+
+/// Multiply a matrix transpose times a vector. If a rotation matrix is provided,
+/// then this transforms the vector from one frame to another (inverse transform).
+inline b2Vec2 b2MulT(const b2Mat22& A, const b2Vec2& v)
+{
+	return b2Vec2(b2Dot(v, A.ex), b2Dot(v, A.ey));
+}
+
+/// Add two vectors component-wise.
+inline b2Vec2 operator + (const b2Vec2& a, const b2Vec2& b)
+{
+	return b2Vec2(a.x + b.x, a.y + b.y);
+}
+
+/// Subtract two vectors component-wise.
+inline b2Vec2 operator - (const b2Vec2& a, const b2Vec2& b)
+{
+	return b2Vec2(a.x - b.x, a.y - b.y);
+}
+
+inline b2Vec2 operator * (float s, const b2Vec2& a)
+{
+	return b2Vec2(s * a.x, s * a.y);
+}
+
+inline bool operator == (const b2Vec2& a, const b2Vec2& b)
+{
+	return a.x == b.x && a.y == b.y;
+}
+
+inline bool operator != (const b2Vec2& a, const b2Vec2& b)
+{
+	return a.x != b.x || a.y != b.y;
+}
+
+inline float b2Distance(const b2Vec2& a, const b2Vec2& b)
+{
+	b2Vec2 c = a - b;
+	return c.Length();
+}
+
+inline float b2DistanceSquared(const b2Vec2& a, const b2Vec2& b)
+{
+	b2Vec2 c = a - b;
+	return b2Dot(c, c);
+}
+
+inline b2Vec3 operator * (float s, const b2Vec3& a)
+{
+	return b2Vec3(s * a.x, s * a.y, s * a.z);
+}
+
+/// Add two vectors component-wise.
+inline b2Vec3 operator + (const b2Vec3& a, const b2Vec3& b)
+{
+	return b2Vec3(a.x + b.x, a.y + b.y, a.z + b.z);
+}
+
+/// Subtract two vectors component-wise.
+inline b2Vec3 operator - (const b2Vec3& a, const b2Vec3& b)
+{
+	return b2Vec3(a.x - b.x, a.y - b.y, a.z - b.z);
+}
+
+/// Perform the dot product on two vectors.
+inline float b2Dot(const b2Vec3& a, const b2Vec3& b)
+{
+	return a.x * b.x + a.y * b.y + a.z * b.z;
+}
+
+/// Perform the cross product on two vectors.
+inline b2Vec3 b2Cross(const b2Vec3& a, const b2Vec3& b)
+{
+	return b2Vec3(a.y * b.z - a.z * b.y, a.z * b.x - a.x * b.z, a.x * b.y - a.y * b.x);
+}
+
+inline b2Mat22 operator + (const b2Mat22& A, const b2Mat22& B)
+{
+	return b2Mat22(A.ex + B.ex, A.ey + B.ey);
+}
+
+// A * B
+inline b2Mat22 b2Mul(const b2Mat22& A, const b2Mat22& B)
+{
+	return b2Mat22(b2Mul(A, B.ex), b2Mul(A, B.ey));
+}
+
+// A^T * B
+inline b2Mat22 b2MulT(const b2Mat22& A, const b2Mat22& B)
+{
+	b2Vec2 c1(b2Dot(A.ex, B.ex), b2Dot(A.ey, B.ex));
+	b2Vec2 c2(b2Dot(A.ex, B.ey), b2Dot(A.ey, B.ey));
+	return b2Mat22(c1, c2);
+}
+
+/// Multiply a matrix times a vector.
+inline b2Vec3 b2Mul(const b2Mat33& A, const b2Vec3& v)
+{
+	return v.x * A.ex + v.y * A.ey + v.z * A.ez;
+}
+
+/// Multiply a matrix times a vector.
+inline b2Vec2 b2Mul22(const b2Mat33& A, const b2Vec2& v)
+{
+	return b2Vec2(A.ex.x * v.x + A.ey.x * v.y, A.ex.y * v.x + A.ey.y * v.y);
+}
+
+/// Multiply two rotations: q * r
+inline b2Rot b2Mul(const b2Rot& q, const b2Rot& r)
+{
+	// [qc -qs] * [rc -rs] = [qc*rc-qs*rs -qc*rs-qs*rc]
+	// [qs  qc]   [rs  rc]   [qs*rc+qc*rs -qs*rs+qc*rc]
+	// s = qs * rc + qc * rs
+	// c = qc * rc - qs * rs
+	b2Rot qr;
+	qr.s = q.s * r.c + q.c * r.s;
+	qr.c = q.c * r.c - q.s * r.s;
+	return qr;
+}
+
+/// Transpose multiply two rotations: qT * r
+inline b2Rot b2MulT(const b2Rot& q, const b2Rot& r)
+{
+	// [ qc qs] * [rc -rs] = [qc*rc+qs*rs -qc*rs+qs*rc]
+	// [-qs qc]   [rs  rc]   [-qs*rc+qc*rs qs*rs+qc*rc]
+	// s = qc * rs - qs * rc
+	// c = qc * rc + qs * rs
+	b2Rot qr;
+	qr.s = q.c * r.s - q.s * r.c;
+	qr.c = q.c * r.c + q.s * r.s;
+	return qr;
+}
+
+/// Rotate a vector
+inline b2Vec2 b2Mul(const b2Rot& q, const b2Vec2& v)
+{
+	return b2Vec2(q.c * v.x - q.s * v.y, q.s * v.x + q.c * v.y);
+}
+
+/// Inverse rotate a vector
+inline b2Vec2 b2MulT(const b2Rot& q, const b2Vec2& v)
+{
+	return b2Vec2(q.c * v.x + q.s * v.y, -q.s * v.x + q.c * v.y);
+}
+
+inline b2Vec2 b2Mul(const b2Transform& T, const b2Vec2& v)
+{
+	float x = (T.q.c * v.x - T.q.s * v.y) + T.p.x;
+	float y = (T.q.s * v.x + T.q.c * v.y) + T.p.y;
+
+	return b2Vec2(x, y);
+}
+
+inline b2Vec2 b2MulT(const b2Transform& T, const b2Vec2& v)
+{
+	float px = v.x - T.p.x;
+	float py = v.y - T.p.y;
+	float x = (T.q.c * px + T.q.s * py);
+	float y = (-T.q.s * px + T.q.c * py);
+
+	return b2Vec2(x, y);
+}
+
+// v2 = A.q.Rot(B.q.Rot(v1) + B.p) + A.p
+//    = (A.q * B.q).Rot(v1) + A.q.Rot(B.p) + A.p
+inline b2Transform b2Mul(const b2Transform& A, const b2Transform& B)
+{
+	b2Transform C;
+	C.q = b2Mul(A.q, B.q);
+	C.p = b2Mul(A.q, B.p) + A.p;
+	return C;
+}
+
+// v2 = A.q' * (B.q * v1 + B.p - A.p)
+//    = A.q' * B.q * v1 + A.q' * (B.p - A.p)
+inline b2Transform b2MulT(const b2Transform& A, const b2Transform& B)
+{
+	b2Transform C;
+	C.q = b2MulT(A.q, B.q);
+	C.p = b2MulT(A.q, B.p - A.p);
+	return C;
+}
+
+template <typename T>
+inline T b2Abs(T a)
+{
+	return a > T(0) ? a : -a;
+}
+
+inline b2Vec2 b2Abs(const b2Vec2& a)
+{
+	return b2Vec2(b2Abs(a.x), b2Abs(a.y));
+}
+
+inline b2Mat22 b2Abs(const b2Mat22& A)
+{
+	return b2Mat22(b2Abs(A.ex), b2Abs(A.ey));
+}
+
+template <typename T>
+inline T b2Min(T a, T b)
+{
+	return a < b ? a : b;
+}
+
+inline b2Vec2 b2Min(const b2Vec2& a, const b2Vec2& b)
+{
+	return b2Vec2(b2Min(a.x, b.x), b2Min(a.y, b.y));
+}
+
+template <typename T>
+inline T b2Max(T a, T b)
+{
+	return a > b ? a : b;
+}
+
+inline b2Vec2 b2Max(const b2Vec2& a, const b2Vec2& b)
+{
+	return b2Vec2(b2Max(a.x, b.x), b2Max(a.y, b.y));
+}
+
+template <typename T>
+inline T b2Clamp(T a, T low, T high)
+{
+	return b2Max(low, b2Min(a, high));
+}
+
+inline b2Vec2 b2Clamp(const b2Vec2& a, const b2Vec2& low, const b2Vec2& high)
+{
+	return b2Max(low, b2Min(a, high));
+}
+
+template<typename T> inline void b2Swap(T& a, T& b)
+{
+	T tmp = a;
+	a = b;
+	b = tmp;
+}
+
+/// "Next Largest Power of 2
+/// Given a binary integer value x, the next largest power of 2 can be computed by a SWAR algorithm
+/// that recursively "folds" the upper bits into the lower bits. This process yields a bit vector with
+/// the same most significant 1 as x, but all 1's below it. Adding 1 to that value yields the next
+/// largest power of 2. For a 32-bit value:"
+inline uint32 b2NextPowerOfTwo(uint32 x)
+{
+	x |= (x >> 1);
+	x |= (x >> 2);
+	x |= (x >> 4);
+	x |= (x >> 8);
+	x |= (x >> 16);
+	return x + 1;
+}
+
+inline bool b2IsPowerOfTwo(uint32 x)
+{
+	bool result = x > 0 && (x & (x - 1)) == 0;
+	return result;
+}
+
+// https://fgiesen.wordpress.com/2012/08/15/linear-interpolation-past-present-and-future/
+inline void b2Sweep::GetTransform(b2Transform* xf, float beta) const
+{
+	xf->p = (1.0f - beta) * c0 + beta * c;
+	float angle = (1.0f - beta) * a0 + beta * a;
+	xf->q.Set(angle);
+
+	// Shift to origin
+	xf->p -= b2Mul(xf->q, localCenter);
+}
+
+inline void b2Sweep::Advance(float alpha)
+{
+	b2Assert(alpha0 < 1.0f);
+	float beta = (alpha - alpha0) / (1.0f - alpha0);
+	c0 += beta * (c - c0);
+	a0 += beta * (a - a0);
+	alpha0 = alpha;
+}
+
+/// Normalize an angle in radians to be between -pi and pi
+inline void b2Sweep::Normalize()
+{
+	float twoPi = 2.0f * b2_pi;
+	float d =  twoPi * floorf(a0 / twoPi);
+	a0 -= d;
+	a -= d;
+}
+
+#endif

3rd/box2d/include/box2d/b2_motor_joint.h

@@ -0,0 +1,138 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#ifndef B2_MOTOR_JOINT_H
+#define B2_MOTOR_JOINT_H
+
+#include "b2_api.h"
+#include "b2_joint.h"
+
+/// Motor joint definition.
+struct B2_API b2MotorJointDef : public b2JointDef
+{
+	b2MotorJointDef()
+	{
+		type = e_motorJoint;
+		linearOffset.SetZero();
+		angularOffset = 0.0f;
+		maxForce = 1.0f;
+		maxTorque = 1.0f;
+		correctionFactor = 0.3f;
+	}
+
+	/// Initialize the bodies and offsets using the current transforms.
+	void Initialize(b2Body* bodyA, b2Body* bodyB);
+
+	/// Position of bodyB minus the position of bodyA, in bodyA's frame, in meters.
+	b2Vec2 linearOffset;
+
+	/// The bodyB angle minus bodyA angle in radians.
+	float angularOffset;
+
+	/// The maximum motor force in N.
+	float maxForce;
+
+	/// The maximum motor torque in N-m.
+	float maxTorque;
+
+	/// Position correction factor in the range [0,1].
+	float correctionFactor;
+};
+
+/// A motor joint is used to control the relative motion
+/// between two bodies. A typical usage is to control the movement
+/// of a dynamic body with respect to the ground.
+class B2_API b2MotorJoint : public b2Joint
+{
+public:
+	b2Vec2 GetAnchorA() const override;
+	b2Vec2 GetAnchorB() const override;
+
+	b2Vec2 GetReactionForce(float inv_dt) const override;
+	float GetReactionTorque(float inv_dt) const override;
+
+	/// Set/get the target linear offset, in frame A, in meters.
+	void SetLinearOffset(const b2Vec2& linearOffset);
+	const b2Vec2& GetLinearOffset() const;
+
+	/// Set/get the target angular offset, in radians.
+	void SetAngularOffset(float angularOffset);
+	float GetAngularOffset() const;
+
+	/// Set the maximum friction force in N.
+	void SetMaxForce(float force);
+
+	/// Get the maximum friction force in N.
+	float GetMaxForce() const;
+
+	/// Set the maximum friction torque in N*m.
+	void SetMaxTorque(float torque);
+
+	/// Get the maximum friction torque in N*m.
+	float GetMaxTorque() const;
+
+	/// Set the position correction factor in the range [0,1].
+	void SetCorrectionFactor(float factor);
+
+	/// Get the position correction factor in the range [0,1].
+	float GetCorrectionFactor() const;
+
+	/// Dump to b2Log
+	void Dump() override;
+
+protected:
+
+	friend class b2Joint;
+
+	b2MotorJoint(const b2MotorJointDef* def);
+
+	void InitVelocityConstraints(const b2SolverData& data) override;
+	void SolveVelocityConstraints(const b2SolverData& data) override;
+	bool SolvePositionConstraints(const b2SolverData& data) override;
+
+	// Solver shared
+	b2Vec2 m_linearOffset;
+	float m_angularOffset;
+	b2Vec2 m_linearImpulse;
+	float m_angularImpulse;
+	float m_maxForce;
+	float m_maxTorque;
+	float m_correctionFactor;
+
+	// Solver temp
+	int32 m_indexA;
+	int32 m_indexB;
+	b2Vec2 m_rA;
+	b2Vec2 m_rB;
+	b2Vec2 m_localCenterA;
+	b2Vec2 m_localCenterB;
+	b2Vec2 m_linearError;
+	float m_angularError;
+	float m_invMassA;
+	float m_invMassB;
+	float m_invIA;
+	float m_invIB;
+	b2Mat22 m_linearMass;
+	float m_angularMass;
+};
+
+#endif

3rd/box2d/include/box2d/b2_mouse_joint.h

@@ -0,0 +1,134 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#ifndef B2_MOUSE_JOINT_H
+#define B2_MOUSE_JOINT_H
+
+#include "b2_api.h"
+#include "b2_joint.h"
+
+/// Mouse joint definition. This requires a world target point,
+/// tuning parameters, and the time step.
+struct B2_API b2MouseJointDef : public b2JointDef
+{
+	b2MouseJointDef()
+	{
+		type = e_mouseJoint;
+		target.Set(0.0f, 0.0f);
+		maxForce = 0.0f;
+		stiffness = 0.0f;
+		damping = 0.0f;
+	}
+
+	/// The initial world target point. This is assumed
+	/// to coincide with the body anchor initially.
+	b2Vec2 target;
+
+	/// The maximum constraint force that can be exerted
+	/// to move the candidate body. Usually you will express
+	/// as some multiple of the weight (multiplier * mass * gravity).
+	float maxForce;
+
+	/// The linear stiffness in N/m
+	float stiffness;
+
+	/// The linear damping in N*s/m
+	float damping;
+};
+
+/// A mouse joint is used to make a point on a body track a
+/// specified world point. This a soft constraint with a maximum
+/// force. This allows the constraint to stretch and without
+/// applying huge forces.
+/// NOTE: this joint is not documented in the manual because it was
+/// developed to be used in the testbed. If you want to learn how to
+/// use the mouse joint, look at the testbed.
+class B2_API b2MouseJoint : public b2Joint
+{
+public:
+
+	/// Implements b2Joint.
+	b2Vec2 GetAnchorA() const override;
+
+	/// Implements b2Joint.
+	b2Vec2 GetAnchorB() const override;
+
+	/// Implements b2Joint.
+	b2Vec2 GetReactionForce(float inv_dt) const override;
+
+	/// Implements b2Joint.
+	float GetReactionTorque(float inv_dt) const override;
+
+	/// Use this to update the target point.
+	void SetTarget(const b2Vec2& target);
+	const b2Vec2& GetTarget() const;
+
+	/// Set/get the maximum force in Newtons.
+	void SetMaxForce(float force);
+	float GetMaxForce() const;
+
+	/// Set/get the linear stiffness in N/m
+	void SetStiffness(float stiffness) { m_stiffness = stiffness; }
+	float GetStiffness() const { return m_stiffness; }
+
+	/// Set/get linear damping in N*s/m
+	void SetDamping(float damping) { m_damping = damping; }
+	float GetDamping() const { return m_damping; }
+
+	/// The mouse joint does not support dumping.
+	void Dump() override { b2Log("Mouse joint dumping is not supported.\n"); }
+
+	/// Implement b2Joint::ShiftOrigin
+	void ShiftOrigin(const b2Vec2& newOrigin) override;
+
+protected:
+	friend class b2Joint;
+
+	b2MouseJoint(const b2MouseJointDef* def);
+
+	void InitVelocityConstraints(const b2SolverData& data) override;
+	void SolveVelocityConstraints(const b2SolverData& data) override;
+	bool SolvePositionConstraints(const b2SolverData& data) override;
+
+	b2Vec2 m_localAnchorB;
+	b2Vec2 m_targetA;
+	float m_stiffness;
+	float m_damping;
+	float m_beta;
+
+	// Solver shared
+	b2Vec2 m_impulse;
+	float m_maxForce;
+	float m_gamma;
+
+	// Solver temp
+	int32 m_indexA;
+	int32 m_indexB;
+	b2Vec2 m_rB;
+	b2Vec2 m_localCenterB;
+	float m_invMassB;
+	float m_invIB;
+	b2Mat22 m_mass;
+	b2Vec2 m_C;
+};
+
+#endif

3rd/box2d/include/box2d/b2_polygon_shape.h

@@ -0,0 +1,93 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+#ifndef B2_POLYGON_SHAPE_H
+#define B2_POLYGON_SHAPE_H
+
+#include "b2_api.h"
+#include "b2_shape.h"
+
+struct b2Hull;
+
+/// A solid convex polygon. It is assumed that the interior of the polygon is to
+/// the left of each edge.
+/// Polygons have a maximum number of vertices equal to b2_maxPolygonVertices.
+/// In most cases you should not need many vertices for a convex polygon.
+class B2_API b2PolygonShape : public b2Shape
+{
+public:
+	b2PolygonShape();
+
+	/// Implement b2Shape.
+	b2Shape* Clone(b2BlockAllocator* allocator) const override;
+
+	/// @see b2Shape::GetChildCount
+	int32 GetChildCount() const override;
+
+	/// Create a convex hull from the given array of local points.
+	/// The count must be in the range [3, b2_maxPolygonVertices].
+	/// @warning the points may be re-ordered, even if they form a convex polygon
+	/// @warning if this fails then the polygon is invalid
+	/// @returns true if valid
+	bool Set(const b2Vec2* points, int32 count);
+
+	/// Create a polygon from a given convex hull (see b2ComputeHull).
+	/// @warning the hull must be valid or this will crash or have unexpected behavior
+	void Set(const b2Hull& hull);
+
+	/// Build vertices to represent an axis-aligned box centered on the local origin.
+	/// @param hx the half-width.
+	/// @param hy the half-height.
+	void SetAsBox(float hx, float hy);
+
+	/// Build vertices to represent an oriented box.
+	/// @param hx the half-width.
+	/// @param hy the half-height.
+	/// @param center the center of the box in local coordinates.
+	/// @param angle the rotation of the box in local coordinates.
+	void SetAsBox(float hx, float hy, const b2Vec2& center, float angle);
+
+	/// @see b2Shape::TestPoint
+	bool TestPoint(const b2Transform& transform, const b2Vec2& p) const override;
+
+	/// Implement b2Shape.
+	/// @note because the polygon is solid, rays that start inside do not hit because the normal is
+	/// not defined.
+	bool RayCast(b2RayCastOutput* output, const b2RayCastInput& input,
+					const b2Transform& transform, int32 childIndex) const override;
+
+	/// @see b2Shape::ComputeAABB
+	void ComputeAABB(b2AABB* aabb, const b2Transform& transform, int32 childIndex) const override;
+
+	/// @see b2Shape::ComputeMass
+	void ComputeMass(b2MassData* massData, float density) const override;
+
+	/// Validate convexity. This is a very time consuming operation.
+	/// @returns true if valid
+	bool Validate() const;
+
+	b2Vec2 m_centroid;
+	b2Vec2 m_vertices[b2_maxPolygonVertices];
+	b2Vec2 m_normals[b2_maxPolygonVertices];
+	int32 m_count;
+};
+
+#endif

3rd/box2d/include/box2d/b2_prismatic_joint.h

@@ -0,0 +1,205 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#ifndef B2_PRISMATIC_JOINT_H
+#define B2_PRISMATIC_JOINT_H
+
+#include "b2_api.h"
+#include "b2_joint.h"
+
+/// Prismatic joint definition. This requires defining a line of
+/// motion using an axis and an anchor point. The definition uses local
+/// anchor points and a local axis so that the initial configuration
+/// can violate the constraint slightly. The joint translation is zero
+/// when the local anchor points coincide in world space. Using local
+/// anchors and a local axis helps when saving and loading a game.
+struct B2_API b2PrismaticJointDef : public b2JointDef
+{
+	b2PrismaticJointDef()
+	{
+		type = e_prismaticJoint;
+		localAnchorA.SetZero();
+		localAnchorB.SetZero();
+		localAxisA.Set(1.0f, 0.0f);
+		referenceAngle = 0.0f;
+		enableLimit = false;
+		lowerTranslation = 0.0f;
+		upperTranslation = 0.0f;
+		enableMotor = false;
+		maxMotorForce = 0.0f;
+		motorSpeed = 0.0f;
+	}
+
+	/// Initialize the bodies, anchors, axis, and reference angle using the world
+	/// anchor and unit world axis.
+	void Initialize(b2Body* bodyA, b2Body* bodyB, const b2Vec2& anchor, const b2Vec2& axis);
+
+	/// The local anchor point relative to bodyA's origin.
+	b2Vec2 localAnchorA;
+
+	/// The local anchor point relative to bodyB's origin.
+	b2Vec2 localAnchorB;
+
+	/// The local translation unit axis in bodyA.
+	b2Vec2 localAxisA;
+
+	/// The constrained angle between the bodies: bodyB_angle - bodyA_angle.
+	float referenceAngle;
+
+	/// Enable/disable the joint limit.
+	bool enableLimit;
+
+	/// The lower translation limit, usually in meters.
+	float lowerTranslation;
+
+	/// The upper translation limit, usually in meters.
+	float upperTranslation;
+
+	/// Enable/disable the joint motor.
+	bool enableMotor;
+
+	/// The maximum motor torque, usually in N-m.
+	float maxMotorForce;
+
+	/// The desired motor speed in radians per second.
+	float motorSpeed;
+};
+
+/// A prismatic joint. This joint provides one degree of freedom: translation
+/// along an axis fixed in bodyA. Relative rotation is prevented. You can
+/// use a joint limit to restrict the range of motion and a joint motor to
+/// drive the motion or to model joint friction.
+class B2_API b2PrismaticJoint : public b2Joint
+{
+public:
+	b2Vec2 GetAnchorA() const override;
+	b2Vec2 GetAnchorB() const override;
+
+	b2Vec2 GetReactionForce(float inv_dt) const override;
+	float GetReactionTorque(float inv_dt) const override;
+
+	/// The local anchor point relative to bodyA's origin.
+	const b2Vec2& GetLocalAnchorA() const { return m_localAnchorA; }
+
+	/// The local anchor point relative to bodyB's origin.
+	const b2Vec2& GetLocalAnchorB() const  { return m_localAnchorB; }
+
+	/// The local joint axis relative to bodyA.
+	const b2Vec2& GetLocalAxisA() const { return m_localXAxisA; }
+
+	/// Get the reference angle.
+	float GetReferenceAngle() const { return m_referenceAngle; }
+
+	/// Get the current joint translation, usually in meters.
+	float GetJointTranslation() const;
+
+	/// Get the current joint translation speed, usually in meters per second.
+	float GetJointSpeed() const;
+
+	/// Is the joint limit enabled?
+	bool IsLimitEnabled() const;
+
+	/// Enable/disable the joint limit.
+	void EnableLimit(bool flag);
+
+	/// Get the lower joint limit, usually in meters.
+	float GetLowerLimit() const;
+
+	/// Get the upper joint limit, usually in meters.
+	float GetUpperLimit() const;
+
+	/// Set the joint limits, usually in meters.
+	void SetLimits(float lower, float upper);
+
+	/// Is the joint motor enabled?
+	bool IsMotorEnabled() const;
+
+	/// Enable/disable the joint motor.
+	void EnableMotor(bool flag);
+
+	/// Set the motor speed, usually in meters per second.
+	void SetMotorSpeed(float speed);
+
+	/// Get the motor speed, usually in meters per second.
+	float GetMotorSpeed() const;
+
+	/// Set the maximum motor force, usually in N.
+	void SetMaxMotorForce(float force);
+	float GetMaxMotorForce() const { return m_maxMotorForce; }
+
+	/// Get the current motor force given the inverse time step, usually in N.
+	float GetMotorForce(float inv_dt) const;
+
+	/// Dump to b2Log
+	void Dump() override;
+
+	///
+	void Draw(b2Draw* draw) const override;
+
+protected:
+	friend class b2Joint;
+	friend class b2GearJoint;
+	b2PrismaticJoint(const b2PrismaticJointDef* def);
+
+	void InitVelocityConstraints(const b2SolverData& data) override;
+	void SolveVelocityConstraints(const b2SolverData& data) override;
+	bool SolvePositionConstraints(const b2SolverData& data) override;
+
+	b2Vec2 m_localAnchorA;
+	b2Vec2 m_localAnchorB;
+	b2Vec2 m_localXAxisA;
+	b2Vec2 m_localYAxisA;
+	float m_referenceAngle;
+	b2Vec2 m_impulse;
+	float m_motorImpulse;
+	float m_lowerImpulse;
+	float m_upperImpulse;
+	float m_lowerTranslation;
+	float m_upperTranslation;
+	float m_maxMotorForce;
+	float m_motorSpeed;
+	bool m_enableLimit;
+	bool m_enableMotor;
+
+	// Solver temp
+	int32 m_indexA;
+	int32 m_indexB;
+	b2Vec2 m_localCenterA;
+	b2Vec2 m_localCenterB;
+	float m_invMassA;
+	float m_invMassB;
+	float m_invIA;
+	float m_invIB;
+	b2Vec2 m_axis, m_perp;
+	float m_s1, m_s2;
+	float m_a1, m_a2;
+	b2Mat22 m_K;
+	float m_translation;
+	float m_axialMass;
+};
+
+inline float b2PrismaticJoint::GetMotorSpeed() const
+{
+	return m_motorSpeed;
+}
+
+#endif

3rd/box2d/include/box2d/b2_pulley_joint.h

@@ -0,0 +1,157 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#ifndef B2_PULLEY_JOINT_H
+#define B2_PULLEY_JOINT_H
+
+#include "b2_api.h"
+#include "b2_joint.h"
+
+const float b2_minPulleyLength = 2.0f;
+
+/// Pulley joint definition. This requires two ground anchors,
+/// two dynamic body anchor points, and a pulley ratio.
+struct B2_API b2PulleyJointDef : public b2JointDef
+{
+	b2PulleyJointDef()
+	{
+		type = e_pulleyJoint;
+		groundAnchorA.Set(-1.0f, 1.0f);
+		groundAnchorB.Set(1.0f, 1.0f);
+		localAnchorA.Set(-1.0f, 0.0f);
+		localAnchorB.Set(1.0f, 0.0f);
+		lengthA = 0.0f;
+		lengthB = 0.0f;
+		ratio = 1.0f;
+		collideConnected = true;
+	}
+
+	/// Initialize the bodies, anchors, lengths, max lengths, and ratio using the world anchors.
+	void Initialize(b2Body* bodyA, b2Body* bodyB,
+					const b2Vec2& groundAnchorA, const b2Vec2& groundAnchorB,
+					const b2Vec2& anchorA, const b2Vec2& anchorB,
+					float ratio);
+
+	/// The first ground anchor in world coordinates. This point never moves.
+	b2Vec2 groundAnchorA;
+
+	/// The second ground anchor in world coordinates. This point never moves.
+	b2Vec2 groundAnchorB;
+
+	/// The local anchor point relative to bodyA's origin.
+	b2Vec2 localAnchorA;
+
+	/// The local anchor point relative to bodyB's origin.
+	b2Vec2 localAnchorB;
+
+	/// The a reference length for the segment attached to bodyA.
+	float lengthA;
+
+	/// The a reference length for the segment attached to bodyB.
+	float lengthB;
+
+	/// The pulley ratio, used to simulate a block-and-tackle.
+	float ratio;
+};
+
+/// The pulley joint is connected to two bodies and two fixed ground points.
+/// The pulley supports a ratio such that:
+/// length1 + ratio * length2 <= constant
+/// Yes, the force transmitted is scaled by the ratio.
+/// Warning: the pulley joint can get a bit squirrelly by itself. They often
+/// work better when combined with prismatic joints. You should also cover the
+/// the anchor points with static shapes to prevent one side from going to
+/// zero length.
+class B2_API b2PulleyJoint : public b2Joint
+{
+public:
+	b2Vec2 GetAnchorA() const override;
+	b2Vec2 GetAnchorB() const override;
+
+	b2Vec2 GetReactionForce(float inv_dt) const override;
+	float GetReactionTorque(float inv_dt) const override;
+
+	/// Get the first ground anchor.
+	b2Vec2 GetGroundAnchorA() const;
+
+	/// Get the second ground anchor.
+	b2Vec2 GetGroundAnchorB() const;
+
+	/// Get the current length of the segment attached to bodyA.
+	float GetLengthA() const;
+
+	/// Get the current length of the segment attached to bodyB.
+	float GetLengthB() const;
+
+	/// Get the pulley ratio.
+	float GetRatio() const;
+
+	/// Get the current length of the segment attached to bodyA.
+	float GetCurrentLengthA() const;
+
+	/// Get the current length of the segment attached to bodyB.
+	float GetCurrentLengthB() const;
+
+	/// Dump joint to dmLog
+	void Dump() override;
+
+	/// Implement b2Joint::ShiftOrigin
+	void ShiftOrigin(const b2Vec2& newOrigin) override;
+
+protected:
+
+	friend class b2Joint;
+	b2PulleyJoint(const b2PulleyJointDef* data);
+
+	void InitVelocityConstraints(const b2SolverData& data) override;
+	void SolveVelocityConstraints(const b2SolverData& data) override;
+	bool SolvePositionConstraints(const b2SolverData& data) override;
+
+	b2Vec2 m_groundAnchorA;
+	b2Vec2 m_groundAnchorB;
+	float m_lengthA;
+	float m_lengthB;
+
+	// Solver shared
+	b2Vec2 m_localAnchorA;
+	b2Vec2 m_localAnchorB;
+	float m_constant;
+	float m_ratio;
+	float m_impulse;
+
+	// Solver temp
+	int32 m_indexA;
+	int32 m_indexB;
+	b2Vec2 m_uA;
+	b2Vec2 m_uB;
+	b2Vec2 m_rA;
+	b2Vec2 m_rB;
+	b2Vec2 m_localCenterA;
+	b2Vec2 m_localCenterB;
+	float m_invMassA;
+	float m_invMassB;
+	float m_invIA;
+	float m_invIB;
+	float m_mass;
+};
+
+#endif

3rd/box2d/include/box2d/b2_revolute_joint.h

@@ -0,0 +1,211 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#ifndef B2_REVOLUTE_JOINT_H
+#define B2_REVOLUTE_JOINT_H
+
+#include "b2_api.h"
+#include "b2_joint.h"
+
+/// Revolute joint definition. This requires defining an anchor point where the
+/// bodies are joined. The definition uses local anchor points so that the
+/// initial configuration can violate the constraint slightly. You also need to
+/// specify the initial relative angle for joint limits. This helps when saving
+/// and loading a game.
+/// The local anchor points are measured from the body's origin
+/// rather than the center of mass because:
+/// 1. you might not know where the center of mass will be.
+/// 2. if you add/remove shapes from a body and recompute the mass,
+///    the joints will be broken.
+struct B2_API b2RevoluteJointDef : public b2JointDef
+{
+	b2RevoluteJointDef()
+	{
+		type = e_revoluteJoint;
+		localAnchorA.Set(0.0f, 0.0f);
+		localAnchorB.Set(0.0f, 0.0f);
+		referenceAngle = 0.0f;
+		lowerAngle = 0.0f;
+		upperAngle = 0.0f;
+		maxMotorTorque = 0.0f;
+		motorSpeed = 0.0f;
+		enableLimit = false;
+		enableMotor = false;
+	}
+
+	/// Initialize the bodies, anchors, and reference angle using a world
+	/// anchor point.
+	void Initialize(b2Body* bodyA, b2Body* bodyB, const b2Vec2& anchor);
+
+	/// The local anchor point relative to bodyA's origin.
+	b2Vec2 localAnchorA;
+
+	/// The local anchor point relative to bodyB's origin.
+	b2Vec2 localAnchorB;
+
+	/// The bodyB angle minus bodyA angle in the reference state (radians).
+	float referenceAngle;
+
+	/// A flag to enable joint limits.
+	bool enableLimit;
+
+	/// The lower angle for the joint limit (radians).
+	float lowerAngle;
+
+	/// The upper angle for the joint limit (radians).
+	float upperAngle;
+
+	/// A flag to enable the joint motor.
+	bool enableMotor;
+
+	/// The desired motor speed. Usually in radians per second.
+	float motorSpeed;
+
+	/// The maximum motor torque used to achieve the desired motor speed.
+	/// Usually in N-m.
+	float maxMotorTorque;
+};
+
+/// A revolute joint constrains two bodies to share a common point while they
+/// are free to rotate about the point. The relative rotation about the shared
+/// point is the joint angle. You can limit the relative rotation with
+/// a joint limit that specifies a lower and upper angle. You can use a motor
+/// to drive the relative rotation about the shared point. A maximum motor torque
+/// is provided so that infinite forces are not generated.
+class B2_API b2RevoluteJoint : public b2Joint
+{
+public:
+	b2Vec2 GetAnchorA() const override;
+	b2Vec2 GetAnchorB() const override;
+
+	/// The local anchor point relative to bodyA's origin.
+	const b2Vec2& GetLocalAnchorA() const { return m_localAnchorA; }
+
+	/// The local anchor point relative to bodyB's origin.
+	const b2Vec2& GetLocalAnchorB() const  { return m_localAnchorB; }
+
+	/// Get the reference angle.
+	float GetReferenceAngle() const { return m_referenceAngle; }
+
+	/// Get the current joint angle in radians.
+	float GetJointAngle() const;
+
+	/// Get the current joint angle speed in radians per second.
+	float GetJointSpeed() const;
+
+	/// Is the joint limit enabled?
+	bool IsLimitEnabled() const;
+
+	/// Enable/disable the joint limit.
+	void EnableLimit(bool flag);
+
+	/// Get the lower joint limit in radians.
+	float GetLowerLimit() const;
+
+	/// Get the upper joint limit in radians.
+	float GetUpperLimit() const;
+
+	/// Set the joint limits in radians.
+	void SetLimits(float lower, float upper);
+
+	/// Is the joint motor enabled?
+	bool IsMotorEnabled() const;
+
+	/// Enable/disable the joint motor.
+	void EnableMotor(bool flag);
+
+	/// Set the motor speed in radians per second.
+	void SetMotorSpeed(float speed);
+
+	/// Get the motor speed in radians per second.
+	float GetMotorSpeed() const;
+
+	/// Set the maximum motor torque, usually in N-m.
+	void SetMaxMotorTorque(float torque);
+	float GetMaxMotorTorque() const { return m_maxMotorTorque; }
+
+	/// Get the reaction force given the inverse time step.
+	/// Unit is N.
+	b2Vec2 GetReactionForce(float inv_dt) const override;
+
+	/// Get the reaction torque due to the joint limit given the inverse time step.
+	/// Unit is N*m.
+	float GetReactionTorque(float inv_dt) const override;
+
+	/// Get the current motor torque given the inverse time step.
+	/// Unit is N*m.
+	float GetMotorTorque(float inv_dt) const;
+
+	/// Dump to b2Log.
+	void Dump() override;
+
+	///
+	void Draw(b2Draw* draw) const override;
+
+protected:
+
+	friend class b2Joint;
+	friend class b2GearJoint;
+
+	b2RevoluteJoint(const b2RevoluteJointDef* def);
+
+	void InitVelocityConstraints(const b2SolverData& data) override;
+	void SolveVelocityConstraints(const b2SolverData& data) override;
+	bool SolvePositionConstraints(const b2SolverData& data) override;
+
+	// Solver shared
+	b2Vec2 m_localAnchorA;
+	b2Vec2 m_localAnchorB;
+	b2Vec2 m_impulse;
+	float m_motorImpulse;
+	float m_lowerImpulse;
+	float m_upperImpulse;
+	bool m_enableMotor;
+	float m_maxMotorTorque;
+	float m_motorSpeed;
+	bool m_enableLimit;
+	float m_referenceAngle;
+	float m_lowerAngle;
+	float m_upperAngle;
+
+	// Solver temp
+	int32 m_indexA;
+	int32 m_indexB;
+	b2Vec2 m_rA;
+	b2Vec2 m_rB;
+	b2Vec2 m_localCenterA;
+	b2Vec2 m_localCenterB;
+	float m_invMassA;
+	float m_invMassB;
+	float m_invIA;
+	float m_invIB;
+	b2Mat22 m_K;
+	float m_angle;
+	float m_axialMass;
+};
+
+inline float b2RevoluteJoint::GetMotorSpeed() const
+{
+	return m_motorSpeed;
+}
+
+#endif

3rd/box2d/include/box2d/b2_rope.h

@@ -0,0 +1,155 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#ifndef B2_ROPE_H
+#define B2_ROPE_H
+
+#include "b2_api.h"
+#include "b2_math.h"
+
+class b2Draw;
+struct b2RopeStretch;
+struct b2RopeBend;
+
+enum b2StretchingModel
+{
+	b2_pbdStretchingModel,
+	b2_xpbdStretchingModel
+};
+
+enum b2BendingModel
+{
+	b2_springAngleBendingModel = 0,
+	b2_pbdAngleBendingModel,
+	b2_xpbdAngleBendingModel,
+	b2_pbdDistanceBendingModel,
+	b2_pbdHeightBendingModel,
+	b2_pbdTriangleBendingModel
+};
+
+///
+struct B2_API b2RopeTuning
+{
+	b2RopeTuning()
+	{
+		stretchingModel = b2_pbdStretchingModel;
+		bendingModel = b2_pbdAngleBendingModel;
+		damping = 0.0f;
+		stretchStiffness = 1.0f;
+		stretchHertz = 1.0f;
+		stretchDamping = 0.0f;
+		bendStiffness = 0.5f;
+		bendHertz = 1.0f;
+		bendDamping = 0.0f;
+		isometric = false;
+		fixedEffectiveMass = false;
+		warmStart = false;
+	}
+
+	b2StretchingModel stretchingModel;
+	b2BendingModel bendingModel;
+	float damping;
+	float stretchStiffness;
+	float stretchHertz;
+	float stretchDamping;
+	float bendStiffness;
+	float bendHertz;
+	float bendDamping;
+	bool isometric;
+	bool fixedEffectiveMass;
+	bool warmStart;
+};
+
+///
+struct B2_API b2RopeDef
+{
+	b2RopeDef()
+	{
+		position.SetZero();
+		vertices = nullptr;
+		count = 0;
+		masses = nullptr;
+		gravity.SetZero();
+	}
+
+	b2Vec2 position;
+	b2Vec2* vertices;
+	int32 count;
+	float* masses;
+	b2Vec2 gravity;
+	b2RopeTuning tuning;
+};
+
+///
+class B2_API b2Rope
+{
+public:
+	b2Rope();
+	~b2Rope();
+
+	///
+	void Create(const b2RopeDef& def);
+
+	///
+	void SetTuning(const b2RopeTuning& tuning);
+
+	///
+	void Step(float timeStep, int32 iterations, const b2Vec2& position);
+
+	///
+	void Reset(const b2Vec2& position);
+
+	///
+	void Draw(b2Draw* draw) const;
+
+private:
+
+	void SolveStretch_PBD();
+	void SolveStretch_XPBD(float dt);
+	void SolveBend_PBD_Angle();
+	void SolveBend_XPBD_Angle(float dt);
+	void SolveBend_PBD_Distance();
+	void SolveBend_PBD_Height();
+	void SolveBend_PBD_Triangle();
+	void ApplyBendForces(float dt);
+
+	b2Vec2 m_position;
+
+	int32 m_count;
+	int32 m_stretchCount;
+	int32 m_bendCount;
+
+	b2RopeStretch* m_stretchConstraints;
+	b2RopeBend* m_bendConstraints;
+
+	b2Vec2* m_bindPositions;
+	b2Vec2* m_ps;
+	b2Vec2* m_p0s;
+	b2Vec2* m_vs;
+
+	float* m_invMasses;
+	b2Vec2 m_gravity;
+
+	b2RopeTuning m_tuning;
+};
+
+#endif

3rd/box2d/include/box2d/b2_settings.h

@@ -0,0 +1,127 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#ifndef B2_SETTINGS_H
+#define B2_SETTINGS_H
+
+#include "b2_types.h"
+#include "b2_api.h"
+
+/// @file
+/// Settings that can be overriden for your application
+///
+
+/// Define this macro in your build if you want to override settings
+#ifdef B2_USER_SETTINGS
+
+/// This is a user file that includes custom definitions of the macros, structs, and functions
+/// defined below.
+#include "b2_user_settings.h"
+
+#else
+
+#include <stdarg.h>
+#include <stdint.h>
+
+// Tunable Constants
+
+/// You can use this to change the length scale used by your game.
+/// For example for inches you could use 39.4.
+#define b2_lengthUnitsPerMeter 1.0f
+
+/// The maximum number of vertices on a convex polygon. You cannot increase
+/// this too much because b2BlockAllocator has a maximum object size.
+#define b2_maxPolygonVertices	8
+
+// User data
+
+/// You can define this to inject whatever data you want in b2Body
+struct B2_API b2BodyUserData
+{
+	b2BodyUserData()
+	{
+		pointer = 0;
+	}
+
+	/// For legacy compatibility
+	uintptr_t pointer;
+};
+
+/// You can define this to inject whatever data you want in b2Fixture
+struct B2_API b2FixtureUserData
+{
+	b2FixtureUserData()
+	{
+		pointer = 0;
+	}
+
+	/// For legacy compatibility
+	uintptr_t pointer;
+};
+
+/// You can define this to inject whatever data you want in b2Joint
+struct B2_API b2JointUserData
+{
+	b2JointUserData()
+	{
+		pointer = 0;
+	}
+
+	/// For legacy compatibility
+	uintptr_t pointer;
+};
+
+// Memory Allocation
+
+/// Default allocation functions
+B2_API void* b2Alloc_Default(int32 size);
+B2_API void b2Free_Default(void* mem);
+
+/// Implement this function to use your own memory allocator.
+inline void* b2Alloc(int32 size)
+{
+	return b2Alloc_Default(size);
+}
+
+/// If you implement b2Alloc, you should also implement this function.
+inline void b2Free(void* mem)
+{
+	b2Free_Default(mem);
+}
+
+/// Default logging function
+B2_API void b2Log_Default(const char* string, va_list args);
+
+/// Implement this to use your own logging.
+inline void b2Log(const char* string, ...)
+{
+	va_list args;
+	va_start(args, string);
+	b2Log_Default(string, args);
+	va_end(args);
+}
+
+#endif // B2_USER_SETTINGS
+
+#include "b2_common.h"
+
+#endif

3rd/box2d/include/box2d/b2_shape.h

@@ -0,0 +1,110 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#ifndef B2_SHAPE_H
+#define B2_SHAPE_H
+
+#include "b2_api.h"
+#include "b2_math.h"
+#include "b2_collision.h"
+
+class b2BlockAllocator;
+
+/// This holds the mass data computed for a shape.
+struct B2_API b2MassData
+{
+	/// The mass of the shape, usually in kilograms.
+	float mass;
+
+	/// The position of the shape's centroid relative to the shape's origin.
+	b2Vec2 center;
+
+	/// The rotational inertia of the shape about the local origin.
+	float I;
+};
+
+/// A shape is used for collision detection. You can create a shape however you like.
+/// Shapes used for simulation in b2World are created automatically when a b2Fixture
+/// is created. Shapes may encapsulate a one or more child shapes.
+class B2_API b2Shape
+{
+public:
+
+	enum Type
+	{
+		e_circle = 0,
+		e_edge = 1,
+		e_polygon = 2,
+		e_chain = 3,
+		e_typeCount = 4
+	};
+
+	virtual ~b2Shape() {}
+
+	/// Clone the concrete shape using the provided allocator.
+	virtual b2Shape* Clone(b2BlockAllocator* allocator) const = 0;
+
+	/// Get the type of this shape. You can use this to down cast to the concrete shape.
+	/// @return the shape type.
+	Type GetType() const;
+
+	/// Get the number of child primitives.
+	virtual int32 GetChildCount() const = 0;
+
+	/// Test a point for containment in this shape. This only works for convex shapes.
+	/// @param xf the shape world transform.
+	/// @param p a point in world coordinates.
+	virtual bool TestPoint(const b2Transform& xf, const b2Vec2& p) const = 0;
+
+	/// Cast a ray against a child shape.
+	/// @param output the ray-cast results.
+	/// @param input the ray-cast input parameters.
+	/// @param transform the transform to be applied to the shape.
+	/// @param childIndex the child shape index
+	virtual bool RayCast(b2RayCastOutput* output, const b2RayCastInput& input,
+						const b2Transform& transform, int32 childIndex) const = 0;
+
+	/// Given a transform, compute the associated axis aligned bounding box for a child shape.
+	/// @param aabb returns the axis aligned box.
+	/// @param xf the world transform of the shape.
+	/// @param childIndex the child shape
+	virtual void ComputeAABB(b2AABB* aabb, const b2Transform& xf, int32 childIndex) const = 0;
+
+	/// Compute the mass properties of this shape using its dimensions and density.
+	/// The inertia tensor is computed about the local origin.
+	/// @param massData returns the mass data for this shape.
+	/// @param density the density in kilograms per meter squared.
+	virtual void ComputeMass(b2MassData* massData, float density) const = 0;
+
+	Type m_type;
+
+	/// Radius of a shape. For polygonal shapes this must be b2_polygonRadius. There is no support for
+	/// making rounded polygons.
+	float m_radius;
+};
+
+inline b2Shape::Type b2Shape::GetType() const
+{
+	return m_type;
+}
+
+#endif

3rd/box2d/include/box2d/b2_stack_allocator.h

@@ -0,0 +1,65 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#ifndef B2_STACK_ALLOCATOR_H
+#define B2_STACK_ALLOCATOR_H
+
+#include "b2_api.h"
+#include "b2_settings.h"
+
+const int32 b2_stackSize = 100 * 1024;	// 100k
+const int32 b2_maxStackEntries = 32;
+
+struct B2_API b2StackEntry
+{
+	char* data;
+	int32 size;
+	bool usedMalloc;
+};
+
+// This is a stack allocator used for fast per step allocations.
+// You must nest allocate/free pairs. The code will assert
+// if you try to interleave multiple allocate/free pairs.
+class B2_API b2StackAllocator
+{
+public:
+	b2StackAllocator();
+	~b2StackAllocator();
+
+	void* Allocate(int32 size);
+	void Free(void* p);
+
+	int32 GetMaxAllocation() const;
+
+private:
+
+	char m_data[b2_stackSize];
+	int32 m_index;
+
+	int32 m_allocation;
+	int32 m_maxAllocation;
+
+	b2StackEntry m_entries[b2_maxStackEntries];
+	int32 m_entryCount;
+};
+
+#endif

3rd/box2d/include/box2d/b2_time_of_impact.h

@@ -0,0 +1,63 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#ifndef B2_TIME_OF_IMPACT_H
+#define B2_TIME_OF_IMPACT_H
+
+#include "b2_api.h"
+#include "b2_math.h"
+#include "b2_distance.h"
+
+/// Input parameters for b2TimeOfImpact
+struct B2_API b2TOIInput
+{
+	b2DistanceProxy proxyA;
+	b2DistanceProxy proxyB;
+	b2Sweep sweepA;
+	b2Sweep sweepB;
+	float tMax;		// defines sweep interval [0, tMax]
+};
+
+/// Output parameters for b2TimeOfImpact.
+struct B2_API b2TOIOutput
+{
+	enum State
+	{
+		e_unknown,
+		e_failed,
+		e_overlapped,
+		e_touching,
+		e_separated
+	};
+
+	State state;
+	float t;
+};
+
+/// Compute the upper bound on time before two shapes penetrate. Time is represented as
+/// a fraction between [0,tMax]. This uses a swept separating axis and may miss some intermediate,
+/// non-tunneling collisions. If you change the time interval, you should call this function
+/// again.
+/// Note: use b2Distance to compute the contact point and normal at the time of impact.
+B2_API void b2TimeOfImpact(b2TOIOutput* output, const b2TOIInput* input);
+
+#endif

3rd/box2d/include/box2d/b2_time_step.h

@@ -0,0 +1,74 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+#ifndef B2_TIME_STEP_H
+#define B2_TIME_STEP_H
+
+#include "b2_api.h"
+#include "b2_math.h"
+
+/// Profiling data. Times are in milliseconds.
+struct B2_API b2Profile
+{
+	float step;
+	float collide;
+	float solve;
+	float solveInit;
+	float solveVelocity;
+	float solvePosition;
+	float broadphase;
+	float solveTOI;
+};
+
+/// This is an internal structure.
+struct B2_API b2TimeStep
+{
+	float dt;			// time step
+	float inv_dt;		// inverse time step (0 if dt == 0).
+	float dtRatio;	// dt * inv_dt0
+	int32 velocityIterations;
+	int32 positionIterations;
+	bool warmStarting;
+};
+
+/// This is an internal structure.
+struct B2_API b2Position
+{
+	b2Vec2 c;
+	float a;
+};
+
+/// This is an internal structure.
+struct B2_API b2Velocity
+{
+	b2Vec2 v;
+	float w;
+};
+
+/// Solver Data
+struct B2_API b2SolverData
+{
+	b2TimeStep step;
+	b2Position* positions;
+	b2Velocity* velocities;
+};
+
+#endif

3rd/box2d/include/box2d/b2_timer.h

@@ -0,0 +1,55 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#ifndef B2_TIMER_H
+#define B2_TIMER_H
+
+#include "b2_api.h"
+#include "b2_settings.h"
+
+/// Timer for profiling. This has platform specific code and may
+/// not work on every platform.
+class B2_API b2Timer
+{
+public:
+
+	/// Constructor
+	b2Timer();
+
+	/// Reset the timer.
+	void Reset();
+
+	/// Get the time since construction or the last reset.
+	float GetMilliseconds() const;
+
+private:
+
+#if defined(_WIN32)
+	double m_start;
+	static double s_invFrequency;
+#elif defined(__linux__) || defined (__APPLE__)
+	unsigned long long m_start_sec;
+	unsigned long long m_start_usec;
+#endif
+};
+
+#endif

3rd/box2d/include/box2d/b2_types.h

@@ -0,0 +1,33 @@
+// MIT License
+
+// Copyright (c) 2020 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#ifndef B2_TYPES_H
+#define B2_TYPES_H
+
+typedef signed char	int8;
+typedef signed short int16;
+typedef signed int int32;
+typedef unsigned char uint8;
+typedef unsigned short uint16;
+typedef unsigned int uint32;
+
+#endif

3rd/box2d/include/box2d/b2_weld_joint.h

@@ -0,0 +1,133 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#ifndef B2_WELD_JOINT_H
+#define B2_WELD_JOINT_H
+
+#include "b2_api.h"
+#include "b2_joint.h"
+
+/// Weld joint definition. You need to specify local anchor points
+/// where they are attached and the relative body angle. The position
+/// of the anchor points is important for computing the reaction torque.
+struct B2_API b2WeldJointDef : public b2JointDef
+{
+	b2WeldJointDef()
+	{
+		type = e_weldJoint;
+		localAnchorA.Set(0.0f, 0.0f);
+		localAnchorB.Set(0.0f, 0.0f);
+		referenceAngle = 0.0f;
+		stiffness = 0.0f;
+		damping = 0.0f;
+	}
+
+	/// Initialize the bodies, anchors, reference angle, stiffness, and damping.
+	/// @param bodyA the first body connected by this joint
+	/// @param bodyB the second body connected by this joint
+	/// @param anchor the point of connection in world coordinates
+	void Initialize(b2Body* bodyA, b2Body* bodyB, const b2Vec2& anchor);
+
+	/// The local anchor point relative to bodyA's origin.
+	b2Vec2 localAnchorA;
+
+	/// The local anchor point relative to bodyB's origin.
+	b2Vec2 localAnchorB;
+
+	/// The bodyB angle minus bodyA angle in the reference state (radians).
+	float referenceAngle;
+
+	/// The rotational stiffness in N*m
+	/// Disable softness with a value of 0
+	float stiffness;
+
+	/// The rotational damping in N*m*s
+	float damping;
+};
+
+/// A weld joint essentially glues two bodies together. A weld joint may
+/// distort somewhat because the island constraint solver is approximate.
+class B2_API b2WeldJoint : public b2Joint
+{
+public:
+	b2Vec2 GetAnchorA() const override;
+	b2Vec2 GetAnchorB() const override;
+
+	b2Vec2 GetReactionForce(float inv_dt) const override;
+	float GetReactionTorque(float inv_dt) const override;
+
+	/// The local anchor point relative to bodyA's origin.
+	const b2Vec2& GetLocalAnchorA() const { return m_localAnchorA; }
+
+	/// The local anchor point relative to bodyB's origin.
+	const b2Vec2& GetLocalAnchorB() const  { return m_localAnchorB; }
+
+	/// Get the reference angle.
+	float GetReferenceAngle() const { return m_referenceAngle; }
+
+	/// Set/get stiffness in N*m
+	void SetStiffness(float stiffness) { m_stiffness = stiffness; }
+	float GetStiffness() const { return m_stiffness; }
+
+	/// Set/get damping in N*m*s
+	void SetDamping(float damping) { m_damping = damping; }
+	float GetDamping() const { return m_damping; }
+
+	/// Dump to b2Log
+	void Dump() override;
+
+protected:
+
+	friend class b2Joint;
+
+	b2WeldJoint(const b2WeldJointDef* def);
+
+	void InitVelocityConstraints(const b2SolverData& data) override;
+	void SolveVelocityConstraints(const b2SolverData& data) override;
+	bool SolvePositionConstraints(const b2SolverData& data) override;
+
+	float m_stiffness;
+	float m_damping;
+	float m_bias;
+
+	// Solver shared
+	b2Vec2 m_localAnchorA;
+	b2Vec2 m_localAnchorB;
+	float m_referenceAngle;
+	float m_gamma;
+	b2Vec3 m_impulse;
+
+	// Solver temp
+	int32 m_indexA;
+	int32 m_indexB;
+	b2Vec2 m_rA;
+	b2Vec2 m_rB;
+	b2Vec2 m_localCenterA;
+	b2Vec2 m_localCenterB;
+	float m_invMassA;
+	float m_invMassB;
+	float m_invIA;
+	float m_invIB;
+	b2Mat33 m_mass;
+};
+
+#endif

3rd/box2d/include/box2d/b2_wheel_joint.h

@@ -0,0 +1,240 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#ifndef B2_WHEEL_JOINT_H
+#define B2_WHEEL_JOINT_H
+
+#include "b2_api.h"
+#include "b2_joint.h"
+
+/// Wheel joint definition. This requires defining a line of
+/// motion using an axis and an anchor point. The definition uses local
+/// anchor points and a local axis so that the initial configuration
+/// can violate the constraint slightly. The joint translation is zero
+/// when the local anchor points coincide in world space. Using local
+/// anchors and a local axis helps when saving and loading a game.
+struct B2_API b2WheelJointDef : public b2JointDef
+{
+	b2WheelJointDef()
+	{
+		type = e_wheelJoint;
+		localAnchorA.SetZero();
+		localAnchorB.SetZero();
+		localAxisA.Set(1.0f, 0.0f);
+		enableLimit = false;
+		lowerTranslation = 0.0f;
+		upperTranslation = 0.0f;
+		enableMotor = false;
+		maxMotorTorque = 0.0f;
+		motorSpeed = 0.0f;
+		stiffness = 0.0f;
+		damping = 0.0f;
+	}
+
+	/// Initialize the bodies, anchors, axis, and reference angle using the world
+	/// anchor and world axis.
+	void Initialize(b2Body* bodyA, b2Body* bodyB, const b2Vec2& anchor, const b2Vec2& axis);
+
+	/// The local anchor point relative to bodyA's origin.
+	b2Vec2 localAnchorA;
+
+	/// The local anchor point relative to bodyB's origin.
+	b2Vec2 localAnchorB;
+
+	/// The local translation axis in bodyA.
+	b2Vec2 localAxisA;
+
+	/// Enable/disable the joint limit.
+	bool enableLimit;
+
+	/// The lower translation limit, usually in meters.
+	float lowerTranslation;
+
+	/// The upper translation limit, usually in meters.
+	float upperTranslation;
+
+	/// Enable/disable the joint motor.
+	bool enableMotor;
+
+	/// The maximum motor torque, usually in N-m.
+	float maxMotorTorque;
+
+	/// The desired motor speed in radians per second.
+	float motorSpeed;
+
+	/// Suspension stiffness. Typically in units N/m.
+	float stiffness;
+
+	/// Suspension damping. Typically in units of N*s/m.
+	float damping;
+};
+
+/// A wheel joint. This joint provides two degrees of freedom: translation
+/// along an axis fixed in bodyA and rotation in the plane. In other words, it is a point to
+/// line constraint with a rotational motor and a linear spring/damper. The spring/damper is
+/// initialized upon creation. This joint is designed for vehicle suspensions.
+class B2_API b2WheelJoint : public b2Joint
+{
+public:
+	b2Vec2 GetAnchorA() const override;
+	b2Vec2 GetAnchorB() const override;
+
+	b2Vec2 GetReactionForce(float inv_dt) const override;
+	float GetReactionTorque(float inv_dt) const override;
+
+	/// The local anchor point relative to bodyA's origin.
+	const b2Vec2& GetLocalAnchorA() const { return m_localAnchorA; }
+
+	/// The local anchor point relative to bodyB's origin.
+	const b2Vec2& GetLocalAnchorB() const  { return m_localAnchorB; }
+
+	/// The local joint axis relative to bodyA.
+	const b2Vec2& GetLocalAxisA() const { return m_localXAxisA; }
+
+	/// Get the current joint translation, usually in meters.
+	float GetJointTranslation() const;
+
+	/// Get the current joint linear speed, usually in meters per second.
+	float GetJointLinearSpeed() const;
+
+	/// Get the current joint angle in radians.
+	float GetJointAngle() const;
+
+	/// Get the current joint angular speed in radians per second.
+	float GetJointAngularSpeed() const;
+
+	/// Is the joint limit enabled?
+	bool IsLimitEnabled() const;
+
+	/// Enable/disable the joint translation limit.
+	void EnableLimit(bool flag);
+
+	/// Get the lower joint translation limit, usually in meters.
+	float GetLowerLimit() const;
+
+	/// Get the upper joint translation limit, usually in meters.
+	float GetUpperLimit() const;
+
+	/// Set the joint translation limits, usually in meters.
+	void SetLimits(float lower, float upper);
+
+	/// Is the joint motor enabled?
+	bool IsMotorEnabled() const;
+
+	/// Enable/disable the joint motor.
+	void EnableMotor(bool flag);
+
+	/// Set the motor speed, usually in radians per second.
+	void SetMotorSpeed(float speed);
+
+	/// Get the motor speed, usually in radians per second.
+	float GetMotorSpeed() const;
+
+	/// Set/Get the maximum motor force, usually in N-m.
+	void SetMaxMotorTorque(float torque);
+	float GetMaxMotorTorque() const;
+
+	/// Get the current motor torque given the inverse time step, usually in N-m.
+	float GetMotorTorque(float inv_dt) const;
+
+	/// Access spring stiffness
+	void SetStiffness(float stiffness);
+	float GetStiffness() const;
+
+	/// Access damping
+	void SetDamping(float damping);
+	float GetDamping() const;
+
+	/// Dump to b2Log
+	void Dump() override;
+
+	///
+	void Draw(b2Draw* draw) const override;
+
+protected:
+
+	friend class b2Joint;
+	b2WheelJoint(const b2WheelJointDef* def);
+
+	void InitVelocityConstraints(const b2SolverData& data) override;
+	void SolveVelocityConstraints(const b2SolverData& data) override;
+	bool SolvePositionConstraints(const b2SolverData& data) override;
+
+	b2Vec2 m_localAnchorA;
+	b2Vec2 m_localAnchorB;
+	b2Vec2 m_localXAxisA;
+	b2Vec2 m_localYAxisA;
+
+	float m_impulse;
+	float m_motorImpulse;
+	float m_springImpulse;
+
+	float m_lowerImpulse;
+	float m_upperImpulse;
+	float m_translation;
+	float m_lowerTranslation;
+	float m_upperTranslation;
+
+	float m_maxMotorTorque;
+	float m_motorSpeed;
+
+	bool m_enableLimit;
+	bool m_enableMotor;
+
+	float m_stiffness;
+	float m_damping;
+
+	// Solver temp
+	int32 m_indexA;
+	int32 m_indexB;
+	b2Vec2 m_localCenterA;
+	b2Vec2 m_localCenterB;
+	float m_invMassA;
+	float m_invMassB;
+	float m_invIA;
+	float m_invIB;
+
+	b2Vec2 m_ax, m_ay;
+	float m_sAx, m_sBx;
+	float m_sAy, m_sBy;
+
+	float m_mass;
+	float m_motorMass;
+	float m_axialMass;
+	float m_springMass;
+
+	float m_bias;
+	float m_gamma;
+
+};
+
+inline float b2WheelJoint::GetMotorSpeed() const
+{
+	return m_motorSpeed;
+}
+
+inline float b2WheelJoint::GetMaxMotorTorque() const
+{
+	return m_maxMotorTorque;
+}
+
+#endif

3rd/box2d/include/box2d/b2_world.h

@@ -0,0 +1,348 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#ifndef B2_WORLD_H
+#define B2_WORLD_H
+
+#include "b2_api.h"
+#include "b2_block_allocator.h"
+#include "b2_contact_manager.h"
+#include "b2_math.h"
+#include "b2_stack_allocator.h"
+#include "b2_time_step.h"
+#include "b2_world_callbacks.h"
+
+struct b2AABB;
+struct b2BodyDef;
+struct b2Color;
+struct b2JointDef;
+class b2Body;
+class b2Draw;
+class b2Fixture;
+class b2Joint;
+
+/// The world class manages all physics entities, dynamic simulation,
+/// and asynchronous queries. The world also contains efficient memory
+/// management facilities.
+class B2_API b2World
+{
+public:
+	/// Construct a world object.
+	/// @param gravity the world gravity vector.
+	b2World(const b2Vec2& gravity);
+
+	/// Destruct the world. All physics entities are destroyed and all heap memory is released.
+	~b2World();
+
+	/// Register a destruction listener. The listener is owned by you and must
+	/// remain in scope.
+	void SetDestructionListener(b2DestructionListener* listener);
+
+	/// Register a contact filter to provide specific control over collision.
+	/// Otherwise the default filter is used (b2_defaultFilter). The listener is
+	/// owned by you and must remain in scope.
+	void SetContactFilter(b2ContactFilter* filter);
+
+	/// Register a contact event listener. The listener is owned by you and must
+	/// remain in scope.
+	void SetContactListener(b2ContactListener* listener);
+
+	/// Register a routine for debug drawing. The debug draw functions are called
+	/// inside with b2World::DebugDraw method. The debug draw object is owned
+	/// by you and must remain in scope.
+	void SetDebugDraw(b2Draw* debugDraw);
+
+	/// Create a rigid body given a definition. No reference to the definition
+	/// is retained.
+	/// @warning This function is locked during callbacks.
+	b2Body* CreateBody(const b2BodyDef* def);
+
+	/// Destroy a rigid body given a definition. No reference to the definition
+	/// is retained. This function is locked during callbacks.
+	/// @warning This automatically deletes all associated shapes and joints.
+	/// @warning This function is locked during callbacks.
+	void DestroyBody(b2Body* body);
+
+	/// Create a joint to constrain bodies together. No reference to the definition
+	/// is retained. This may cause the connected bodies to cease colliding.
+	/// @warning This function is locked during callbacks.
+	b2Joint* CreateJoint(const b2JointDef* def);
+
+	/// Destroy a joint. This may cause the connected bodies to begin colliding.
+	/// @warning This function is locked during callbacks.
+	void DestroyJoint(b2Joint* joint);
+
+	/// Take a time step. This performs collision detection, integration,
+	/// and constraint solution.
+	/// @param timeStep the amount of time to simulate, this should not vary.
+	/// @param velocityIterations for the velocity constraint solver.
+	/// @param positionIterations for the position constraint solver.
+	void Step(	float timeStep,
+				int32 velocityIterations,
+				int32 positionIterations);
+
+	/// Manually clear the force buffer on all bodies. By default, forces are cleared automatically
+	/// after each call to Step. The default behavior is modified by calling SetAutoClearForces.
+	/// The purpose of this function is to support sub-stepping. Sub-stepping is often used to maintain
+	/// a fixed sized time step under a variable frame-rate.
+	/// When you perform sub-stepping you will disable auto clearing of forces and instead call
+	/// ClearForces after all sub-steps are complete in one pass of your game loop.
+	/// @see SetAutoClearForces
+	void ClearForces();
+
+	/// Call this to draw shapes and other debug draw data. This is intentionally non-const.
+	void DebugDraw();
+
+	/// Query the world for all fixtures that potentially overlap the
+	/// provided AABB.
+	/// @param callback a user implemented callback class.
+	/// @param aabb the query box.
+	void QueryAABB(b2QueryCallback* callback, const b2AABB& aabb) const;
+
+	/// Ray-cast the world for all fixtures in the path of the ray. Your callback
+	/// controls whether you get the closest point, any point, or n-points.
+	/// The ray-cast ignores shapes that contain the starting point.
+	/// @param callback a user implemented callback class.
+	/// @param point1 the ray starting point
+	/// @param point2 the ray ending point
+	void RayCast(b2RayCastCallback* callback, const b2Vec2& point1, const b2Vec2& point2) const;
+
+	/// Get the world body list. With the returned body, use b2Body::GetNext to get
+	/// the next body in the world list. A nullptr body indicates the end of the list.
+	/// @return the head of the world body list.
+	b2Body* GetBodyList();
+	const b2Body* GetBodyList() const;
+
+	/// Get the world joint list. With the returned joint, use b2Joint::GetNext to get
+	/// the next joint in the world list. A nullptr joint indicates the end of the list.
+	/// @return the head of the world joint list.
+	b2Joint* GetJointList();
+	const b2Joint* GetJointList() const;
+
+	/// Get the world contact list. With the returned contact, use b2Contact::GetNext to get
+	/// the next contact in the world list. A nullptr contact indicates the end of the list.
+	/// @return the head of the world contact list.
+	/// @warning contacts are created and destroyed in the middle of a time step.
+	/// Use b2ContactListener to avoid missing contacts.
+	b2Contact* GetContactList();
+	const b2Contact* GetContactList() const;
+
+	/// Enable/disable sleep.
+	void SetAllowSleeping(bool flag);
+	bool GetAllowSleeping() const { return m_allowSleep; }
+
+	/// Enable/disable warm starting. For testing.
+	void SetWarmStarting(bool flag) { m_warmStarting = flag; }
+	bool GetWarmStarting() const { return m_warmStarting; }
+
+	/// Enable/disable continuous physics. For testing.
+	void SetContinuousPhysics(bool flag) { m_continuousPhysics = flag; }
+	bool GetContinuousPhysics() const { return m_continuousPhysics; }
+
+	/// Enable/disable single stepped continuous physics. For testing.
+	void SetSubStepping(bool flag) { m_subStepping = flag; }
+	bool GetSubStepping() const { return m_subStepping; }
+
+	/// Get the number of broad-phase proxies.
+	int32 GetProxyCount() const;
+
+	/// Get the number of bodies.
+	int32 GetBodyCount() const;
+
+	/// Get the number of joints.
+	int32 GetJointCount() const;
+
+	/// Get the number of contacts (each may have 0 or more contact points).
+	int32 GetContactCount() const;
+
+	/// Get the height of the dynamic tree.
+	int32 GetTreeHeight() const;
+
+	/// Get the balance of the dynamic tree.
+	int32 GetTreeBalance() const;
+
+	/// Get the quality metric of the dynamic tree. The smaller the better.
+	/// The minimum is 1.
+	float GetTreeQuality() const;
+
+	/// Change the global gravity vector.
+	void SetGravity(const b2Vec2& gravity);
+
+	/// Get the global gravity vector.
+	b2Vec2 GetGravity() const;
+
+	/// Is the world locked (in the middle of a time step).
+	bool IsLocked() const;
+
+	/// Set flag to control automatic clearing of forces after each time step.
+	void SetAutoClearForces(bool flag);
+
+	/// Get the flag that controls automatic clearing of forces after each time step.
+	bool GetAutoClearForces() const;
+
+	/// Shift the world origin. Useful for large worlds.
+	/// The body shift formula is: position -= newOrigin
+	/// @param newOrigin the new origin with respect to the old origin
+	void ShiftOrigin(const b2Vec2& newOrigin);
+
+	/// Get the contact manager for testing.
+	const b2ContactManager& GetContactManager() const;
+
+	/// Get the current profile.
+	const b2Profile& GetProfile() const;
+
+	/// Dump the world into the log file.
+	/// @warning this should be called outside of a time step.
+	void Dump();
+
+private:
+
+	friend class b2Body;
+	friend class b2Fixture;
+	friend class b2ContactManager;
+	friend class b2Controller;
+
+	b2World(const b2World&) = delete;
+	void operator=(const b2World&) = delete;
+
+	void Solve(const b2TimeStep& step);
+	void SolveTOI(const b2TimeStep& step);
+
+	void DrawShape(b2Fixture* shape, const b2Transform& xf, const b2Color& color);
+
+	b2BlockAllocator m_blockAllocator;
+	b2StackAllocator m_stackAllocator;
+
+	b2ContactManager m_contactManager;
+
+	b2Body* m_bodyList;
+	b2Joint* m_jointList;
+
+	int32 m_bodyCount;
+	int32 m_jointCount;
+
+	b2Vec2 m_gravity;
+	bool m_allowSleep;
+
+	b2DestructionListener* m_destructionListener;
+	b2Draw* m_debugDraw;
+
+	// This is used to compute the time step ratio to
+	// support a variable time step.
+	float m_inv_dt0;
+
+	bool m_newContacts;
+	bool m_locked;
+	bool m_clearForces;
+
+	// These are for debugging the solver.
+	bool m_warmStarting;
+	bool m_continuousPhysics;
+	bool m_subStepping;
+
+	bool m_stepComplete;
+
+	b2Profile m_profile;
+};
+
+inline b2Body* b2World::GetBodyList()
+{
+	return m_bodyList;
+}
+
+inline const b2Body* b2World::GetBodyList() const
+{
+	return m_bodyList;
+}
+
+inline b2Joint* b2World::GetJointList()
+{
+	return m_jointList;
+}
+
+inline const b2Joint* b2World::GetJointList() const
+{
+	return m_jointList;
+}
+
+inline b2Contact* b2World::GetContactList()
+{
+	return m_contactManager.m_contactList;
+}
+
+inline const b2Contact* b2World::GetContactList() const
+{
+	return m_contactManager.m_contactList;
+}
+
+inline int32 b2World::GetBodyCount() const
+{
+	return m_bodyCount;
+}
+
+inline int32 b2World::GetJointCount() const
+{
+	return m_jointCount;
+}
+
+inline int32 b2World::GetContactCount() const
+{
+	return m_contactManager.m_contactCount;
+}
+
+inline void b2World::SetGravity(const b2Vec2& gravity)
+{
+	m_gravity = gravity;
+}
+
+inline b2Vec2 b2World::GetGravity() const
+{
+	return m_gravity;
+}
+
+inline bool b2World::IsLocked() const
+{
+	return m_locked;
+}
+
+inline void b2World::SetAutoClearForces(bool flag)
+{
+	m_clearForces = flag;
+}
+
+/// Get the flag that controls automatic clearing of forces after each time step.
+inline bool b2World::GetAutoClearForces() const
+{
+	return m_clearForces;
+}
+
+inline const b2ContactManager& b2World::GetContactManager() const
+{
+	return m_contactManager;
+}
+
+inline const b2Profile& b2World::GetProfile() const
+{
+	return m_profile;
+}
+
+#endif

3rd/box2d/include/box2d/b2_world_callbacks.h

@@ -0,0 +1,161 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#ifndef B2_WORLD_CALLBACKS_H
+#define B2_WORLD_CALLBACKS_H
+
+#include "b2_api.h"
+#include "b2_settings.h"
+
+struct b2Vec2;
+struct b2Transform;
+class b2Fixture;
+class b2Body;
+class b2Joint;
+class b2Contact;
+struct b2ContactResult;
+struct b2Manifold;
+
+/// Joints and fixtures are destroyed when their associated
+/// body is destroyed. Implement this listener so that you
+/// may nullify references to these joints and shapes.
+class B2_API b2DestructionListener
+{
+public:
+	virtual ~b2DestructionListener() {}
+
+	/// Called when any joint is about to be destroyed due
+	/// to the destruction of one of its attached bodies.
+	virtual void SayGoodbye(b2Joint* joint) = 0;
+
+	/// Called when any fixture is about to be destroyed due
+	/// to the destruction of its parent body.
+	virtual void SayGoodbye(b2Fixture* fixture) = 0;
+};
+
+/// Implement this class to provide collision filtering. In other words, you can implement
+/// this class if you want finer control over contact creation.
+class B2_API b2ContactFilter
+{
+public:
+	virtual ~b2ContactFilter() {}
+
+	/// Return true if contact calculations should be performed between these two shapes.
+	/// @warning for performance reasons this is only called when the AABBs begin to overlap.
+	virtual bool ShouldCollide(b2Fixture* fixtureA, b2Fixture* fixtureB);
+};
+
+/// Contact impulses for reporting. Impulses are used instead of forces because
+/// sub-step forces may approach infinity for rigid body collisions. These
+/// match up one-to-one with the contact points in b2Manifold.
+struct B2_API b2ContactImpulse
+{
+	float normalImpulses[b2_maxManifoldPoints];
+	float tangentImpulses[b2_maxManifoldPoints];
+	int32 count;
+};
+
+/// Implement this class to get contact information. You can use these results for
+/// things like sounds and game logic. You can also get contact results by
+/// traversing the contact lists after the time step. However, you might miss
+/// some contacts because continuous physics leads to sub-stepping.
+/// Additionally you may receive multiple callbacks for the same contact in a
+/// single time step.
+/// You should strive to make your callbacks efficient because there may be
+/// many callbacks per time step.
+/// @warning You cannot create/destroy Box2D entities inside these callbacks.
+class B2_API b2ContactListener
+{
+public:
+	virtual ~b2ContactListener() {}
+
+	/// Called when two fixtures begin to touch.
+	virtual void BeginContact(b2Contact* contact) { B2_NOT_USED(contact); }
+
+	/// Called when two fixtures cease to touch.
+	virtual void EndContact(b2Contact* contact) { B2_NOT_USED(contact); }
+
+	/// This is called after a contact is updated. This allows you to inspect a
+	/// contact before it goes to the solver. If you are careful, you can modify the
+	/// contact manifold (e.g. disable contact).
+	/// A copy of the old manifold is provided so that you can detect changes.
+	/// Note: this is called only for awake bodies.
+	/// Note: this is called even when the number of contact points is zero.
+	/// Note: this is not called for sensors.
+	/// Note: if you set the number of contact points to zero, you will not
+	/// get an EndContact callback. However, you may get a BeginContact callback
+	/// the next step.
+	virtual void PreSolve(b2Contact* contact, const b2Manifold* oldManifold)
+	{
+		B2_NOT_USED(contact);
+		B2_NOT_USED(oldManifold);
+	}
+
+	/// This lets you inspect a contact after the solver is finished. This is useful
+	/// for inspecting impulses.
+	/// Note: the contact manifold does not include time of impact impulses, which can be
+	/// arbitrarily large if the sub-step is small. Hence the impulse is provided explicitly
+	/// in a separate data structure.
+	/// Note: this is only called for contacts that are touching, solid, and awake.
+	virtual void PostSolve(b2Contact* contact, const b2ContactImpulse* impulse)
+	{
+		B2_NOT_USED(contact);
+		B2_NOT_USED(impulse);
+	}
+};
+
+/// Callback class for AABB queries.
+/// See b2World::Query
+class B2_API b2QueryCallback
+{
+public:
+	virtual ~b2QueryCallback() {}
+
+	/// Called for each fixture found in the query AABB.
+	/// @return false to terminate the query.
+	virtual bool ReportFixture(b2Fixture* fixture) = 0;
+};
+
+/// Callback class for ray casts.
+/// See b2World::RayCast
+class B2_API b2RayCastCallback
+{
+public:
+	virtual ~b2RayCastCallback() {}
+
+	/// Called for each fixture found in the query. You control how the ray cast
+	/// proceeds by returning a float:
+	/// return -1: ignore this fixture and continue
+	/// return 0: terminate the ray cast
+	/// return fraction: clip the ray to this point
+	/// return 1: don't clip the ray and continue
+	/// @param fixture the fixture hit by the ray
+	/// @param point the point of initial intersection
+	/// @param normal the normal vector at the point of intersection
+	/// @param fraction the fraction along the ray at the point of intersection
+	/// @return -1 to filter, 0 to terminate, fraction to clip the ray for
+	/// closest hit, 1 to continue
+	virtual float ReportFixture(	b2Fixture* fixture, const b2Vec2& point,
+									const b2Vec2& normal, float fraction) = 0;
+};
+
+#endif

3rd/box2d/include/box2d/box2d.h

@@ -0,0 +1,58 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#ifndef BOX2D_H
+#define BOX2D_H
+
+// These include files constitute the main Box2D API
+
+#include "b2_settings.h"
+#include "b2_draw.h"
+#include "b2_timer.h"
+
+#include "b2_chain_shape.h"
+#include "b2_circle_shape.h"
+#include "b2_edge_shape.h"
+#include "b2_polygon_shape.h"
+
+#include "b2_broad_phase.h"
+#include "b2_dynamic_tree.h"
+
+#include "b2_body.h"
+#include "b2_contact.h"
+#include "b2_fixture.h"
+#include "b2_time_step.h"
+#include "b2_world.h"
+#include "b2_world_callbacks.h"
+
+#include "b2_distance_joint.h"
+#include "b2_friction_joint.h"
+#include "b2_gear_joint.h"
+#include "b2_motor_joint.h"
+#include "b2_mouse_joint.h"
+#include "b2_prismatic_joint.h"
+#include "b2_pulley_joint.h"
+#include "b2_revolute_joint.h"
+#include "b2_weld_joint.h"
+#include "b2_wheel_joint.h"
+
+#endif

3rd/box2d/include/box2d_bindings.hpp

@@ -0,0 +1,144 @@
+#pragma once
+
+#include "box2d/box2d.h"
+#include "pocketpy/pocketpy.h"
+#include <cstdlib>
+
+namespace pkpy{
+
+template<>
+inline b2Vec2 py_cast<b2Vec2>(VM* vm, PyObject* obj){
+    Vec2 v = py_cast<Vec2>(vm, obj);
+    return b2Vec2(v.x, v.y);
+}
+
+template<>
+inline b2Vec2 _py_cast<b2Vec2>(VM* vm, PyObject* obj){
+    Vec2 v = _py_cast<Vec2>(vm, obj);
+    return b2Vec2(v.x, v.y);
+}
+
+inline PyObject* py_var(VM* vm, b2Vec2 v){
+    return py_var(vm, Vec2(v.x, v.y));
+}
+
+namespace imbox2d{
+
+struct Body final{
+    b2Body* body;
+    b2Fixture* fixture;
+    PyObject* obj;
+    Vec4 debug_color;
+
+    Body(b2World* world, PyObject* obj){
+        b2BodyDef def;
+        def.type = b2_dynamicBody;
+        // a weak reference to the object, no need to mark it
+        def.userData.pointer = reinterpret_cast<uintptr_t>(this);
+        body = world->CreateBody(&def);
+        fixture = nullptr;
+        this->obj = obj;
+        this->debug_color = Vec4(std::rand() / float(RAND_MAX), std::rand() / float(RAND_MAX), std::rand() / float(RAND_MAX), 1.0f);
+    }
+
+    void _update_fixture(b2Shape* shape){
+        body->DestroyFixture(fixture);  // this takes care of NULL case
+        fixture = body->CreateFixture(shape, 1.0f);
+    }
+
+    Vec4 get_debug_color() const{ return debug_color; }
+
+    b2Vec2 get_position() const{ return body->GetPosition(); }
+    void set_position(b2Vec2 v){ body->SetTransform(v, get_rotation()); }
+
+    void set_rotation(float angle){ body->SetTransform(get_position(), angle); }
+    float get_rotation() const{ return body->GetAngle(); }
+
+    void set_velocity(b2Vec2 v){ body->SetLinearVelocity(v); }
+    b2Vec2 get_velocity() const{ return body->GetLinearVelocity(); }
+
+    void set_angular_velocity(float omega){ body->SetAngularVelocity(omega); }
+    float get_angular_velocity() const{ return body->GetAngularVelocity(); }
+
+    void set_linear_damping(float damping){ body->SetLinearDamping(damping); }
+    float get_linear_damping(){ return body->GetLinearDamping(); }
+
+    void set_angular_damping(float damping){ body->SetAngularDamping(damping); }
+    float get_angular_damping() const{ return body->GetAngularDamping(); }
+
+    void set_gravity_scale(float scale){ body->SetGravityScale(scale); }
+    float get_gravity_scale() const{ return body->GetGravityScale(); }
+
+    void set_type(int type){ body->SetType(static_cast<b2BodyType>(type)); }
+    int get_type() const{ return static_cast<int>(body->GetType()); }
+
+    float get_mass() const{ return body->GetMass(); }
+    float get_inertia() const{ return body->GetInertia(); }
+
+    // fixture settings
+    float get_density() const{ return fixture->GetDensity(); }
+    void set_density(float density){ fixture->SetDensity(density); }
+
+    float get_friction() const{ return fixture->GetFriction(); }
+    void set_friction(float friction){ fixture->SetFriction(friction); }
+
+    float get_restitution() const{ return fixture->GetRestitution(); }
+    void set_restitution(float restitution){ fixture->SetRestitution(restitution); }
+
+    float get_restitution_threshold() const{ return fixture->GetRestitutionThreshold(); }
+    void set_restitution_threshold(float threshold){ fixture->SetRestitutionThreshold(threshold); }
+
+    bool get_is_trigger() const{ return fixture->IsSensor(); }
+    void set_is_trigger(bool trigger){ fixture->SetSensor(trigger); }
+
+    // methods
+    void apply_force(b2Vec2 force, b2Vec2 point){
+        body->ApplyForce(force, point, true);
+    }
+
+    void apply_force_to_center(b2Vec2 force){
+        body->ApplyForceToCenter(force, true);
+    }
+
+    void apply_torque(float torque){
+        body->ApplyTorque(torque, true);
+    }
+
+    void apply_linear_impulse(b2Vec2 impulse, b2Vec2 point){
+        body->ApplyLinearImpulse(impulse, point, true);
+    }
+
+    void apply_linear_impulse_to_center(b2Vec2 impulse){
+        body->ApplyLinearImpulseToCenter(impulse, true);
+    }
+
+    void apply_angular_impulse(float impulse){
+        body->ApplyAngularImpulse(impulse, true);
+    }
+
+    void destroy(){
+        if(body == nullptr) return;
+        body->GetWorld()->DestroyBody(body);
+        body = nullptr;
+    }
+};
+
+struct PyBody: OpaquePointer<Body>{
+    PY_CLASS(PyBody, box2d, Body)
+
+    using OpaquePointer<Body>::OpaquePointer;
+    static void _register(VM* vm, PyObject* mod, PyObject* type);
+};
+
+struct PyWorld: OpaquePointer<b2World>{
+    PY_CLASS(PyWorld, box2d, World)
+
+    using OpaquePointer<b2World>::OpaquePointer;
+    static void _register(VM* vm, PyObject* mod, PyObject* type);
+};
+
+}   // namespace imbox2d
+
+void add_module_box2d(VM* vm);
+
+}   // namespace pkpy

3rd/box2d/src/box2d_bindings.cpp

@@ -0,0 +1,321 @@
+#include "box2d_bindings.hpp"
+
+namespace pkpy{
+
+void add_module_box2d(VM *vm){
+    PyObject* mod = vm->new_module("box2d");
+    imbox2d::PyBody::register_class(vm, mod);
+    imbox2d::PyWorld::register_class(vm, mod);
+}
+
+namespace imbox2d{
+
+// maybe we will use this class later
+class PyDebugDraw: public b2Draw{
+    VM* vm;
+public:
+    PyDebugDraw(VM* vm): vm(vm){}
+
+    void DrawPolygon(const b2Vec2* vertices, int32 vertexCount, const b2Color& color) override{
+    }
+
+    void DrawSolidPolygon(const b2Vec2* vertices, int32 vertexCount, const b2Color& color) override{
+    }
+
+    void DrawCircle(const b2Vec2& center, float radius, const b2Color& color) override{
+    }
+
+    void DrawSolidCircle(const b2Vec2& center, float radius, const b2Vec2& axis, const b2Color& color) override{
+    }
+
+    void DrawSegment(const b2Vec2& p1, const b2Vec2& p2, const b2Color& color) override{
+    }
+
+    void DrawTransform(const b2Transform& xf) override{
+    }
+
+    void DrawPoint(const b2Vec2& p, float size, const b2Color& color) override{
+    }
+};
+
+class PyContactListener : public b2ContactListener{
+    VM* vm;
+public:
+    PyContactListener(VM* vm): vm(vm){}
+
+    void _contact_f(b2Contact* contact, StrName name){
+        auto a = contact->GetFixtureA()->GetBody()->GetUserData().pointer;
+        auto b = contact->GetFixtureB()->GetBody()->GetUserData().pointer;
+        Body* bodyA = reinterpret_cast<Body*>(a);
+        Body* bodyB = reinterpret_cast<Body*>(b);
+        PyObject* self;
+        PyObject* f;
+        f = vm->get_unbound_method(bodyA->obj, name, &self, false);
+        if(f != nullptr) vm->call_method(self, f, VAR_T(PyBody, bodyB));
+        f = vm->get_unbound_method(bodyB->obj, name, &self, false);
+        if(f != nullptr) vm->call_method(self, f, VAR_T(PyBody, bodyA));
+    }
+
+	void BeginContact(b2Contact* contact) override {
+        DEF_SNAME(on_contact_begin);
+        _contact_f(contact, on_contact_begin);
+    }
+
+    void EndContact(b2Contact* contact) override {
+        DEF_SNAME(on_contact_end);
+        _contact_f(contact, on_contact_end);
+    }
+};
+
+    void PyBody::_register(VM* vm, PyObject* mod, PyObject* type){
+        vm->bind_notimplemented_constructor<PyBody>(type);
+        PK_REGISTER_READONLY_PROPERTY(PyBody, debug_color, "vec4");
+
+        PK_REGISTER_PROPERTY(PyBody, position, "vec2");
+        PK_REGISTER_PROPERTY(PyBody, rotation, "float");
+        PK_REGISTER_PROPERTY(PyBody, velocity, "vec2");
+        PK_REGISTER_PROPERTY(PyBody, angular_velocity, "float");
+        PK_REGISTER_PROPERTY(PyBody, linear_damping, "float");
+        PK_REGISTER_PROPERTY(PyBody, angular_damping, "float");
+        PK_REGISTER_PROPERTY(PyBody, gravity_scale, "float");
+        PK_REGISTER_PROPERTY(PyBody, type, "int");
+        PK_REGISTER_READONLY_PROPERTY(PyBody, mass, "float");
+        PK_REGISTER_READONLY_PROPERTY(PyBody, inertia, "float");
+
+        // fixture settings
+        PK_REGISTER_PROPERTY(PyBody, density, "float");
+        PK_REGISTER_PROPERTY(PyBody, friction, "float");
+        PK_REGISTER_PROPERTY(PyBody, restitution, "float");
+        PK_REGISTER_PROPERTY(PyBody, restitution_threshold, "float");
+        PK_REGISTER_PROPERTY(PyBody, is_trigger, "bool");
+
+        // methods
+        _bind_opaque<PyBody>(vm, type, "apply_force(self, force: vec2, point: vec2)", &Body::apply_force);
+        _bind_opaque<PyBody>(vm, type, "apply_force_to_center(self, force: vec2)", &Body::apply_force_to_center);
+        _bind_opaque<PyBody>(vm, type, "apply_torque(self, torque: float)", &Body::apply_torque);
+        _bind_opaque<PyBody>(vm, type, "apply_linear_impulse(self, impulse: vec2, point: vec2)", &Body::apply_linear_impulse);
+        _bind_opaque<PyBody>(vm, type, "apply_linear_impulse_to_center(self, impulse: vec2)", &Body::apply_linear_impulse_to_center);
+        _bind_opaque<PyBody>(vm, type, "apply_angular_impulse(self, impulse: float)", &Body::apply_angular_impulse);
+
+        vm->bind__eq__(PK_OBJ_GET(Type, type), [](VM* vm, PyObject* lhs, PyObject* rhs){
+            PyBody& self = _CAST(PyBody&, lhs);
+            if(is_non_tagged_type(rhs, PyBody::_type(vm))) return vm->NotImplemented;
+            PyBody& other = _CAST(PyBody&, rhs);
+            return VAR(self->body == other->body);
+        });
+
+        vm->bind__repr__(PK_OBJ_GET(Type, type), [](VM* vm, PyObject* obj){
+            PyBody& self = _CAST(PyBody&, obj);
+            return VAR(fmt("<Body* at ", self->body, ">"));
+        });
+
+        // destroy
+        _bind_opaque<PyBody>(vm, type, "destroy(self)", &Body::destroy);
+
+        // contacts
+        vm->bind(type, "get_contacts(self) -> list", [](VM* vm, ArgsView args){
+            PyBody& self = _CAST(PyBody&, args[0]);
+            b2ContactEdge* edge = self->body->GetContactList();
+            List list;
+            while(edge){
+                b2Fixture* fixtureB = edge->contact->GetFixtureB();
+                b2Body* bodyB = fixtureB->GetBody();
+                PyObject* objB = reinterpret_cast<Body*>(bodyB->GetUserData().pointer)->obj;
+                list.push_back(objB);
+                edge = edge->next;
+            }
+            return VAR(std::move(list));
+        });
+
+        // userdata
+        vm->bind(type, "get_node(self)", [](VM* vm, ArgsView args){
+            PyBody& self = _CAST(PyBody&, args[0]);
+            return self->obj;
+        });
+
+        // shape
+        vm->bind(type, "set_box_shape(self, hx: float, hy: float)", [](VM* vm, ArgsView args){
+            PyBody& self = _CAST(PyBody&, args[0]);
+            float hx = CAST(float, args[1]);
+            float hy = CAST(float, args[2]);
+            b2PolygonShape shape;
+            shape.SetAsBox(hx, hy);
+            self->_update_fixture(&shape);
+            return vm->None;
+        });
+
+        vm->bind(type, "set_circle_shape(self, radius: float)", [](VM* vm, ArgsView args){
+            PyBody& self = _CAST(PyBody&, args[0]);
+            float radius = CAST(float, args[1]);
+            b2CircleShape shape;
+            shape.m_radius = radius;
+            self->_update_fixture(&shape);
+            return vm->None;
+        });
+
+        vm->bind(type, "set_polygon_shape(self, points: list[vec2])", [](VM* vm, ArgsView args){
+            PyBody& self = _CAST(PyBody&, args[0]);
+            List& points = CAST(List&, args[1]);
+            if(points.size() > b2_maxPolygonVertices || points.size() < 3){
+                vm->ValueError(fmt("invalid polygon vertices count: ", points.size()));
+                return vm->None;
+            }
+            std::vector<b2Vec2> vertices(points.size());
+            for(int i = 0; i < points.size(); ++i){
+                vertices[i] = CAST(b2Vec2, points[i]);
+            }
+            b2PolygonShape shape;
+            shape.Set(vertices.data(), vertices.size());
+            self->_update_fixture(&shape);
+            return vm->None;
+        });
+
+        vm->bind(type, "set_chain_shape(self, points: list[vec2])", [](VM* vm, ArgsView args){
+            PyBody& self = _CAST(PyBody&, args[0]);
+            List& points = CAST(List&, args[1]);
+            std::vector<b2Vec2> vertices(points.size());
+            for(int i = 0; i < points.size(); ++i){
+                vertices[i] = CAST(b2Vec2, points[i]);
+            }
+            b2ChainShape shape;
+            shape.CreateLoop(vertices.data(), vertices.size());
+            self->_update_fixture(&shape);
+            return vm->None;
+        });
+
+        vm->bind(type, "get_shape_info(self) -> tuple", [](VM* vm, ArgsView args){
+            PyBody& self = _CAST(PyBody&, args[0]);
+            b2Shape* shape = self->fixture->GetShape();
+            switch(shape->GetType()){
+                case b2Shape::e_polygon:{
+                    b2PolygonShape* poly = static_cast<b2PolygonShape*>(shape);
+                    Tuple points(poly->m_count + 1);
+                    for(int i = 0; i < poly->m_count; ++i){
+                        points[i] = VAR(poly->m_vertices[i]);
+                    }
+                    points[poly->m_count] = points[0];
+                    return VAR(Tuple({
+                        VAR("polygon"), VAR(std::move(points))
+                    }));
+                }
+                case b2Shape::e_circle:{
+                    b2CircleShape* circle = static_cast<b2CircleShape*>(shape);
+                    return VAR(Tuple({
+                        VAR("circle"), VAR(circle->m_radius)
+                    }));
+                }
+                case b2Shape::e_chain:{
+                    b2ChainShape* chain = static_cast<b2ChainShape*>(shape);
+                    Tuple points(chain->m_count);
+                    for(int i = 0; i < chain->m_count; ++i){
+                        points[i] = VAR(chain->m_vertices[i]);
+                    }
+                    return VAR(Tuple({
+                        VAR("chain"), VAR(std::move(points))
+                    }));
+                }
+                default:
+                    vm->ValueError("unsupported shape type");
+                    return vm->None;
+            }
+        });
+    }
+
+// This class captures the closest hit shape.
+class MyRayCastCallback : public b2RayCastCallback
+{
+    VM* vm;
+public:
+    List result;
+    MyRayCastCallback(VM* vm): vm(vm) {}
+ 
+    float ReportFixture(b2Fixture* fixture, const b2Vec2& point,
+                        const b2Vec2& normal, float fraction)
+    {
+        auto userdata = fixture->GetBody()->GetUserData().pointer;
+        Body* body = reinterpret_cast<Body*>(userdata);
+        result.push_back(VAR_T(PyBody, body));
+        // if(only_one) return 0;
+        return fraction;
+    }
+};
+
+
+    void PyWorld::_register(VM* vm, PyObject* mod, PyObject* type){
+        vm->bind(type, "__new__(cls)", [](VM* vm, ArgsView args){
+            b2World* w = new b2World(b2Vec2(0, 0));
+            w->SetAllowSleeping(true);
+            w->SetAutoClearForces(true);
+            // the contact listener will leak memory after the world is destroyed
+            // but it's not a big deal since the world is only destroyed when the game exits
+            w->SetContactListener(new PyContactListener(vm));
+            w->SetDebugDraw(new PyDebugDraw(vm));
+            return VAR_T(PyWorld, w);
+        });
+
+        // gravity
+        vm->bind_property(type, "gravity", "vec2", [](VM* vm, ArgsView args){
+            PyWorld& self = _CAST(PyWorld&, args[0]);
+            return VAR(self->GetGravity());
+        }, [](VM* vm, ArgsView args){
+            PyWorld& self = _CAST(PyWorld&, args[0]);
+            self->SetGravity(CAST(b2Vec2, args[1]));
+            return vm->None;
+        });
+
+        // body
+        vm->bind(type, "create_body(self, obj) -> Body", [](VM* vm, ArgsView args){
+            PyWorld& self = _CAST(PyWorld&, args[0]);
+            return VAR_T(PyBody, new Body(self.ptr, args[1]));
+        });
+        vm->bind(type, "get_bodies(self) -> list[Body]", [](VM* vm, ArgsView args){
+            PyWorld& self = _CAST(PyWorld&, args[0]);
+            List list;
+            b2Body* p = self->GetBodyList();
+            while(p != nullptr){
+                Body* body = (Body*)p->GetUserData().pointer;
+                list.push_back(VAR_T(PyBody, body));
+                p = p->GetNext();
+            }
+            return VAR(std::move(list));
+        });
+
+        // step
+        vm->bind(type, "step(self, dt: float, velocity_iterations: int, position_iterations: int)",
+            [](VM* vm, ArgsView args){
+                PyWorld& self = _CAST(PyWorld&, args[0]);
+                float dt = CAST(float, args[1]);
+                int velocity_iterations = CAST(int, args[2]);
+                int position_iterations = CAST(int, args[3]);
+
+                auto f = [](VM* vm, b2Body* p, StrName name){
+                    while(p != nullptr){
+                        Body* body = (Body*)p->GetUserData().pointer;
+                        vm->call_method(body->obj, name);
+                        p = p->GetNext();
+                    }
+                };
+
+                DEF_SNAME(on_box2d_pre_step);
+                DEF_SNAME(on_box2d_post_step);
+                f(vm, self->GetBodyList(), on_box2d_pre_step);
+                self->Step(dt, velocity_iterations, position_iterations);
+                f(vm, self->GetBodyList(), on_box2d_post_step);
+                return vm->None;
+            });
+
+        // raycast
+        vm->bind(type, "raycast(self, start: vec2, end: vec2) -> list[Body]", [](VM* vm, ArgsView args){
+            auto _lock = vm->heap.gc_scope_lock();
+            PyWorld& self = _CAST(PyWorld&, args[0]);
+            b2Vec2 start = CAST(b2Vec2, args[1]);
+            b2Vec2 end = CAST(b2Vec2, args[2]);
+            MyRayCastCallback callback(vm);
+            self->RayCast(&callback, start, end);
+            return VAR(std::move(callback.result));
+        });
+    }
+
+}
+
+}   // namespace pkpy

3rd/box2d/src/collision/b2_broad_phase.cpp

@@ -0,0 +1,131 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#include "box2d/b2_broad_phase.h"
+#include <string.h>
+
+b2BroadPhase::b2BroadPhase()
+{
+	m_proxyCount = 0;
+
+	m_pairCapacity = 16;
+	m_pairCount = 0;
+	m_pairBuffer = (b2Pair*)b2Alloc(m_pairCapacity * sizeof(b2Pair));
+
+	m_moveCapacity = 16;
+	m_moveCount = 0;
+	m_moveBuffer = (int32*)b2Alloc(m_moveCapacity * sizeof(int32));
+}
+
+b2BroadPhase::~b2BroadPhase()
+{
+	b2Free(m_moveBuffer);
+	b2Free(m_pairBuffer);
+}
+
+int32 b2BroadPhase::CreateProxy(const b2AABB& aabb, void* userData)
+{
+	int32 proxyId = m_tree.CreateProxy(aabb, userData);
+	++m_proxyCount;
+	BufferMove(proxyId);
+	return proxyId;
+}
+
+void b2BroadPhase::DestroyProxy(int32 proxyId)
+{
+	UnBufferMove(proxyId);
+	--m_proxyCount;
+	m_tree.DestroyProxy(proxyId);
+}
+
+void b2BroadPhase::MoveProxy(int32 proxyId, const b2AABB& aabb, const b2Vec2& displacement)
+{
+	bool buffer = m_tree.MoveProxy(proxyId, aabb, displacement);
+	if (buffer)
+	{
+		BufferMove(proxyId);
+	}
+}
+
+void b2BroadPhase::TouchProxy(int32 proxyId)
+{
+	BufferMove(proxyId);
+}
+
+void b2BroadPhase::BufferMove(int32 proxyId)
+{
+	if (m_moveCount == m_moveCapacity)
+	{
+		int32* oldBuffer = m_moveBuffer;
+		m_moveCapacity *= 2;
+		m_moveBuffer = (int32*)b2Alloc(m_moveCapacity * sizeof(int32));
+		memcpy(m_moveBuffer, oldBuffer, m_moveCount * sizeof(int32));
+		b2Free(oldBuffer);
+	}
+
+	m_moveBuffer[m_moveCount] = proxyId;
+	++m_moveCount;
+}
+
+void b2BroadPhase::UnBufferMove(int32 proxyId)
+{
+	for (int32 i = 0; i < m_moveCount; ++i)
+	{
+		if (m_moveBuffer[i] == proxyId)
+		{
+			m_moveBuffer[i] = e_nullProxy;
+		}
+	}
+}
+
+// This is called from b2DynamicTree::Query when we are gathering pairs.
+bool b2BroadPhase::QueryCallback(int32 proxyId)
+{
+	// A proxy cannot form a pair with itself.
+	if (proxyId == m_queryProxyId)
+	{
+		return true;
+	}
+
+	const bool moved = m_tree.WasMoved(proxyId);
+	if (moved && proxyId > m_queryProxyId)
+	{
+		// Both proxies are moving. Avoid duplicate pairs.
+		return true;
+	}
+
+	// Grow the pair buffer as needed.
+	if (m_pairCount == m_pairCapacity)
+	{
+		b2Pair* oldBuffer = m_pairBuffer;
+		m_pairCapacity = m_pairCapacity + (m_pairCapacity >> 1);
+		m_pairBuffer = (b2Pair*)b2Alloc(m_pairCapacity * sizeof(b2Pair));
+		memcpy(m_pairBuffer, oldBuffer, m_pairCount * sizeof(b2Pair));
+		b2Free(oldBuffer);
+	}
+
+	m_pairBuffer[m_pairCount].proxyIdA = b2Min(proxyId, m_queryProxyId);
+	m_pairBuffer[m_pairCount].proxyIdB = b2Max(proxyId, m_queryProxyId);
+	++m_pairCount;
+
+	return true;
+}

3rd/box2d/src/collision/b2_chain_shape.cpp

@@ -0,0 +1,185 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#include "box2d/b2_chain_shape.h"
+#include "box2d/b2_edge_shape.h"
+
+#include "box2d/b2_block_allocator.h"
+
+#include <new>
+#include <string.h>
+
+b2ChainShape::~b2ChainShape()
+{
+	Clear();
+}
+
+void b2ChainShape::Clear()
+{
+	b2Free(m_vertices);
+	m_vertices = nullptr;
+	m_count = 0;
+}
+
+void b2ChainShape::CreateLoop(const b2Vec2* vertices, int32 count)
+{
+	b2Assert(m_vertices == nullptr && m_count == 0);
+	b2Assert(count >= 3);
+	if (count < 3)
+	{
+		return;
+	}
+
+	for (int32 i = 1; i < count; ++i)
+	{
+		b2Vec2 v1 = vertices[i-1];
+		b2Vec2 v2 = vertices[i];
+		// If the code crashes here, it means your vertices are too close together.
+		b2Assert(b2DistanceSquared(v1, v2) > b2_linearSlop * b2_linearSlop);
+	}
+
+	m_count = count + 1;
+	m_vertices = (b2Vec2*)b2Alloc(m_count * sizeof(b2Vec2));
+	memcpy(m_vertices, vertices, count * sizeof(b2Vec2));
+	m_vertices[count] = m_vertices[0];
+	m_prevVertex = m_vertices[m_count - 2];
+	m_nextVertex = m_vertices[1];
+}
+
+void b2ChainShape::CreateChain(const b2Vec2* vertices, int32 count,	const b2Vec2& prevVertex, const b2Vec2& nextVertex)
+{
+	b2Assert(m_vertices == nullptr && m_count == 0);
+	b2Assert(count >= 2);
+	for (int32 i = 1; i < count; ++i)
+	{
+		// If the code crashes here, it means your vertices are too close together.
+		b2Assert(b2DistanceSquared(vertices[i-1], vertices[i]) > b2_linearSlop * b2_linearSlop);
+	}
+
+	m_count = count;
+	m_vertices = (b2Vec2*)b2Alloc(count * sizeof(b2Vec2));
+	memcpy(m_vertices, vertices, m_count * sizeof(b2Vec2));
+
+	m_prevVertex = prevVertex;
+	m_nextVertex = nextVertex;
+}
+
+b2Shape* b2ChainShape::Clone(b2BlockAllocator* allocator) const
+{
+	void* mem = allocator->Allocate(sizeof(b2ChainShape));
+	b2ChainShape* clone = new (mem) b2ChainShape;
+	clone->CreateChain(m_vertices, m_count, m_prevVertex, m_nextVertex);
+	return clone;
+}
+
+int32 b2ChainShape::GetChildCount() const
+{
+	// edge count = vertex count - 1
+	return m_count - 1;
+}
+
+void b2ChainShape::GetChildEdge(b2EdgeShape* edge, int32 index) const
+{
+	b2Assert(0 <= index && index < m_count - 1);
+	edge->m_type = b2Shape::e_edge;
+	edge->m_radius = m_radius;
+
+	edge->m_vertex1 = m_vertices[index + 0];
+	edge->m_vertex2 = m_vertices[index + 1];
+	edge->m_oneSided = true;
+
+	if (index > 0)
+	{
+		edge->m_vertex0 = m_vertices[index - 1];
+	}
+	else
+	{
+		edge->m_vertex0 = m_prevVertex;
+	}
+
+	if (index < m_count - 2)
+	{
+		edge->m_vertex3 = m_vertices[index + 2];
+	}
+	else
+	{
+		edge->m_vertex3 = m_nextVertex;
+	}
+}
+
+bool b2ChainShape::TestPoint(const b2Transform& xf, const b2Vec2& p) const
+{
+	B2_NOT_USED(xf);
+	B2_NOT_USED(p);
+	return false;
+}
+
+bool b2ChainShape::RayCast(b2RayCastOutput* output, const b2RayCastInput& input,
+							const b2Transform& xf, int32 childIndex) const
+{
+	b2Assert(childIndex < m_count);
+
+	b2EdgeShape edgeShape;
+
+	int32 i1 = childIndex;
+	int32 i2 = childIndex + 1;
+	if (i2 == m_count)
+	{
+		i2 = 0;
+	}
+
+	edgeShape.m_vertex1 = m_vertices[i1];
+	edgeShape.m_vertex2 = m_vertices[i2];
+
+	return edgeShape.RayCast(output, input, xf, 0);
+}
+
+void b2ChainShape::ComputeAABB(b2AABB* aabb, const b2Transform& xf, int32 childIndex) const
+{
+	b2Assert(childIndex < m_count);
+
+	int32 i1 = childIndex;
+	int32 i2 = childIndex + 1;
+	if (i2 == m_count)
+	{
+		i2 = 0;
+	}
+
+	b2Vec2 v1 = b2Mul(xf, m_vertices[i1]);
+	b2Vec2 v2 = b2Mul(xf, m_vertices[i2]);
+
+	b2Vec2 lower = b2Min(v1, v2);
+	b2Vec2 upper = b2Max(v1, v2);
+
+	b2Vec2 r(m_radius, m_radius);
+	aabb->lowerBound = lower - r;
+	aabb->upperBound = upper + r;
+}
+
+void b2ChainShape::ComputeMass(b2MassData* massData, float density) const
+{
+	B2_NOT_USED(density);
+
+	massData->mass = 0.0f;
+	massData->center.SetZero();
+	massData->I = 0.0f;
+}

3rd/box2d/src/collision/b2_circle_shape.cpp

@@ -0,0 +1,105 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#include "box2d/b2_circle_shape.h"
+#include "box2d/b2_block_allocator.h"
+
+#include <new>
+
+b2Shape* b2CircleShape::Clone(b2BlockAllocator* allocator) const
+{
+	void* mem = allocator->Allocate(sizeof(b2CircleShape));
+	b2CircleShape* clone = new (mem) b2CircleShape;
+	*clone = *this;
+	return clone;
+}
+
+int32 b2CircleShape::GetChildCount() const
+{
+	return 1;
+}
+
+bool b2CircleShape::TestPoint(const b2Transform& transform, const b2Vec2& p) const
+{
+	b2Vec2 center = transform.p + b2Mul(transform.q, m_p);
+	b2Vec2 d = p - center;
+	return b2Dot(d, d) <= m_radius * m_radius;
+}
+
+// Collision Detection in Interactive 3D Environments by Gino van den Bergen
+// From Section 3.1.2
+// x = s + a * r
+// norm(x) = radius
+bool b2CircleShape::RayCast(b2RayCastOutput* output, const b2RayCastInput& input,
+							const b2Transform& transform, int32 childIndex) const
+{
+	B2_NOT_USED(childIndex);
+
+	b2Vec2 position = transform.p + b2Mul(transform.q, m_p);
+	b2Vec2 s = input.p1 - position;
+	float b = b2Dot(s, s) - m_radius * m_radius;
+
+	// Solve quadratic equation.
+	b2Vec2 r = input.p2 - input.p1;
+	float c =  b2Dot(s, r);
+	float rr = b2Dot(r, r);
+	float sigma = c * c - rr * b;
+
+	// Check for negative discriminant and short segment.
+	if (sigma < 0.0f || rr < b2_epsilon)
+	{
+		return false;
+	}
+
+	// Find the point of intersection of the line with the circle.
+	float a = -(c + b2Sqrt(sigma));
+
+	// Is the intersection point on the segment?
+	if (0.0f <= a && a <= input.maxFraction * rr)
+	{
+		a /= rr;
+		output->fraction = a;
+		output->normal = s + a * r;
+		output->normal.Normalize();
+		return true;
+	}
+
+	return false;
+}
+
+void b2CircleShape::ComputeAABB(b2AABB* aabb, const b2Transform& transform, int32 childIndex) const
+{
+	B2_NOT_USED(childIndex);
+
+	b2Vec2 p = transform.p + b2Mul(transform.q, m_p);
+	aabb->lowerBound.Set(p.x - m_radius, p.y - m_radius);
+	aabb->upperBound.Set(p.x + m_radius, p.y + m_radius);
+}
+
+void b2CircleShape::ComputeMass(b2MassData* massData, float density) const
+{
+	massData->mass = density * b2_pi * m_radius * m_radius;
+	massData->center = m_p;
+
+	// inertia about the local origin
+	massData->I = massData->mass * (0.5f * m_radius * m_radius + b2Dot(m_p, m_p));
+}

3rd/box2d/src/collision/b2_collide_circle.cpp

@@ -0,0 +1,158 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#include "box2d/b2_collision.h"
+#include "box2d/b2_circle_shape.h"
+#include "box2d/b2_polygon_shape.h"
+
+void b2CollideCircles(
+	b2Manifold* manifold,
+	const b2CircleShape* circleA, const b2Transform& xfA,
+	const b2CircleShape* circleB, const b2Transform& xfB)
+{
+	manifold->pointCount = 0;
+
+	b2Vec2 pA = b2Mul(xfA, circleA->m_p);
+	b2Vec2 pB = b2Mul(xfB, circleB->m_p);
+
+	b2Vec2 d = pB - pA;
+	float distSqr = b2Dot(d, d);
+	float rA = circleA->m_radius, rB = circleB->m_radius;
+	float radius = rA + rB;
+	if (distSqr > radius * radius)
+	{
+		return;
+	}
+
+	manifold->type = b2Manifold::e_circles;
+	manifold->localPoint = circleA->m_p;
+	manifold->localNormal.SetZero();
+	manifold->pointCount = 1;
+
+	manifold->points[0].localPoint = circleB->m_p;
+	manifold->points[0].id.key = 0;
+}
+
+void b2CollidePolygonAndCircle(
+	b2Manifold* manifold,
+	const b2PolygonShape* polygonA, const b2Transform& xfA,
+	const b2CircleShape* circleB, const b2Transform& xfB)
+{
+	manifold->pointCount = 0;
+
+	// Compute circle position in the frame of the polygon.
+	b2Vec2 c = b2Mul(xfB, circleB->m_p);
+	b2Vec2 cLocal = b2MulT(xfA, c);
+
+	// Find the min separating edge.
+	int32 normalIndex = 0;
+	float separation = -b2_maxFloat;
+	float radius = polygonA->m_radius + circleB->m_radius;
+	int32 vertexCount = polygonA->m_count;
+	const b2Vec2* vertices = polygonA->m_vertices;
+	const b2Vec2* normals = polygonA->m_normals;
+
+	for (int32 i = 0; i < vertexCount; ++i)
+	{
+		float s = b2Dot(normals[i], cLocal - vertices[i]);
+
+		if (s > radius)
+		{
+			// Early out.
+			return;
+		}
+
+		if (s > separation)
+		{
+			separation = s;
+			normalIndex = i;
+		}
+	}
+
+	// Vertices that subtend the incident face.
+	int32 vertIndex1 = normalIndex;
+	int32 vertIndex2 = vertIndex1 + 1 < vertexCount ? vertIndex1 + 1 : 0;
+	b2Vec2 v1 = vertices[vertIndex1];
+	b2Vec2 v2 = vertices[vertIndex2];
+
+	// If the center is inside the polygon ...
+	if (separation < b2_epsilon)
+	{
+		manifold->pointCount = 1;
+		manifold->type = b2Manifold::e_faceA;
+		manifold->localNormal = normals[normalIndex];
+		manifold->localPoint = 0.5f * (v1 + v2);
+		manifold->points[0].localPoint = circleB->m_p;
+		manifold->points[0].id.key = 0;
+		return;
+	}
+
+	// Compute barycentric coordinates
+	float u1 = b2Dot(cLocal - v1, v2 - v1);
+	float u2 = b2Dot(cLocal - v2, v1 - v2);
+	if (u1 <= 0.0f)
+	{
+		if (b2DistanceSquared(cLocal, v1) > radius * radius)
+		{
+			return;
+		}
+
+		manifold->pointCount = 1;
+		manifold->type = b2Manifold::e_faceA;
+		manifold->localNormal = cLocal - v1;
+		manifold->localNormal.Normalize();
+		manifold->localPoint = v1;
+		manifold->points[0].localPoint = circleB->m_p;
+		manifold->points[0].id.key = 0;
+	}
+	else if (u2 <= 0.0f)
+	{
+		if (b2DistanceSquared(cLocal, v2) > radius * radius)
+		{
+			return;
+		}
+
+		manifold->pointCount = 1;
+		manifold->type = b2Manifold::e_faceA;
+		manifold->localNormal = cLocal - v2;
+		manifold->localNormal.Normalize();
+		manifold->localPoint = v2;
+		manifold->points[0].localPoint = circleB->m_p;
+		manifold->points[0].id.key = 0;
+	}
+	else
+	{
+		b2Vec2 faceCenter = 0.5f * (v1 + v2);
+		float s = b2Dot(cLocal - faceCenter, normals[vertIndex1]);
+		if (s > radius)
+		{
+			return;
+		}
+
+		manifold->pointCount = 1;
+		manifold->type = b2Manifold::e_faceA;
+		manifold->localNormal = normals[vertIndex1];
+		manifold->localPoint = faceCenter;
+		manifold->points[0].localPoint = circleB->m_p;
+		manifold->points[0].id.key = 0;
+	}
+}

3rd/box2d/src/collision/b2_collide_edge.cpp

@@ -0,0 +1,524 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#include "box2d/b2_collision.h"
+#include "box2d/b2_circle_shape.h"
+#include "box2d/b2_edge_shape.h"
+#include "box2d/b2_polygon_shape.h"
+
+
+// Compute contact points for edge versus circle.
+// This accounts for edge connectivity.
+void b2CollideEdgeAndCircle(b2Manifold* manifold,
+							const b2EdgeShape* edgeA, const b2Transform& xfA,
+							const b2CircleShape* circleB, const b2Transform& xfB)
+{
+	manifold->pointCount = 0;
+	
+	// Compute circle in frame of edge
+	b2Vec2 Q = b2MulT(xfA, b2Mul(xfB, circleB->m_p));
+	
+	b2Vec2 A = edgeA->m_vertex1, B = edgeA->m_vertex2;
+	b2Vec2 e = B - A;
+	
+	// Normal points to the right for a CCW winding
+	b2Vec2 n(e.y, -e.x);
+	float offset = b2Dot(n, Q - A);
+
+	bool oneSided = edgeA->m_oneSided;
+	if (oneSided && offset < 0.0f)
+	{
+		return;
+	}
+
+	// Barycentric coordinates
+	float u = b2Dot(e, B - Q);
+	float v = b2Dot(e, Q - A);
+	
+	float radius = edgeA->m_radius + circleB->m_radius;
+	
+	b2ContactFeature cf;
+	cf.indexB = 0;
+	cf.typeB = b2ContactFeature::e_vertex;
+	
+	// Region A
+	if (v <= 0.0f)
+	{
+		b2Vec2 P = A;
+		b2Vec2 d = Q - P;
+		float dd = b2Dot(d, d);
+		if (dd > radius * radius)
+		{
+			return;
+		}
+		
+		// Is there an edge connected to A?
+		if (edgeA->m_oneSided)
+		{
+			b2Vec2 A1 = edgeA->m_vertex0;
+			b2Vec2 B1 = A;
+			b2Vec2 e1 = B1 - A1;
+			float u1 = b2Dot(e1, B1 - Q);
+			
+			// Is the circle in Region AB of the previous edge?
+			if (u1 > 0.0f)
+			{
+				return;
+			}
+		}
+		
+		cf.indexA = 0;
+		cf.typeA = b2ContactFeature::e_vertex;
+		manifold->pointCount = 1;
+		manifold->type = b2Manifold::e_circles;
+		manifold->localNormal.SetZero();
+		manifold->localPoint = P;
+		manifold->points[0].id.key = 0;
+		manifold->points[0].id.cf = cf;
+		manifold->points[0].localPoint = circleB->m_p;
+		return;
+	}
+	
+	// Region B
+	if (u <= 0.0f)
+	{
+		b2Vec2 P = B;
+		b2Vec2 d = Q - P;
+		float dd = b2Dot(d, d);
+		if (dd > radius * radius)
+		{
+			return;
+		}
+		
+		// Is there an edge connected to B?
+		if (edgeA->m_oneSided)
+		{
+			b2Vec2 B2 = edgeA->m_vertex3;
+			b2Vec2 A2 = B;
+			b2Vec2 e2 = B2 - A2;
+			float v2 = b2Dot(e2, Q - A2);
+			
+			// Is the circle in Region AB of the next edge?
+			if (v2 > 0.0f)
+			{
+				return;
+			}
+		}
+		
+		cf.indexA = 1;
+		cf.typeA = b2ContactFeature::e_vertex;
+		manifold->pointCount = 1;
+		manifold->type = b2Manifold::e_circles;
+		manifold->localNormal.SetZero();
+		manifold->localPoint = P;
+		manifold->points[0].id.key = 0;
+		manifold->points[0].id.cf = cf;
+		manifold->points[0].localPoint = circleB->m_p;
+		return;
+	}
+	
+	// Region AB
+	float den = b2Dot(e, e);
+	b2Assert(den > 0.0f);
+	b2Vec2 P = (1.0f / den) * (u * A + v * B);
+	b2Vec2 d = Q - P;
+	float dd = b2Dot(d, d);
+	if (dd > radius * radius)
+	{
+		return;
+	}
+	
+	if (offset < 0.0f)
+	{
+		n.Set(-n.x, -n.y);
+	}
+	n.Normalize();
+	
+	cf.indexA = 0;
+	cf.typeA = b2ContactFeature::e_face;
+	manifold->pointCount = 1;
+	manifold->type = b2Manifold::e_faceA;
+	manifold->localNormal = n;
+	manifold->localPoint = A;
+	manifold->points[0].id.key = 0;
+	manifold->points[0].id.cf = cf;
+	manifold->points[0].localPoint = circleB->m_p;
+}
+
+// This structure is used to keep track of the best separating axis.
+struct b2EPAxis
+{
+	enum Type
+	{
+		e_unknown,
+		e_edgeA,
+		e_edgeB
+	};
+	
+	b2Vec2 normal;
+	Type type;
+	int32 index;
+	float separation;
+};
+
+// This holds polygon B expressed in frame A.
+struct b2TempPolygon
+{
+	b2Vec2 vertices[b2_maxPolygonVertices];
+	b2Vec2 normals[b2_maxPolygonVertices];
+	int32 count;
+};
+
+// Reference face used for clipping
+struct b2ReferenceFace
+{
+	int32 i1, i2;
+	b2Vec2 v1, v2;
+	b2Vec2 normal;
+	
+	b2Vec2 sideNormal1;
+	float sideOffset1;
+	
+	b2Vec2 sideNormal2;
+	float sideOffset2;
+};
+
+static b2EPAxis b2ComputeEdgeSeparation(const b2TempPolygon& polygonB, const b2Vec2& v1, const b2Vec2& normal1)
+{
+	b2EPAxis axis;
+	axis.type = b2EPAxis::e_edgeA;
+	axis.index = -1;
+	axis.separation = -FLT_MAX;
+	axis.normal.SetZero();
+
+	b2Vec2 axes[2] = { normal1, -normal1 };
+
+	// Find axis with least overlap (min-max problem)
+	for (int32 j = 0; j < 2; ++j)
+	{
+		float sj = FLT_MAX;
+
+		// Find deepest polygon vertex along axis j
+		for (int32 i = 0; i < polygonB.count; ++i)
+		{
+			float si = b2Dot(axes[j], polygonB.vertices[i] - v1);
+			if (si < sj)
+			{
+				sj = si;
+			}
+		}
+
+		if (sj > axis.separation)
+		{
+			axis.index = j;
+			axis.separation = sj;
+			axis.normal = axes[j];
+		}
+	}
+
+	return axis;
+}
+
+static b2EPAxis b2ComputePolygonSeparation(const b2TempPolygon& polygonB, const b2Vec2& v1, const b2Vec2& v2)
+{
+	b2EPAxis axis;
+	axis.type = b2EPAxis::e_unknown;
+	axis.index = -1;
+	axis.separation = -FLT_MAX;
+	axis.normal.SetZero();
+
+	for (int32 i = 0; i < polygonB.count; ++i)
+	{
+		b2Vec2 n = -polygonB.normals[i];
+
+		float s1 = b2Dot(n, polygonB.vertices[i] - v1);
+		float s2 = b2Dot(n, polygonB.vertices[i] - v2);
+		float s = b2Min(s1, s2);
+
+		if (s > axis.separation)
+		{
+			axis.type = b2EPAxis::e_edgeB;
+			axis.index = i;
+			axis.separation = s;
+			axis.normal = n;
+		}
+	}
+
+	return axis;
+}
+
+void b2CollideEdgeAndPolygon(b2Manifold* manifold,
+							const b2EdgeShape* edgeA, const b2Transform& xfA,
+							const b2PolygonShape* polygonB, const b2Transform& xfB)
+{
+	manifold->pointCount = 0;
+
+	b2Transform xf = b2MulT(xfA, xfB);
+
+	b2Vec2 centroidB = b2Mul(xf, polygonB->m_centroid);
+
+	b2Vec2 v1 = edgeA->m_vertex1;
+	b2Vec2 v2 = edgeA->m_vertex2;
+
+	b2Vec2 edge1 = v2 - v1;
+	edge1.Normalize();
+
+	// Normal points to the right for a CCW winding
+	b2Vec2 normal1(edge1.y, -edge1.x);
+	float offset1 = b2Dot(normal1, centroidB - v1);
+
+	bool oneSided = edgeA->m_oneSided;
+	if (oneSided && offset1 < 0.0f)
+	{
+		return;
+	}
+
+	// Get polygonB in frameA
+	b2TempPolygon tempPolygonB;
+	tempPolygonB.count = polygonB->m_count;
+	for (int32 i = 0; i < polygonB->m_count; ++i)
+	{
+		tempPolygonB.vertices[i] = b2Mul(xf, polygonB->m_vertices[i]);
+		tempPolygonB.normals[i] = b2Mul(xf.q, polygonB->m_normals[i]);
+	}
+
+	float radius = polygonB->m_radius + edgeA->m_radius;
+
+	b2EPAxis edgeAxis = b2ComputeEdgeSeparation(tempPolygonB, v1, normal1);
+	if (edgeAxis.separation > radius)
+	{
+		return;
+	}
+
+	b2EPAxis polygonAxis = b2ComputePolygonSeparation(tempPolygonB, v1, v2);
+	if (polygonAxis.separation > radius)
+	{
+		return;
+	}
+
+	// Use hysteresis for jitter reduction.
+	const float k_relativeTol = 0.98f;
+	const float k_absoluteTol = 0.001f;
+
+	b2EPAxis primaryAxis;
+	if (polygonAxis.separation - radius > k_relativeTol * (edgeAxis.separation - radius) + k_absoluteTol)
+	{
+		primaryAxis = polygonAxis;
+	}
+	else
+	{
+		primaryAxis = edgeAxis;
+	}
+
+	if (oneSided)
+	{
+		// Smooth collision
+		// See https://box2d.org/posts/2020/06/ghost-collisions/
+
+		b2Vec2 edge0 = v1 - edgeA->m_vertex0;
+		edge0.Normalize();
+		b2Vec2 normal0(edge0.y, -edge0.x);
+		bool convex1 = b2Cross(edge0, edge1) >= 0.0f;
+
+		b2Vec2 edge2 = edgeA->m_vertex3 - v2;
+		edge2.Normalize();
+		b2Vec2 normal2(edge2.y, -edge2.x);
+		bool convex2 = b2Cross(edge1, edge2) >= 0.0f;
+
+		const float sinTol = 0.1f;
+		bool side1 = b2Dot(primaryAxis.normal, edge1) <= 0.0f;
+
+		// Check Gauss Map
+		if (side1)
+		{
+			if (convex1)
+			{
+				if (b2Cross(primaryAxis.normal, normal0) > sinTol)
+				{
+					// Skip region
+					return;
+				}
+
+				// Admit region
+			}
+			else
+			{
+				// Snap region
+				primaryAxis = edgeAxis;
+			}
+		}
+		else
+		{
+			if (convex2)
+			{
+				if (b2Cross(normal2, primaryAxis.normal) > sinTol)
+				{
+					// Skip region
+					return;
+				}
+
+				// Admit region
+			}
+			else
+			{
+				// Snap region
+				primaryAxis = edgeAxis;
+			}
+		}
+	}
+
+	b2ClipVertex clipPoints[2];
+	b2ReferenceFace ref;
+	if (primaryAxis.type == b2EPAxis::e_edgeA)
+	{
+		manifold->type = b2Manifold::e_faceA;
+
+		// Search for the polygon normal that is most anti-parallel to the edge normal.
+		int32 bestIndex = 0;
+		float bestValue = b2Dot(primaryAxis.normal, tempPolygonB.normals[0]);
+		for (int32 i = 1; i < tempPolygonB.count; ++i)
+		{
+			float value = b2Dot(primaryAxis.normal, tempPolygonB.normals[i]);
+			if (value < bestValue)
+			{
+				bestValue = value;
+				bestIndex = i;
+			}
+		}
+
+		int32 i1 = bestIndex;
+		int32 i2 = i1 + 1 < tempPolygonB.count ? i1 + 1 : 0;
+
+		clipPoints[0].v = tempPolygonB.vertices[i1];
+		clipPoints[0].id.cf.indexA = 0;
+		clipPoints[0].id.cf.indexB = static_cast<uint8>(i1);
+		clipPoints[0].id.cf.typeA = b2ContactFeature::e_face;
+		clipPoints[0].id.cf.typeB = b2ContactFeature::e_vertex;
+
+		clipPoints[1].v = tempPolygonB.vertices[i2];
+		clipPoints[1].id.cf.indexA = 0;
+		clipPoints[1].id.cf.indexB = static_cast<uint8>(i2);
+		clipPoints[1].id.cf.typeA = b2ContactFeature::e_face;
+		clipPoints[1].id.cf.typeB = b2ContactFeature::e_vertex;
+
+		ref.i1 = 0;
+		ref.i2 = 1;
+		ref.v1 = v1;
+		ref.v2 = v2;
+		ref.normal = primaryAxis.normal;
+		ref.sideNormal1 = -edge1;
+		ref.sideNormal2 = edge1;
+	}
+	else
+	{
+		manifold->type = b2Manifold::e_faceB;
+
+		clipPoints[0].v = v2;
+		clipPoints[0].id.cf.indexA = 1;
+		clipPoints[0].id.cf.indexB = static_cast<uint8>(primaryAxis.index);
+		clipPoints[0].id.cf.typeA = b2ContactFeature::e_vertex;
+		clipPoints[0].id.cf.typeB = b2ContactFeature::e_face;
+
+		clipPoints[1].v = v1;
+		clipPoints[1].id.cf.indexA = 0;
+		clipPoints[1].id.cf.indexB = static_cast<uint8>(primaryAxis.index);		
+		clipPoints[1].id.cf.typeA = b2ContactFeature::e_vertex;
+		clipPoints[1].id.cf.typeB = b2ContactFeature::e_face;
+
+		ref.i1 = primaryAxis.index;
+		ref.i2 = ref.i1 + 1 < tempPolygonB.count ? ref.i1 + 1 : 0;
+		ref.v1 = tempPolygonB.vertices[ref.i1];
+		ref.v2 = tempPolygonB.vertices[ref.i2];
+		ref.normal = tempPolygonB.normals[ref.i1];
+
+		// CCW winding
+		ref.sideNormal1.Set(ref.normal.y, -ref.normal.x);
+		ref.sideNormal2 = -ref.sideNormal1;
+	}
+
+	ref.sideOffset1 = b2Dot(ref.sideNormal1, ref.v1);
+	ref.sideOffset2 = b2Dot(ref.sideNormal2, ref.v2);
+
+	// Clip incident edge against reference face side planes
+	b2ClipVertex clipPoints1[2];
+	b2ClipVertex clipPoints2[2];
+	int32 np;
+
+	// Clip to side 1
+	np = b2ClipSegmentToLine(clipPoints1, clipPoints, ref.sideNormal1, ref.sideOffset1, ref.i1);
+
+	if (np < b2_maxManifoldPoints)
+	{
+		return;
+	}
+
+	// Clip to side 2
+	np = b2ClipSegmentToLine(clipPoints2, clipPoints1, ref.sideNormal2, ref.sideOffset2, ref.i2);
+
+	if (np < b2_maxManifoldPoints)
+	{
+		return;
+	}
+
+	// Now clipPoints2 contains the clipped points.
+	if (primaryAxis.type == b2EPAxis::e_edgeA)
+	{
+		manifold->localNormal = ref.normal;
+		manifold->localPoint = ref.v1;
+	}
+	else
+	{
+		manifold->localNormal = polygonB->m_normals[ref.i1];
+		manifold->localPoint = polygonB->m_vertices[ref.i1];
+	}
+
+	int32 pointCount = 0;
+	for (int32 i = 0; i < b2_maxManifoldPoints; ++i)
+	{
+		float separation;
+
+		separation = b2Dot(ref.normal, clipPoints2[i].v - ref.v1);
+
+		if (separation <= radius)
+		{
+			b2ManifoldPoint* cp = manifold->points + pointCount;
+
+			if (primaryAxis.type == b2EPAxis::e_edgeA)
+			{
+				cp->localPoint = b2MulT(xf, clipPoints2[i].v);
+				cp->id = clipPoints2[i].id;
+			}
+			else
+			{
+				cp->localPoint = clipPoints2[i].v;
+				cp->id.cf.typeA = clipPoints2[i].id.cf.typeB;
+				cp->id.cf.typeB = clipPoints2[i].id.cf.typeA;
+				cp->id.cf.indexA = clipPoints2[i].id.cf.indexB;
+				cp->id.cf.indexB = clipPoints2[i].id.cf.indexA;
+			}
+
+			++pointCount;
+		}
+	}
+
+	manifold->pointCount = pointCount;
+}

3rd/box2d/src/collision/b2_collide_polygon.cpp

@@ -0,0 +1,243 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#include "box2d/b2_collision.h"
+#include "box2d/b2_polygon_shape.h"
+
+// Find the max separation between poly1 and poly2 using edge normals from poly1.
+static float b2FindMaxSeparation(int32* edgeIndex,
+								 const b2PolygonShape* poly1, const b2Transform& xf1,
+								 const b2PolygonShape* poly2, const b2Transform& xf2)
+{
+	int32 count1 = poly1->m_count;
+	int32 count2 = poly2->m_count;
+	const b2Vec2* n1s = poly1->m_normals;
+	const b2Vec2* v1s = poly1->m_vertices;
+	const b2Vec2* v2s = poly2->m_vertices;
+	b2Transform xf = b2MulT(xf2, xf1);
+
+	int32 bestIndex = 0;
+	float maxSeparation = -b2_maxFloat;
+	for (int32 i = 0; i < count1; ++i)
+	{
+		// Get poly1 normal in frame2.
+		b2Vec2 n = b2Mul(xf.q, n1s[i]);
+		b2Vec2 v1 = b2Mul(xf, v1s[i]);
+
+		// Find deepest point for normal i.
+		float si = b2_maxFloat;
+		for (int32 j = 0; j < count2; ++j)
+		{
+			float sij = b2Dot(n, v2s[j] - v1);
+			if (sij < si)
+			{
+				si = sij;
+			}
+		}
+
+		if (si > maxSeparation)
+		{
+			maxSeparation = si;
+			bestIndex = i;
+		}
+	}
+
+	*edgeIndex = bestIndex;
+	return maxSeparation;
+}
+
+static void b2FindIncidentEdge(b2ClipVertex c[2],
+							 const b2PolygonShape* poly1, const b2Transform& xf1, int32 edge1,
+							 const b2PolygonShape* poly2, const b2Transform& xf2)
+{
+	const b2Vec2* normals1 = poly1->m_normals;
+
+	int32 count2 = poly2->m_count;
+	const b2Vec2* vertices2 = poly2->m_vertices;
+	const b2Vec2* normals2 = poly2->m_normals;
+
+	b2Assert(0 <= edge1 && edge1 < poly1->m_count);
+
+	// Get the normal of the reference edge in poly2's frame.
+	b2Vec2 normal1 = b2MulT(xf2.q, b2Mul(xf1.q, normals1[edge1]));
+
+	// Find the incident edge on poly2.
+	int32 index = 0;
+	float minDot = b2_maxFloat;
+	for (int32 i = 0; i < count2; ++i)
+	{
+		float dot = b2Dot(normal1, normals2[i]);
+		if (dot < minDot)
+		{
+			minDot = dot;
+			index = i;
+		}
+	}
+
+	// Build the clip vertices for the incident edge.
+	int32 i1 = index;
+	int32 i2 = i1 + 1 < count2 ? i1 + 1 : 0;
+
+	c[0].v = b2Mul(xf2, vertices2[i1]);
+	c[0].id.cf.indexA = (uint8)edge1;
+	c[0].id.cf.indexB = (uint8)i1;
+	c[0].id.cf.typeA = b2ContactFeature::e_face;
+	c[0].id.cf.typeB = b2ContactFeature::e_vertex;
+
+	c[1].v = b2Mul(xf2, vertices2[i2]);
+	c[1].id.cf.indexA = (uint8)edge1;
+	c[1].id.cf.indexB = (uint8)i2;
+	c[1].id.cf.typeA = b2ContactFeature::e_face;
+	c[1].id.cf.typeB = b2ContactFeature::e_vertex;
+}
+
+// Find edge normal of max separation on A - return if separating axis is found
+// Find edge normal of max separation on B - return if separation axis is found
+// Choose reference edge as min(minA, minB)
+// Find incident edge
+// Clip
+
+// The normal points from 1 to 2
+void b2CollidePolygons(b2Manifold* manifold,
+					  const b2PolygonShape* polyA, const b2Transform& xfA,
+					  const b2PolygonShape* polyB, const b2Transform& xfB)
+{
+	manifold->pointCount = 0;
+	float totalRadius = polyA->m_radius + polyB->m_radius;
+
+	int32 edgeA = 0;
+	float separationA = b2FindMaxSeparation(&edgeA, polyA, xfA, polyB, xfB);
+	if (separationA > totalRadius)
+		return;
+
+	int32 edgeB = 0;
+	float separationB = b2FindMaxSeparation(&edgeB, polyB, xfB, polyA, xfA);
+	if (separationB > totalRadius)
+		return;
+
+	const b2PolygonShape* poly1;	// reference polygon
+	const b2PolygonShape* poly2;	// incident polygon
+	b2Transform xf1, xf2;
+	int32 edge1;					// reference edge
+	uint8 flip;
+	const float k_tol = 0.1f * b2_linearSlop;
+
+	if (separationB > separationA + k_tol)
+	{
+		poly1 = polyB;
+		poly2 = polyA;
+		xf1 = xfB;
+		xf2 = xfA;
+		edge1 = edgeB;
+		manifold->type = b2Manifold::e_faceB;
+		flip = 1;
+	}
+	else
+	{
+		poly1 = polyA;
+		poly2 = polyB;
+		xf1 = xfA;
+		xf2 = xfB;
+		edge1 = edgeA;
+		manifold->type = b2Manifold::e_faceA;
+		flip = 0;
+	}
+
+	b2ClipVertex incidentEdge[2];
+	b2FindIncidentEdge(incidentEdge, poly1, xf1, edge1, poly2, xf2);
+
+	int32 count1 = poly1->m_count;
+	const b2Vec2* vertices1 = poly1->m_vertices;
+
+	int32 iv1 = edge1;
+	int32 iv2 = edge1 + 1 < count1 ? edge1 + 1 : 0;
+
+	b2Vec2 v11 = vertices1[iv1];
+	b2Vec2 v12 = vertices1[iv2];
+
+	b2Vec2 localTangent = v12 - v11;
+	localTangent.Normalize();
+	
+	b2Vec2 localNormal = b2Cross(localTangent, 1.0f);
+	b2Vec2 planePoint = 0.5f * (v11 + v12);
+
+	b2Vec2 tangent = b2Mul(xf1.q, localTangent);
+	b2Vec2 normal = b2Cross(tangent, 1.0f);
+	
+	v11 = b2Mul(xf1, v11);
+	v12 = b2Mul(xf1, v12);
+
+	// Face offset.
+	float frontOffset = b2Dot(normal, v11);
+
+	// Side offsets, extended by polytope skin thickness.
+	float sideOffset1 = -b2Dot(tangent, v11) + totalRadius;
+	float sideOffset2 = b2Dot(tangent, v12) + totalRadius;
+
+	// Clip incident edge against extruded edge1 side edges.
+	b2ClipVertex clipPoints1[2];
+	b2ClipVertex clipPoints2[2];
+	int np;
+
+	// Clip to box side 1
+	np = b2ClipSegmentToLine(clipPoints1, incidentEdge, -tangent, sideOffset1, iv1);
+
+	if (np < 2)
+		return;
+
+	// Clip to negative box side 1
+	np = b2ClipSegmentToLine(clipPoints2, clipPoints1,  tangent, sideOffset2, iv2);
+
+	if (np < 2)
+	{
+		return;
+	}
+
+	// Now clipPoints2 contains the clipped points.
+	manifold->localNormal = localNormal;
+	manifold->localPoint = planePoint;
+
+	int32 pointCount = 0;
+	for (int32 i = 0; i < b2_maxManifoldPoints; ++i)
+	{
+		float separation = b2Dot(normal, clipPoints2[i].v) - frontOffset;
+
+		if (separation <= totalRadius)
+		{
+			b2ManifoldPoint* cp = manifold->points + pointCount;
+			cp->localPoint = b2MulT(xf2, clipPoints2[i].v);
+			cp->id = clipPoints2[i].id;
+			if (flip)
+			{
+				// Swap features
+				b2ContactFeature cf = cp->id.cf;
+				cp->id.cf.indexA = cf.indexB;
+				cp->id.cf.indexB = cf.indexA;
+				cp->id.cf.typeA = cf.typeB;
+				cp->id.cf.typeB = cf.typeA;
+			}
+			++pointCount;
+		}
+	}
+
+	manifold->pointCount = pointCount;
+}

3rd/box2d/src/collision/b2_collision.cpp

@@ -0,0 +1,580 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#include "box2d/b2_collision.h"
+#include "box2d/b2_distance.h"
+
+void b2WorldManifold::Initialize(const b2Manifold* manifold,
+						  const b2Transform& xfA, float radiusA,
+						  const b2Transform& xfB, float radiusB)
+{
+	if (manifold->pointCount == 0)
+	{
+		return;
+	}
+
+	switch (manifold->type)
+	{
+	case b2Manifold::e_circles:
+		{
+			normal.Set(1.0f, 0.0f);
+			b2Vec2 pointA = b2Mul(xfA, manifold->localPoint);
+			b2Vec2 pointB = b2Mul(xfB, manifold->points[0].localPoint);
+			if (b2DistanceSquared(pointA, pointB) > b2_epsilon * b2_epsilon)
+			{
+				normal = pointB - pointA;
+				normal.Normalize();
+			}
+
+			b2Vec2 cA = pointA + radiusA * normal;
+			b2Vec2 cB = pointB - radiusB * normal;
+			points[0] = 0.5f * (cA + cB);
+			separations[0] = b2Dot(cB - cA, normal);
+		}
+		break;
+
+	case b2Manifold::e_faceA:
+		{
+			normal = b2Mul(xfA.q, manifold->localNormal);
+			b2Vec2 planePoint = b2Mul(xfA, manifold->localPoint);
+			
+			for (int32 i = 0; i < manifold->pointCount; ++i)
+			{
+				b2Vec2 clipPoint = b2Mul(xfB, manifold->points[i].localPoint);
+				b2Vec2 cA = clipPoint + (radiusA - b2Dot(clipPoint - planePoint, normal)) * normal;
+				b2Vec2 cB = clipPoint - radiusB * normal;
+				points[i] = 0.5f * (cA + cB);
+				separations[i] = b2Dot(cB - cA, normal);
+			}
+		}
+		break;
+
+	case b2Manifold::e_faceB:
+		{
+			normal = b2Mul(xfB.q, manifold->localNormal);
+			b2Vec2 planePoint = b2Mul(xfB, manifold->localPoint);
+
+			for (int32 i = 0; i < manifold->pointCount; ++i)
+			{
+				b2Vec2 clipPoint = b2Mul(xfA, manifold->points[i].localPoint);
+				b2Vec2 cB = clipPoint + (radiusB - b2Dot(clipPoint - planePoint, normal)) * normal;
+				b2Vec2 cA = clipPoint - radiusA * normal;
+				points[i] = 0.5f * (cA + cB);
+				separations[i] = b2Dot(cA - cB, normal);
+			}
+
+			// Ensure normal points from A to B.
+			normal = -normal;
+		}
+		break;
+	}
+}
+
+void b2GetPointStates(b2PointState state1[b2_maxManifoldPoints], b2PointState state2[b2_maxManifoldPoints],
+					  const b2Manifold* manifold1, const b2Manifold* manifold2)
+{
+	for (int32 i = 0; i < b2_maxManifoldPoints; ++i)
+	{
+		state1[i] = b2_nullState;
+		state2[i] = b2_nullState;
+	}
+
+	// Detect persists and removes.
+	for (int32 i = 0; i < manifold1->pointCount; ++i)
+	{
+		b2ContactID id = manifold1->points[i].id;
+
+		state1[i] = b2_removeState;
+
+		for (int32 j = 0; j < manifold2->pointCount; ++j)
+		{
+			if (manifold2->points[j].id.key == id.key)
+			{
+				state1[i] = b2_persistState;
+				break;
+			}
+		}
+	}
+
+	// Detect persists and adds.
+	for (int32 i = 0; i < manifold2->pointCount; ++i)
+	{
+		b2ContactID id = manifold2->points[i].id;
+
+		state2[i] = b2_addState;
+
+		for (int32 j = 0; j < manifold1->pointCount; ++j)
+		{
+			if (manifold1->points[j].id.key == id.key)
+			{
+				state2[i] = b2_persistState;
+				break;
+			}
+		}
+	}
+}
+
+// From Real-time Collision Detection, p179.
+bool b2AABB::RayCast(b2RayCastOutput* output, const b2RayCastInput& input) const
+{
+	float tmin = -b2_maxFloat;
+	float tmax = b2_maxFloat;
+
+	b2Vec2 p = input.p1;
+	b2Vec2 d = input.p2 - input.p1;
+	b2Vec2 absD = b2Abs(d);
+
+	b2Vec2 normal;
+
+	for (int32 i = 0; i < 2; ++i)
+	{
+		if (absD(i) < b2_epsilon)
+		{
+			// Parallel.
+			if (p(i) < lowerBound(i) || upperBound(i) < p(i))
+			{
+				return false;
+			}
+		}
+		else
+		{
+			float inv_d = 1.0f / d(i);
+			float t1 = (lowerBound(i) - p(i)) * inv_d;
+			float t2 = (upperBound(i) - p(i)) * inv_d;
+
+			// Sign of the normal vector.
+			float s = -1.0f;
+
+			if (t1 > t2)
+			{
+				b2Swap(t1, t2);
+				s = 1.0f;
+			}
+
+			// Push the min up
+			if (t1 > tmin)
+			{
+				normal.SetZero();
+				normal(i) = s;
+				tmin = t1;
+			}
+
+			// Pull the max down
+			tmax = b2Min(tmax, t2);
+
+			if (tmin > tmax)
+			{
+				return false;
+			}
+		}
+	}
+
+	// Does the ray start inside the box?
+	// Does the ray intersect beyond the max fraction?
+	if (tmin < 0.0f || input.maxFraction < tmin)
+	{
+		return false;
+	}
+
+	// Intersection.
+	output->fraction = tmin;
+	output->normal = normal;
+	return true;
+}
+
+// Sutherland-Hodgman clipping.
+int32 b2ClipSegmentToLine(b2ClipVertex vOut[2], const b2ClipVertex vIn[2],
+						const b2Vec2& normal, float offset, int32 vertexIndexA)
+{
+	// Start with no output points
+	int32 count = 0;
+
+	// Calculate the distance of end points to the line
+	float distance0 = b2Dot(normal, vIn[0].v) - offset;
+	float distance1 = b2Dot(normal, vIn[1].v) - offset;
+
+	// If the points are behind the plane
+	if (distance0 <= 0.0f) vOut[count++] = vIn[0];
+	if (distance1 <= 0.0f) vOut[count++] = vIn[1];
+
+	// If the points are on different sides of the plane
+	if (distance0 * distance1 < 0.0f)
+	{
+		// Find intersection point of edge and plane
+		float interp = distance0 / (distance0 - distance1);
+		vOut[count].v = vIn[0].v + interp * (vIn[1].v - vIn[0].v);
+
+		// VertexA is hitting edgeB.
+		vOut[count].id.cf.indexA = static_cast<uint8>(vertexIndexA);
+		vOut[count].id.cf.indexB = vIn[0].id.cf.indexB;
+		vOut[count].id.cf.typeA = b2ContactFeature::e_vertex;
+		vOut[count].id.cf.typeB = b2ContactFeature::e_face;
+		++count;
+
+		b2Assert(count == 2);
+	}
+
+	return count;
+}
+
+bool b2TestOverlap(	const b2Shape* shapeA, int32 indexA,
+					const b2Shape* shapeB, int32 indexB,
+					const b2Transform& xfA, const b2Transform& xfB)
+{
+	b2DistanceInput input;
+	input.proxyA.Set(shapeA, indexA);
+	input.proxyB.Set(shapeB, indexB);
+	input.transformA = xfA;
+	input.transformB = xfB;
+	input.useRadii = true;
+
+	b2SimplexCache cache;
+	cache.count = 0;
+
+	b2DistanceOutput output;
+
+	b2Distance(&output, &cache, &input);
+
+	return output.distance < 10.0f * b2_epsilon;
+}
+
+// quickhull recursion
+static b2Hull b2RecurseHull(b2Vec2 p1, b2Vec2 p2, b2Vec2* ps, int32 count)
+{
+	b2Hull hull;
+	hull.count = 0;
+
+	if (count == 0)
+	{
+		return hull;
+	}
+
+	// create an edge vector pointing from p1 to p2
+	b2Vec2 e = p2 - p1;
+	e.Normalize();
+
+	// discard points left of e and find point furthest to the right of e
+	b2Vec2 rightPoints[b2_maxPolygonVertices]{};
+	int32 rightCount = 0;
+
+	int32 bestIndex = 0;
+	float bestDistance = b2Cross(ps[bestIndex] - p1, e);
+	if (bestDistance > 0.0f)
+	{
+		rightPoints[rightCount++] = ps[bestIndex];
+	}
+
+	for (int32 i = 1; i < count; ++i)
+	{
+		float distance = b2Cross(ps[i] - p1, e);
+		if (distance > bestDistance)
+		{
+			bestIndex = i;
+			bestDistance = distance;
+		}
+
+		if (distance > 0.0f)
+		{
+			rightPoints[rightCount++] = ps[i];
+		}
+	}
+
+	if (bestDistance < 2.0f * b2_linearSlop)
+	{
+		return hull;
+	}
+
+	b2Vec2 bestPoint = ps[bestIndex];
+
+	// compute hull to the right of p1-bestPoint
+	b2Hull hull1 = b2RecurseHull(p1, bestPoint, rightPoints, rightCount);
+
+	// compute hull to the right of bestPoint-p2
+	b2Hull hull2 = b2RecurseHull(bestPoint, p2, rightPoints, rightCount);
+
+	// stich together hulls
+	for (int32 i = 0; i < hull1.count; ++i)
+	{
+		hull.points[hull.count++] = hull1.points[i];
+	}
+
+	hull.points[hull.count++] = bestPoint;
+
+	for (int32 i = 0; i < hull2.count; ++i)
+	{
+		hull.points[hull.count++] = hull2.points[i];
+	}
+
+	b2Assert(hull.count < b2_maxPolygonVertices);
+
+	return hull;
+}
+
+// quickhull algorithm
+// - merges vertices based on b2_linearSlop
+// - removes collinear points using b2_linearSlop
+// - returns an empty hull if it fails
+b2Hull b2ComputeHull(const b2Vec2* points, int32 count)
+{
+	b2Hull hull;
+	hull.count = 0;
+
+	if (count < 3 || count > b2_maxPolygonVertices)
+	{
+		// check your data
+		return hull;
+	}
+
+	count = b2Min(count, b2_maxPolygonVertices);
+
+	b2AABB aabb = { {b2_maxFloat, b2_maxFloat}, {-b2_maxFloat, -b2_maxFloat} };
+
+	// Perform aggressive point welding. First point always remains.
+	// Also compute the bounding box for later.
+	b2Vec2 ps[b2_maxPolygonVertices];
+	int32 n = 0;
+	const float tolSqr = 16.0f * b2_linearSlop * b2_linearSlop;
+	for (int32 i = 0; i < count; ++i)
+	{
+		aabb.lowerBound = b2Min(aabb.lowerBound, points[i]);
+		aabb.upperBound = b2Max(aabb.upperBound, points[i]);
+
+		b2Vec2 vi = points[i];
+
+		bool unique = true;
+		for (int32 j = 0; j < i; ++j)
+		{
+			b2Vec2 vj = points[j];
+
+			float distSqr = b2DistanceSquared(vi, vj);
+			if (distSqr < tolSqr)
+			{
+				unique = false;
+				break;
+			}
+		}
+
+		if (unique)
+		{
+			ps[n++] = vi;
+		}
+	}
+
+	if (n < 3)
+	{
+		// all points very close together, check your data and check your scale
+		return hull;
+	}
+
+	// Find an extreme point as the first point on the hull
+	b2Vec2 c = aabb.GetCenter();
+	int32 i1 = 0;
+	float dsq1 = b2DistanceSquared(c, ps[i1]);
+	for (int32 i = 1; i < n; ++i)
+	{
+		float dsq = b2DistanceSquared(c, ps[i]);
+		if (dsq > dsq1)
+		{
+			i1 = i;
+			dsq1 = dsq;
+		}
+	}
+
+	// remove p1 from working set
+	b2Vec2 p1 = ps[i1];
+	ps[i1] = ps[n - 1];
+	n = n - 1;
+
+	int32 i2 = 0;
+	float dsq2 = b2DistanceSquared(p1, ps[i2]);
+	for (int32 i = 1; i < n; ++i)
+	{
+		float dsq = b2DistanceSquared(p1, ps[i]);
+		if (dsq > dsq2)
+		{
+			i2 = i;
+			dsq2 = dsq;
+		}
+	}
+
+	// remove p2 from working set
+	b2Vec2 p2 = ps[i2];
+	ps[i2] = ps[n - 1];
+	n = n - 1;
+
+	// split the points into points that are left and right of the line p1-p2.
+	b2Vec2 rightPoints[b2_maxPolygonVertices - 2];
+	int32 rightCount = 0;
+
+	b2Vec2 leftPoints[b2_maxPolygonVertices - 2];
+	int32 leftCount = 0;
+
+	b2Vec2 e = p2 - p1;
+	e.Normalize();
+
+	for (int32 i = 0; i < n; ++i)
+	{
+		float d = b2Cross(ps[i] - p1, e);
+
+		// slop used here to skip points that are very close to the line p1-p2
+		if (d >= 2.0f * b2_linearSlop)
+		{
+			rightPoints[rightCount++] = ps[i];
+		}
+		else if (d <= -2.0f * b2_linearSlop)
+		{
+			leftPoints[leftCount++] = ps[i];
+		}
+	}
+
+	// compute hulls on right and left
+	b2Hull hull1 = b2RecurseHull(p1, p2, rightPoints, rightCount);
+	b2Hull hull2 = b2RecurseHull(p2, p1, leftPoints, leftCount);
+
+	if (hull1.count == 0 && hull2.count == 0)
+	{
+		// all points collinear
+		return hull;
+	}
+
+	// stitch hulls together, preserving CCW winding order
+	hull.points[hull.count++] = p1;
+
+	for (int32 i = 0; i < hull1.count; ++i)
+	{
+		hull.points[hull.count++] = hull1.points[i];
+	}
+
+	hull.points[hull.count++] = p2;
+
+	for (int32 i = 0; i < hull2.count; ++i)
+	{
+		hull.points[hull.count++] = hull2.points[i];
+	}
+
+	b2Assert(hull.count <= b2_maxPolygonVertices);
+
+	// merge collinear
+	bool searching = true;
+	while (searching && hull.count > 2)
+	{
+		searching = false;
+
+		for (int32 i = 0; i < hull.count; ++i)
+		{
+			int32 i1 = i;
+			int32 i2 = (i + 1) % hull.count;
+			int32 i3 = (i + 2) % hull.count;
+
+			b2Vec2 p1 = hull.points[i1];
+			b2Vec2 p2 = hull.points[i2];
+			b2Vec2 p3 = hull.points[i3];
+
+			b2Vec2 e = p3 - p1;
+			e.Normalize();
+
+			b2Vec2 v = p2 - p1;
+			float distance = b2Cross(p2 - p1, e);
+			if (distance <= 2.0f * b2_linearSlop)
+			{
+				// remove midpoint from hull
+				for (int32 j = i2; j < hull.count - 1; ++j)
+				{
+					hull.points[j] = hull.points[j + 1];
+				}
+				hull.count -= 1;
+
+				// continue searching for collinear points
+				searching = true;
+
+				break;
+			}
+		}
+	}
+
+	if (hull.count < 3)
+	{
+		// all points collinear, shouldn't be reached since this was validated above
+		hull.count = 0;
+	}
+
+	return hull;
+}
+
+bool b2ValidateHull(const b2Hull& hull)
+{
+	if (hull.count < 3 || b2_maxPolygonVertices < hull.count)
+	{
+		return false;
+	}
+
+	// test that every point is behind every edge
+	for (int32 i = 0; i < hull.count; ++i)
+	{
+		// create an edge vector
+		int32 i1 = i;
+		int32 i2 = i < hull.count - 1 ? i1 + 1 : 0;
+		b2Vec2 p = hull.points[i1];
+		b2Vec2 e = hull.points[i2] - p;
+		e.Normalize();
+
+		for (int32 j = 0; j < hull.count; ++j)
+		{
+			// skip points that subtend the current edge
+			if (j == i1 || j == i2)
+			{
+				continue;
+			}
+
+			float distance = b2Cross(hull.points[j] - p, e);
+			if (distance >= 0.0f)
+			{
+				return false;
+			}
+		}
+	}
+
+	// test for collinear points
+	for (int32 i = 0; i < hull.count; ++i)
+	{
+		int32 i1 = i;
+		int32 i2 = (i + 1) % hull.count;
+		int32 i3 = (i + 2) % hull.count;
+
+		b2Vec2 p1 = hull.points[i1];
+		b2Vec2 p2 = hull.points[i2];
+		b2Vec2 p3 = hull.points[i3];
+
+		b2Vec2 e = p3 - p1;
+		e.Normalize();
+
+		b2Vec2 v = p2 - p1;
+		float distance = b2Cross(p2 - p1, e);
+		if (distance <= b2_linearSlop)
+		{
+			// p1-p2-p3 are collinear
+			return false;
+		}
+	}
+
+	return true;
+}

3rd/box2d/src/collision/b2_distance.cpp

@@ -0,0 +1,744 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#include "box2d/b2_circle_shape.h"
+#include "box2d/b2_distance.h"
+#include "box2d/b2_edge_shape.h"
+#include "box2d/b2_chain_shape.h"
+#include "box2d/b2_polygon_shape.h"
+
+// GJK using Voronoi regions (Christer Ericson) and Barycentric coordinates.
+B2_API int32 b2_gjkCalls, b2_gjkIters, b2_gjkMaxIters;
+
+void b2DistanceProxy::Set(const b2Shape* shape, int32 index)
+{
+	switch (shape->GetType())
+	{
+	case b2Shape::e_circle:
+		{
+			const b2CircleShape* circle = static_cast<const b2CircleShape*>(shape);
+			m_vertices = &circle->m_p;
+			m_count = 1;
+			m_radius = circle->m_radius;
+		}
+		break;
+
+	case b2Shape::e_polygon:
+		{
+			const b2PolygonShape* polygon = static_cast<const b2PolygonShape*>(shape);
+			m_vertices = polygon->m_vertices;
+			m_count = polygon->m_count;
+			m_radius = polygon->m_radius;
+		}
+		break;
+
+	case b2Shape::e_chain:
+		{
+			const b2ChainShape* chain = static_cast<const b2ChainShape*>(shape);
+			b2Assert(0 <= index && index < chain->m_count);
+
+			m_buffer[0] = chain->m_vertices[index];
+			if (index + 1 < chain->m_count)
+			{
+				m_buffer[1] = chain->m_vertices[index + 1];
+			}
+			else
+			{
+				m_buffer[1] = chain->m_vertices[0];
+			}
+
+			m_vertices = m_buffer;
+			m_count = 2;
+			m_radius = chain->m_radius;
+		}
+		break;
+
+	case b2Shape::e_edge:
+		{
+			const b2EdgeShape* edge = static_cast<const b2EdgeShape*>(shape);
+			m_vertices = &edge->m_vertex1;
+			m_count = 2;
+			m_radius = edge->m_radius;
+		}
+		break;
+
+	default:
+		b2Assert(false);
+	}
+}
+
+void b2DistanceProxy::Set(const b2Vec2* vertices, int32 count, float radius)
+{
+    m_vertices = vertices;
+    m_count = count;
+    m_radius = radius;
+}
+
+struct b2SimplexVertex
+{
+	b2Vec2 wA;		// support point in proxyA
+	b2Vec2 wB;		// support point in proxyB
+	b2Vec2 w;		// wB - wA
+	float a;		// barycentric coordinate for closest point
+	int32 indexA;	// wA index
+	int32 indexB;	// wB index
+};
+
+struct b2Simplex
+{
+	void ReadCache(	const b2SimplexCache* cache,
+					const b2DistanceProxy* proxyA, const b2Transform& transformA,
+					const b2DistanceProxy* proxyB, const b2Transform& transformB)
+	{
+		b2Assert(cache->count <= 3);
+		
+		// Copy data from cache.
+		m_count = cache->count;
+		b2SimplexVertex* vertices = &m_v1;
+		for (int32 i = 0; i < m_count; ++i)
+		{
+			b2SimplexVertex* v = vertices + i;
+			v->indexA = cache->indexA[i];
+			v->indexB = cache->indexB[i];
+			b2Vec2 wALocal = proxyA->GetVertex(v->indexA);
+			b2Vec2 wBLocal = proxyB->GetVertex(v->indexB);
+			v->wA = b2Mul(transformA, wALocal);
+			v->wB = b2Mul(transformB, wBLocal);
+			v->w = v->wB - v->wA;
+			v->a = 0.0f;
+		}
+
+		// Compute the new simplex metric, if it is substantially different than
+		// old metric then flush the simplex.
+		if (m_count > 1)
+		{
+			float metric1 = cache->metric;
+			float metric2 = GetMetric();
+			if (metric2 < 0.5f * metric1 || 2.0f * metric1 < metric2 || metric2 < b2_epsilon)
+			{
+				// Reset the simplex.
+				m_count = 0;
+			}
+		}
+
+		// If the cache is empty or invalid ...
+		if (m_count == 0)
+		{
+			b2SimplexVertex* v = vertices + 0;
+			v->indexA = 0;
+			v->indexB = 0;
+			b2Vec2 wALocal = proxyA->GetVertex(0);
+			b2Vec2 wBLocal = proxyB->GetVertex(0);
+			v->wA = b2Mul(transformA, wALocal);
+			v->wB = b2Mul(transformB, wBLocal);
+			v->w = v->wB - v->wA;
+			v->a = 1.0f;
+			m_count = 1;
+		}
+	}
+
+	void WriteCache(b2SimplexCache* cache) const
+	{
+		cache->metric = GetMetric();
+		cache->count = uint16(m_count);
+		const b2SimplexVertex* vertices = &m_v1;
+		for (int32 i = 0; i < m_count; ++i)
+		{
+			cache->indexA[i] = uint8(vertices[i].indexA);
+			cache->indexB[i] = uint8(vertices[i].indexB);
+		}
+	}
+
+	b2Vec2 GetSearchDirection() const
+	{
+		switch (m_count)
+		{
+		case 1:
+			return -m_v1.w;
+
+		case 2:
+			{
+				b2Vec2 e12 = m_v2.w - m_v1.w;
+				float sgn = b2Cross(e12, -m_v1.w);
+				if (sgn > 0.0f)
+				{
+					// Origin is left of e12.
+					return b2Cross(1.0f, e12);
+				}
+				else
+				{
+					// Origin is right of e12.
+					return b2Cross(e12, 1.0f);
+				}
+			}
+
+		default:
+			b2Assert(false);
+			return b2Vec2_zero;
+		}
+	}
+
+	b2Vec2 GetClosestPoint() const
+	{
+		switch (m_count)
+		{
+		case 0:
+			b2Assert(false);
+			return b2Vec2_zero;
+
+		case 1:
+			return m_v1.w;
+
+		case 2:
+			return m_v1.a * m_v1.w + m_v2.a * m_v2.w;
+
+		case 3:
+			return b2Vec2_zero;
+
+		default:
+			b2Assert(false);
+			return b2Vec2_zero;
+		}
+	}
+
+	void GetWitnessPoints(b2Vec2* pA, b2Vec2* pB) const
+	{
+		switch (m_count)
+		{
+		case 0:
+			b2Assert(false);
+			break;
+
+		case 1:
+			*pA = m_v1.wA;
+			*pB = m_v1.wB;
+			break;
+
+		case 2:
+			*pA = m_v1.a * m_v1.wA + m_v2.a * m_v2.wA;
+			*pB = m_v1.a * m_v1.wB + m_v2.a * m_v2.wB;
+			break;
+
+		case 3:
+			*pA = m_v1.a * m_v1.wA + m_v2.a * m_v2.wA + m_v3.a * m_v3.wA;
+			*pB = *pA;
+			break;
+
+		default:
+			b2Assert(false);
+			break;
+		}
+	}
+
+	float GetMetric() const
+	{
+		switch (m_count)
+		{
+		case 0:
+			b2Assert(false);
+			return 0.0f;
+
+		case 1:
+			return 0.0f;
+
+		case 2:
+			return b2Distance(m_v1.w, m_v2.w);
+
+		case 3:
+			return b2Cross(m_v2.w - m_v1.w, m_v3.w - m_v1.w);
+
+		default:
+			b2Assert(false);
+			return 0.0f;
+		}
+	}
+
+	void Solve2();
+	void Solve3();
+
+	b2SimplexVertex m_v1, m_v2, m_v3;
+	int32 m_count;
+};
+
+
+// Solve a line segment using barycentric coordinates.
+//
+// p = a1 * w1 + a2 * w2
+// a1 + a2 = 1
+//
+// The vector from the origin to the closest point on the line is
+// perpendicular to the line.
+// e12 = w2 - w1
+// dot(p, e) = 0
+// a1 * dot(w1, e) + a2 * dot(w2, e) = 0
+//
+// 2-by-2 linear system
+// [1      1     ][a1] = [1]
+// [w1.e12 w2.e12][a2] = [0]
+//
+// Define
+// d12_1 =  dot(w2, e12)
+// d12_2 = -dot(w1, e12)
+// d12 = d12_1 + d12_2
+//
+// Solution
+// a1 = d12_1 / d12
+// a2 = d12_2 / d12
+void b2Simplex::Solve2()
+{
+	b2Vec2 w1 = m_v1.w;
+	b2Vec2 w2 = m_v2.w;
+	b2Vec2 e12 = w2 - w1;
+
+	// w1 region
+	float d12_2 = -b2Dot(w1, e12);
+	if (d12_2 <= 0.0f)
+	{
+		// a2 <= 0, so we clamp it to 0
+		m_v1.a = 1.0f;
+		m_count = 1;
+		return;
+	}
+
+	// w2 region
+	float d12_1 = b2Dot(w2, e12);
+	if (d12_1 <= 0.0f)
+	{
+		// a1 <= 0, so we clamp it to 0
+		m_v2.a = 1.0f;
+		m_count = 1;
+		m_v1 = m_v2;
+		return;
+	}
+
+	// Must be in e12 region.
+	float inv_d12 = 1.0f / (d12_1 + d12_2);
+	m_v1.a = d12_1 * inv_d12;
+	m_v2.a = d12_2 * inv_d12;
+	m_count = 2;
+}
+
+// Possible regions:
+// - points[2]
+// - edge points[0]-points[2]
+// - edge points[1]-points[2]
+// - inside the triangle
+void b2Simplex::Solve3()
+{
+	b2Vec2 w1 = m_v1.w;
+	b2Vec2 w2 = m_v2.w;
+	b2Vec2 w3 = m_v3.w;
+
+	// Edge12
+	// [1      1     ][a1] = [1]
+	// [w1.e12 w2.e12][a2] = [0]
+	// a3 = 0
+	b2Vec2 e12 = w2 - w1;
+	float w1e12 = b2Dot(w1, e12);
+	float w2e12 = b2Dot(w2, e12);
+	float d12_1 = w2e12;
+	float d12_2 = -w1e12;
+
+	// Edge13
+	// [1      1     ][a1] = [1]
+	// [w1.e13 w3.e13][a3] = [0]
+	// a2 = 0
+	b2Vec2 e13 = w3 - w1;
+	float w1e13 = b2Dot(w1, e13);
+	float w3e13 = b2Dot(w3, e13);
+	float d13_1 = w3e13;
+	float d13_2 = -w1e13;
+
+	// Edge23
+	// [1      1     ][a2] = [1]
+	// [w2.e23 w3.e23][a3] = [0]
+	// a1 = 0
+	b2Vec2 e23 = w3 - w2;
+	float w2e23 = b2Dot(w2, e23);
+	float w3e23 = b2Dot(w3, e23);
+	float d23_1 = w3e23;
+	float d23_2 = -w2e23;
+	
+	// Triangle123
+	float n123 = b2Cross(e12, e13);
+
+	float d123_1 = n123 * b2Cross(w2, w3);
+	float d123_2 = n123 * b2Cross(w3, w1);
+	float d123_3 = n123 * b2Cross(w1, w2);
+
+	// w1 region
+	if (d12_2 <= 0.0f && d13_2 <= 0.0f)
+	{
+		m_v1.a = 1.0f;
+		m_count = 1;
+		return;
+	}
+
+	// e12
+	if (d12_1 > 0.0f && d12_2 > 0.0f && d123_3 <= 0.0f)
+	{
+		float inv_d12 = 1.0f / (d12_1 + d12_2);
+		m_v1.a = d12_1 * inv_d12;
+		m_v2.a = d12_2 * inv_d12;
+		m_count = 2;
+		return;
+	}
+
+	// e13
+	if (d13_1 > 0.0f && d13_2 > 0.0f && d123_2 <= 0.0f)
+	{
+		float inv_d13 = 1.0f / (d13_1 + d13_2);
+		m_v1.a = d13_1 * inv_d13;
+		m_v3.a = d13_2 * inv_d13;
+		m_count = 2;
+		m_v2 = m_v3;
+		return;
+	}
+
+	// w2 region
+	if (d12_1 <= 0.0f && d23_2 <= 0.0f)
+	{
+		m_v2.a = 1.0f;
+		m_count = 1;
+		m_v1 = m_v2;
+		return;
+	}
+
+	// w3 region
+	if (d13_1 <= 0.0f && d23_1 <= 0.0f)
+	{
+		m_v3.a = 1.0f;
+		m_count = 1;
+		m_v1 = m_v3;
+		return;
+	}
+
+	// e23
+	if (d23_1 > 0.0f && d23_2 > 0.0f && d123_1 <= 0.0f)
+	{
+		float inv_d23 = 1.0f / (d23_1 + d23_2);
+		m_v2.a = d23_1 * inv_d23;
+		m_v3.a = d23_2 * inv_d23;
+		m_count = 2;
+		m_v1 = m_v3;
+		return;
+	}
+
+	// Must be in triangle123
+	float inv_d123 = 1.0f / (d123_1 + d123_2 + d123_3);
+	m_v1.a = d123_1 * inv_d123;
+	m_v2.a = d123_2 * inv_d123;
+	m_v3.a = d123_3 * inv_d123;
+	m_count = 3;
+}
+
+void b2Distance(b2DistanceOutput* output,
+				b2SimplexCache* cache,
+				const b2DistanceInput* input)
+{
+	++b2_gjkCalls;
+
+	const b2DistanceProxy* proxyA = &input->proxyA;
+	const b2DistanceProxy* proxyB = &input->proxyB;
+
+	b2Transform transformA = input->transformA;
+	b2Transform transformB = input->transformB;
+
+	// Initialize the simplex.
+	b2Simplex simplex;
+	simplex.ReadCache(cache, proxyA, transformA, proxyB, transformB);
+
+	// Get simplex vertices as an array.
+	b2SimplexVertex* vertices = &simplex.m_v1;
+	const int32 k_maxIters = 20;
+
+	// These store the vertices of the last simplex so that we
+	// can check for duplicates and prevent cycling.
+	int32 saveA[3], saveB[3];
+	int32 saveCount = 0;
+
+	// Main iteration loop.
+	int32 iter = 0;
+	while (iter < k_maxIters)
+	{
+		// Copy simplex so we can identify duplicates.
+		saveCount = simplex.m_count;
+		for (int32 i = 0; i < saveCount; ++i)
+		{
+			saveA[i] = vertices[i].indexA;
+			saveB[i] = vertices[i].indexB;
+		}
+
+		switch (simplex.m_count)
+		{
+		case 1:
+			break;
+
+		case 2:
+			simplex.Solve2();
+			break;
+
+		case 3:
+			simplex.Solve3();
+			break;
+
+		default:
+			b2Assert(false);
+		}
+
+		// If we have 3 points, then the origin is in the corresponding triangle.
+		if (simplex.m_count == 3)
+		{
+			break;
+		}
+
+		// Get search direction.
+		b2Vec2 d = simplex.GetSearchDirection();
+
+		// Ensure the search direction is numerically fit.
+		if (d.LengthSquared() < b2_epsilon * b2_epsilon)
+		{
+			// The origin is probably contained by a line segment
+			// or triangle. Thus the shapes are overlapped.
+
+			// We can't return zero here even though there may be overlap.
+			// In case the simplex is a point, segment, or triangle it is difficult
+			// to determine if the origin is contained in the CSO or very close to it.
+			break;
+		}
+
+		// Compute a tentative new simplex vertex using support points.
+		b2SimplexVertex* vertex = vertices + simplex.m_count;
+		vertex->indexA = proxyA->GetSupport(b2MulT(transformA.q, -d));
+		vertex->wA = b2Mul(transformA, proxyA->GetVertex(vertex->indexA));
+		vertex->indexB = proxyB->GetSupport(b2MulT(transformB.q, d));
+		vertex->wB = b2Mul(transformB, proxyB->GetVertex(vertex->indexB));
+		vertex->w = vertex->wB - vertex->wA;
+
+		// Iteration count is equated to the number of support point calls.
+		++iter;
+		++b2_gjkIters;
+
+		// Check for duplicate support points. This is the main termination criteria.
+		bool duplicate = false;
+		for (int32 i = 0; i < saveCount; ++i)
+		{
+			if (vertex->indexA == saveA[i] && vertex->indexB == saveB[i])
+			{
+				duplicate = true;
+				break;
+			}
+		}
+
+		// If we found a duplicate support point we must exit to avoid cycling.
+		if (duplicate)
+		{
+			break;
+		}
+
+		// New vertex is ok and needed.
+		++simplex.m_count;
+	}
+
+	b2_gjkMaxIters = b2Max(b2_gjkMaxIters, iter);
+
+	// Prepare output.
+	simplex.GetWitnessPoints(&output->pointA, &output->pointB);
+	output->distance = b2Distance(output->pointA, output->pointB);
+	output->iterations = iter;
+
+	// Cache the simplex.
+	simplex.WriteCache(cache);
+
+	// Apply radii if requested
+	if (input->useRadii)
+	{
+		if (output->distance < b2_epsilon)
+		{
+			// Shapes are too close to safely compute normal
+			b2Vec2 p = 0.5f * (output->pointA + output->pointB);
+			output->pointA = p;
+			output->pointB = p;
+			output->distance = 0.0f;
+		}
+		else
+		{
+			// Keep closest points on perimeter even if overlapped, this way
+			// the points move smoothly.
+			float rA = proxyA->m_radius;
+			float rB = proxyB->m_radius;
+			b2Vec2 normal = output->pointB - output->pointA;
+			normal.Normalize();
+			output->distance = b2Max(0.0f, output->distance - rA - rB);
+			output->pointA += rA * normal;
+			output->pointB -= rB * normal;
+		}
+	}
+}
+
+// GJK-raycast
+// Algorithm by Gino van den Bergen.
+// "Smooth Mesh Contacts with GJK" in Game Physics Pearls. 2010
+bool b2ShapeCast(b2ShapeCastOutput * output, const b2ShapeCastInput * input)
+{
+    output->iterations = 0;
+    output->lambda = 1.0f;
+    output->normal.SetZero();
+    output->point.SetZero();
+
+	const b2DistanceProxy* proxyA = &input->proxyA;
+	const b2DistanceProxy* proxyB = &input->proxyB;
+
+    float radiusA = b2Max(proxyA->m_radius, b2_polygonRadius);
+    float radiusB = b2Max(proxyB->m_radius, b2_polygonRadius);
+    float radius = radiusA + radiusB;
+
+	b2Transform xfA = input->transformA;
+	b2Transform xfB = input->transformB;
+
+	b2Vec2 r = input->translationB;
+	b2Vec2 n(0.0f, 0.0f);
+	float lambda = 0.0f;
+
+	// Initial simplex
+	b2Simplex simplex;
+	simplex.m_count = 0;
+
+	// Get simplex vertices as an array.
+	b2SimplexVertex* vertices = &simplex.m_v1;
+
+	// Get support point in -r direction
+	int32 indexA = proxyA->GetSupport(b2MulT(xfA.q, -r));
+	b2Vec2 wA = b2Mul(xfA, proxyA->GetVertex(indexA));
+	int32 indexB = proxyB->GetSupport(b2MulT(xfB.q, r));
+	b2Vec2 wB = b2Mul(xfB, proxyB->GetVertex(indexB));
+    b2Vec2 v = wA - wB;
+
+    // Sigma is the target distance between polygons
+    float sigma = b2Max(b2_polygonRadius, radius - b2_polygonRadius);
+	const float tolerance = 0.5f * b2_linearSlop;
+
+	// Main iteration loop.
+	const int32 k_maxIters = 20;
+	int32 iter = 0;
+	while (iter < k_maxIters && v.Length() - sigma > tolerance)
+	{
+		b2Assert(simplex.m_count < 3);
+
+        output->iterations += 1;
+
+		// Support in direction -v (A - B)
+		indexA = proxyA->GetSupport(b2MulT(xfA.q, -v));
+		wA = b2Mul(xfA, proxyA->GetVertex(indexA));
+		indexB = proxyB->GetSupport(b2MulT(xfB.q, v));
+		wB = b2Mul(xfB, proxyB->GetVertex(indexB));
+        b2Vec2 p = wA - wB;
+
+        // -v is a normal at p
+        v.Normalize();
+
+        // Intersect ray with plane
+		float vp = b2Dot(v, p);
+        float vr = b2Dot(v, r);
+		if (vp - sigma > lambda * vr)
+		{
+			if (vr <= 0.0f)
+			{
+				return false;
+			}
+
+			lambda = (vp - sigma) / vr;
+			if (lambda > 1.0f)
+			{
+				return false;
+			}
+
+            n = -v;
+            simplex.m_count = 0;
+		}
+
+        // Reverse simplex since it works with B - A.
+        // Shift by lambda * r because we want the closest point to the current clip point.
+        // Note that the support point p is not shifted because we want the plane equation
+        // to be formed in unshifted space.
+		b2SimplexVertex* vertex = vertices + simplex.m_count;
+		vertex->indexA = indexB;
+		vertex->wA = wB + lambda * r;
+		vertex->indexB = indexA;
+		vertex->wB = wA;
+		vertex->w = vertex->wB - vertex->wA;
+		vertex->a = 1.0f;
+		simplex.m_count += 1;
+
+		switch (simplex.m_count)
+		{
+		case 1:
+			break;
+
+		case 2:
+			simplex.Solve2();
+			break;
+
+		case 3:
+			simplex.Solve3();
+			break;
+
+		default:
+			b2Assert(false);
+		}
+		
+		// If we have 3 points, then the origin is in the corresponding triangle.
+		if (simplex.m_count == 3)
+		{
+			// Overlap
+			return false;
+		}
+
+		// Get search direction.
+		v = simplex.GetClosestPoint();
+
+		// Iteration count is equated to the number of support point calls.
+		++iter;
+	}
+
+	if (iter == 0)
+	{
+		// Initial overlap
+		return false;
+	}
+
+	// Prepare output.
+	b2Vec2 pointA, pointB;
+	simplex.GetWitnessPoints(&pointB, &pointA);
+
+	if (v.LengthSquared() > 0.0f)
+	{
+        n = -v;
+		n.Normalize();
+	}
+
+    output->point = pointA + radiusA * n;
+	output->normal = n;
+	output->lambda = lambda;
+	output->iterations = iter;
+	return true;
+}

3rd/box2d/src/collision/b2_dynamic_tree.cpp

@@ -0,0 +1,801 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+#include "box2d/b2_dynamic_tree.h"
+#include <string.h>
+
+b2DynamicTree::b2DynamicTree()
+{
+	m_root = b2_nullNode;
+
+	m_nodeCapacity = 16;
+	m_nodeCount = 0;
+	m_nodes = (b2TreeNode*)b2Alloc(m_nodeCapacity * sizeof(b2TreeNode));
+	memset(m_nodes, 0, m_nodeCapacity * sizeof(b2TreeNode));
+
+	// Build a linked list for the free list.
+	for (int32 i = 0; i < m_nodeCapacity - 1; ++i)
+	{
+		m_nodes[i].next = i + 1;
+		m_nodes[i].height = -1;
+	}
+	m_nodes[m_nodeCapacity-1].next = b2_nullNode;
+	m_nodes[m_nodeCapacity-1].height = -1;
+	m_freeList = 0;
+
+	m_insertionCount = 0;
+}
+
+b2DynamicTree::~b2DynamicTree()
+{
+	// This frees the entire tree in one shot.
+	b2Free(m_nodes);
+}
+
+// Allocate a node from the pool. Grow the pool if necessary.
+int32 b2DynamicTree::AllocateNode()
+{
+	// Expand the node pool as needed.
+	if (m_freeList == b2_nullNode)
+	{
+		b2Assert(m_nodeCount == m_nodeCapacity);
+
+		// The free list is empty. Rebuild a bigger pool.
+		b2TreeNode* oldNodes = m_nodes;
+		m_nodeCapacity *= 2;
+		m_nodes = (b2TreeNode*)b2Alloc(m_nodeCapacity * sizeof(b2TreeNode));
+		memcpy(m_nodes, oldNodes, m_nodeCount * sizeof(b2TreeNode));
+		b2Free(oldNodes);
+
+		// Build a linked list for the free list. The parent
+		// pointer becomes the "next" pointer.
+		for (int32 i = m_nodeCount; i < m_nodeCapacity - 1; ++i)
+		{
+			m_nodes[i].next = i + 1;
+			m_nodes[i].height = -1;
+		}
+		m_nodes[m_nodeCapacity-1].next = b2_nullNode;
+		m_nodes[m_nodeCapacity-1].height = -1;
+		m_freeList = m_nodeCount;
+	}
+
+	// Peel a node off the free list.
+	int32 nodeId = m_freeList;
+	m_freeList = m_nodes[nodeId].next;
+	m_nodes[nodeId].parent = b2_nullNode;
+	m_nodes[nodeId].child1 = b2_nullNode;
+	m_nodes[nodeId].child2 = b2_nullNode;
+	m_nodes[nodeId].height = 0;
+	m_nodes[nodeId].userData = nullptr;
+	m_nodes[nodeId].moved = false;
+	++m_nodeCount;
+	return nodeId;
+}
+
+// Return a node to the pool.
+void b2DynamicTree::FreeNode(int32 nodeId)
+{
+	b2Assert(0 <= nodeId && nodeId < m_nodeCapacity);
+	b2Assert(0 < m_nodeCount);
+	m_nodes[nodeId].next = m_freeList;
+	m_nodes[nodeId].height = -1;
+	m_freeList = nodeId;
+	--m_nodeCount;
+}
+
+// Create a proxy in the tree as a leaf node. We return the index
+// of the node instead of a pointer so that we can grow
+// the node pool.
+int32 b2DynamicTree::CreateProxy(const b2AABB& aabb, void* userData)
+{
+	int32 proxyId = AllocateNode();
+
+	// Fatten the aabb.
+	b2Vec2 r(b2_aabbExtension, b2_aabbExtension);
+	m_nodes[proxyId].aabb.lowerBound = aabb.lowerBound - r;
+	m_nodes[proxyId].aabb.upperBound = aabb.upperBound + r;
+	m_nodes[proxyId].userData = userData;
+	m_nodes[proxyId].height = 0;
+	m_nodes[proxyId].moved = true;
+
+	InsertLeaf(proxyId);
+
+	return proxyId;
+}
+
+void b2DynamicTree::DestroyProxy(int32 proxyId)
+{
+	b2Assert(0 <= proxyId && proxyId < m_nodeCapacity);
+	b2Assert(m_nodes[proxyId].IsLeaf());
+
+	RemoveLeaf(proxyId);
+	FreeNode(proxyId);
+}
+
+bool b2DynamicTree::MoveProxy(int32 proxyId, const b2AABB& aabb, const b2Vec2& displacement)
+{
+	b2Assert(0 <= proxyId && proxyId < m_nodeCapacity);
+
+	b2Assert(m_nodes[proxyId].IsLeaf());
+
+	// Extend AABB
+	b2AABB fatAABB;
+	b2Vec2 r(b2_aabbExtension, b2_aabbExtension);
+	fatAABB.lowerBound = aabb.lowerBound - r;
+	fatAABB.upperBound = aabb.upperBound + r;
+
+	// Predict AABB movement
+	b2Vec2 d = b2_aabbMultiplier * displacement;
+
+	if (d.x < 0.0f)
+	{
+		fatAABB.lowerBound.x += d.x;
+	}
+	else
+	{
+		fatAABB.upperBound.x += d.x;
+	}
+
+	if (d.y < 0.0f)
+	{
+		fatAABB.lowerBound.y += d.y;
+	}
+	else
+	{
+		fatAABB.upperBound.y += d.y;
+	}
+
+	const b2AABB& treeAABB = m_nodes[proxyId].aabb;
+	if (treeAABB.Contains(aabb))
+	{
+		// The tree AABB still contains the object, but it might be too large.
+		// Perhaps the object was moving fast but has since gone to sleep.
+		// The huge AABB is larger than the new fat AABB.
+		b2AABB hugeAABB;
+		hugeAABB.lowerBound = fatAABB.lowerBound - 4.0f * r;
+		hugeAABB.upperBound = fatAABB.upperBound + 4.0f * r;
+
+		if (hugeAABB.Contains(treeAABB))
+		{
+			// The tree AABB contains the object AABB and the tree AABB is
+			// not too large. No tree update needed.
+			return false;
+		}
+
+		// Otherwise the tree AABB is huge and needs to be shrunk
+	}
+
+	RemoveLeaf(proxyId);
+
+	m_nodes[proxyId].aabb = fatAABB;
+
+	InsertLeaf(proxyId);
+
+	m_nodes[proxyId].moved = true;
+
+	return true;
+}
+
+void b2DynamicTree::InsertLeaf(int32 leaf)
+{
+	++m_insertionCount;
+
+	if (m_root == b2_nullNode)
+	{
+		m_root = leaf;
+		m_nodes[m_root].parent = b2_nullNode;
+		return;
+	}
+
+	// Find the best sibling for this node
+	b2AABB leafAABB = m_nodes[leaf].aabb;
+	int32 index = m_root;
+	while (m_nodes[index].IsLeaf() == false)
+	{
+		int32 child1 = m_nodes[index].child1;
+		int32 child2 = m_nodes[index].child2;
+
+		float area = m_nodes[index].aabb.GetPerimeter();
+
+		b2AABB combinedAABB;
+		combinedAABB.Combine(m_nodes[index].aabb, leafAABB);
+		float combinedArea = combinedAABB.GetPerimeter();
+
+		// Cost of creating a new parent for this node and the new leaf
+		float cost = 2.0f * combinedArea;
+
+		// Minimum cost of pushing the leaf further down the tree
+		float inheritanceCost = 2.0f * (combinedArea - area);
+
+		// Cost of descending into child1
+		float cost1;
+		if (m_nodes[child1].IsLeaf())
+		{
+			b2AABB aabb;
+			aabb.Combine(leafAABB, m_nodes[child1].aabb);
+			cost1 = aabb.GetPerimeter() + inheritanceCost;
+		}
+		else
+		{
+			b2AABB aabb;
+			aabb.Combine(leafAABB, m_nodes[child1].aabb);
+			float oldArea = m_nodes[child1].aabb.GetPerimeter();
+			float newArea = aabb.GetPerimeter();
+			cost1 = (newArea - oldArea) + inheritanceCost;
+		}
+
+		// Cost of descending into child2
+		float cost2;
+		if (m_nodes[child2].IsLeaf())
+		{
+			b2AABB aabb;
+			aabb.Combine(leafAABB, m_nodes[child2].aabb);
+			cost2 = aabb.GetPerimeter() + inheritanceCost;
+		}
+		else
+		{
+			b2AABB aabb;
+			aabb.Combine(leafAABB, m_nodes[child2].aabb);
+			float oldArea = m_nodes[child2].aabb.GetPerimeter();
+			float newArea = aabb.GetPerimeter();
+			cost2 = newArea - oldArea + inheritanceCost;
+		}
+
+		// Descend according to the minimum cost.
+		if (cost < cost1 && cost < cost2)
+		{
+			break;
+		}
+
+		// Descend
+		if (cost1 < cost2)
+		{
+			index = child1;
+		}
+		else
+		{
+			index = child2;
+		}
+	}
+
+	int32 sibling = index;
+
+	// Create a new parent.
+	int32 oldParent = m_nodes[sibling].parent;
+	int32 newParent = AllocateNode();
+	m_nodes[newParent].parent = oldParent;
+	m_nodes[newParent].userData = nullptr;
+	m_nodes[newParent].aabb.Combine(leafAABB, m_nodes[sibling].aabb);
+	m_nodes[newParent].height = m_nodes[sibling].height + 1;
+
+	if (oldParent != b2_nullNode)
+	{
+		// The sibling was not the root.
+		if (m_nodes[oldParent].child1 == sibling)
+		{
+			m_nodes[oldParent].child1 = newParent;
+		}
+		else
+		{
+			m_nodes[oldParent].child2 = newParent;
+		}
+
+		m_nodes[newParent].child1 = sibling;
+		m_nodes[newParent].child2 = leaf;
+		m_nodes[sibling].parent = newParent;
+		m_nodes[leaf].parent = newParent;
+	}
+	else
+	{
+		// The sibling was the root.
+		m_nodes[newParent].child1 = sibling;
+		m_nodes[newParent].child2 = leaf;
+		m_nodes[sibling].parent = newParent;
+		m_nodes[leaf].parent = newParent;
+		m_root = newParent;
+	}
+
+	// Walk back up the tree fixing heights and AABBs
+	index = m_nodes[leaf].parent;
+	while (index != b2_nullNode)
+	{
+		index = Balance(index);
+
+		int32 child1 = m_nodes[index].child1;
+		int32 child2 = m_nodes[index].child2;
+
+		b2Assert(child1 != b2_nullNode);
+		b2Assert(child2 != b2_nullNode);
+
+		m_nodes[index].height = 1 + b2Max(m_nodes[child1].height, m_nodes[child2].height);
+		m_nodes[index].aabb.Combine(m_nodes[child1].aabb, m_nodes[child2].aabb);
+
+		index = m_nodes[index].parent;
+	}
+
+	//Validate();
+}
+
+void b2DynamicTree::RemoveLeaf(int32 leaf)
+{
+	if (leaf == m_root)
+	{
+		m_root = b2_nullNode;
+		return;
+	}
+
+	int32 parent = m_nodes[leaf].parent;
+	int32 grandParent = m_nodes[parent].parent;
+	int32 sibling;
+	if (m_nodes[parent].child1 == leaf)
+	{
+		sibling = m_nodes[parent].child2;
+	}
+	else
+	{
+		sibling = m_nodes[parent].child1;
+	}
+
+	if (grandParent != b2_nullNode)
+	{
+		// Destroy parent and connect sibling to grandParent.
+		if (m_nodes[grandParent].child1 == parent)
+		{
+			m_nodes[grandParent].child1 = sibling;
+		}
+		else
+		{
+			m_nodes[grandParent].child2 = sibling;
+		}
+		m_nodes[sibling].parent = grandParent;
+		FreeNode(parent);
+
+		// Adjust ancestor bounds.
+		int32 index = grandParent;
+		while (index != b2_nullNode)
+		{
+			index = Balance(index);
+
+			int32 child1 = m_nodes[index].child1;
+			int32 child2 = m_nodes[index].child2;
+
+			m_nodes[index].aabb.Combine(m_nodes[child1].aabb, m_nodes[child2].aabb);
+			m_nodes[index].height = 1 + b2Max(m_nodes[child1].height, m_nodes[child2].height);
+
+			index = m_nodes[index].parent;
+		}
+	}
+	else
+	{
+		m_root = sibling;
+		m_nodes[sibling].parent = b2_nullNode;
+		FreeNode(parent);
+	}
+
+	//Validate();
+}
+
+// Perform a left or right rotation if node A is imbalanced.
+// Returns the new root index.
+int32 b2DynamicTree::Balance(int32 iA)
+{
+	b2Assert(iA != b2_nullNode);
+
+	b2TreeNode* A = m_nodes + iA;
+	if (A->IsLeaf() || A->height < 2)
+	{
+		return iA;
+	}
+
+	int32 iB = A->child1;
+	int32 iC = A->child2;
+	b2Assert(0 <= iB && iB < m_nodeCapacity);
+	b2Assert(0 <= iC && iC < m_nodeCapacity);
+
+	b2TreeNode* B = m_nodes + iB;
+	b2TreeNode* C = m_nodes + iC;
+
+	int32 balance = C->height - B->height;
+
+	// Rotate C up
+	if (balance > 1)
+	{
+		int32 iF = C->child1;
+		int32 iG = C->child2;
+		b2TreeNode* F = m_nodes + iF;
+		b2TreeNode* G = m_nodes + iG;
+		b2Assert(0 <= iF && iF < m_nodeCapacity);
+		b2Assert(0 <= iG && iG < m_nodeCapacity);
+
+		// Swap A and C
+		C->child1 = iA;
+		C->parent = A->parent;
+		A->parent = iC;
+
+		// A's old parent should point to C
+		if (C->parent != b2_nullNode)
+		{
+			if (m_nodes[C->parent].child1 == iA)
+			{
+				m_nodes[C->parent].child1 = iC;
+			}
+			else
+			{
+				b2Assert(m_nodes[C->parent].child2 == iA);
+				m_nodes[C->parent].child2 = iC;
+			}
+		}
+		else
+		{
+			m_root = iC;
+		}
+
+		// Rotate
+		if (F->height > G->height)
+		{
+			C->child2 = iF;
+			A->child2 = iG;
+			G->parent = iA;
+			A->aabb.Combine(B->aabb, G->aabb);
+			C->aabb.Combine(A->aabb, F->aabb);
+
+			A->height = 1 + b2Max(B->height, G->height);
+			C->height = 1 + b2Max(A->height, F->height);
+		}
+		else
+		{
+			C->child2 = iG;
+			A->child2 = iF;
+			F->parent = iA;
+			A->aabb.Combine(B->aabb, F->aabb);
+			C->aabb.Combine(A->aabb, G->aabb);
+
+			A->height = 1 + b2Max(B->height, F->height);
+			C->height = 1 + b2Max(A->height, G->height);
+		}
+
+		return iC;
+	}
+	
+	// Rotate B up
+	if (balance < -1)
+	{
+		int32 iD = B->child1;
+		int32 iE = B->child2;
+		b2TreeNode* D = m_nodes + iD;
+		b2TreeNode* E = m_nodes + iE;
+		b2Assert(0 <= iD && iD < m_nodeCapacity);
+		b2Assert(0 <= iE && iE < m_nodeCapacity);
+
+		// Swap A and B
+		B->child1 = iA;
+		B->parent = A->parent;
+		A->parent = iB;
+
+		// A's old parent should point to B
+		if (B->parent != b2_nullNode)
+		{
+			if (m_nodes[B->parent].child1 == iA)
+			{
+				m_nodes[B->parent].child1 = iB;
+			}
+			else
+			{
+				b2Assert(m_nodes[B->parent].child2 == iA);
+				m_nodes[B->parent].child2 = iB;
+			}
+		}
+		else
+		{
+			m_root = iB;
+		}
+
+		// Rotate
+		if (D->height > E->height)
+		{
+			B->child2 = iD;
+			A->child1 = iE;
+			E->parent = iA;
+			A->aabb.Combine(C->aabb, E->aabb);
+			B->aabb.Combine(A->aabb, D->aabb);
+
+			A->height = 1 + b2Max(C->height, E->height);
+			B->height = 1 + b2Max(A->height, D->height);
+		}
+		else
+		{
+			B->child2 = iE;
+			A->child1 = iD;
+			D->parent = iA;
+			A->aabb.Combine(C->aabb, D->aabb);
+			B->aabb.Combine(A->aabb, E->aabb);
+
+			A->height = 1 + b2Max(C->height, D->height);
+			B->height = 1 + b2Max(A->height, E->height);
+		}
+
+		return iB;
+	}
+
+	return iA;
+}
+
+int32 b2DynamicTree::GetHeight() const
+{
+	if (m_root == b2_nullNode)
+	{
+		return 0;
+	}
+
+	return m_nodes[m_root].height;
+}
+
+//
+float b2DynamicTree::GetAreaRatio() const
+{
+	if (m_root == b2_nullNode)
+	{
+		return 0.0f;
+	}
+
+	const b2TreeNode* root = m_nodes + m_root;
+	float rootArea = root->aabb.GetPerimeter();
+
+	float totalArea = 0.0f;
+	for (int32 i = 0; i < m_nodeCapacity; ++i)
+	{
+		const b2TreeNode* node = m_nodes + i;
+		if (node->height < 0)
+		{
+			// Free node in pool
+			continue;
+		}
+
+		totalArea += node->aabb.GetPerimeter();
+	}
+
+	return totalArea / rootArea;
+}
+
+// Compute the height of a sub-tree.
+int32 b2DynamicTree::ComputeHeight(int32 nodeId) const
+{
+	b2Assert(0 <= nodeId && nodeId < m_nodeCapacity);
+	b2TreeNode* node = m_nodes + nodeId;
+
+	if (node->IsLeaf())
+	{
+		return 0;
+	}
+
+	int32 height1 = ComputeHeight(node->child1);
+	int32 height2 = ComputeHeight(node->child2);
+	return 1 + b2Max(height1, height2);
+}
+
+int32 b2DynamicTree::ComputeHeight() const
+{
+	int32 height = ComputeHeight(m_root);
+	return height;
+}
+
+void b2DynamicTree::ValidateStructure(int32 index) const
+{
+	if (index == b2_nullNode)
+	{
+		return;
+	}
+
+	if (index == m_root)
+	{
+		b2Assert(m_nodes[index].parent == b2_nullNode);
+	}
+
+	const b2TreeNode* node = m_nodes + index;
+
+	int32 child1 = node->child1;
+	int32 child2 = node->child2;
+
+	if (node->IsLeaf())
+	{
+		b2Assert(child1 == b2_nullNode);
+		b2Assert(child2 == b2_nullNode);
+		b2Assert(node->height == 0);
+		return;
+	}
+
+	b2Assert(0 <= child1 && child1 < m_nodeCapacity);
+	b2Assert(0 <= child2 && child2 < m_nodeCapacity);
+
+	b2Assert(m_nodes[child1].parent == index);
+	b2Assert(m_nodes[child2].parent == index);
+
+	ValidateStructure(child1);
+	ValidateStructure(child2);
+}
+
+void b2DynamicTree::ValidateMetrics(int32 index) const
+{
+	if (index == b2_nullNode)
+	{
+		return;
+	}
+
+	const b2TreeNode* node = m_nodes + index;
+
+	int32 child1 = node->child1;
+	int32 child2 = node->child2;
+
+	if (node->IsLeaf())
+	{
+		b2Assert(child1 == b2_nullNode);
+		b2Assert(child2 == b2_nullNode);
+		b2Assert(node->height == 0);
+		return;
+	}
+
+	b2Assert(0 <= child1 && child1 < m_nodeCapacity);
+	b2Assert(0 <= child2 && child2 < m_nodeCapacity);
+
+	int32 height1 = m_nodes[child1].height;
+	int32 height2 = m_nodes[child2].height;
+	int32 height;
+	height = 1 + b2Max(height1, height2);
+	b2Assert(node->height == height);
+
+	b2AABB aabb;
+	aabb.Combine(m_nodes[child1].aabb, m_nodes[child2].aabb);
+
+	b2Assert(aabb.lowerBound == node->aabb.lowerBound);
+	b2Assert(aabb.upperBound == node->aabb.upperBound);
+
+	ValidateMetrics(child1);
+	ValidateMetrics(child2);
+}
+
+void b2DynamicTree::Validate() const
+{
+#if defined(b2DEBUG)
+	ValidateStructure(m_root);
+	ValidateMetrics(m_root);
+
+	int32 freeCount = 0;
+	int32 freeIndex = m_freeList;
+	while (freeIndex != b2_nullNode)
+	{
+		b2Assert(0 <= freeIndex && freeIndex < m_nodeCapacity);
+		freeIndex = m_nodes[freeIndex].next;
+		++freeCount;
+	}
+
+	b2Assert(GetHeight() == ComputeHeight());
+
+	b2Assert(m_nodeCount + freeCount == m_nodeCapacity);
+#endif
+}
+
+int32 b2DynamicTree::GetMaxBalance() const
+{
+	int32 maxBalance = 0;
+	for (int32 i = 0; i < m_nodeCapacity; ++i)
+	{
+		const b2TreeNode* node = m_nodes + i;
+		if (node->height <= 1)
+		{
+			continue;
+		}
+
+		b2Assert(node->IsLeaf() == false);
+
+		int32 child1 = node->child1;
+		int32 child2 = node->child2;
+		int32 balance = b2Abs(m_nodes[child2].height - m_nodes[child1].height);
+		maxBalance = b2Max(maxBalance, balance);
+	}
+
+	return maxBalance;
+}
+
+void b2DynamicTree::RebuildBottomUp()
+{
+	int32* nodes = (int32*)b2Alloc(m_nodeCount * sizeof(int32));
+	int32 count = 0;
+
+	// Build array of leaves. Free the rest.
+	for (int32 i = 0; i < m_nodeCapacity; ++i)
+	{
+		if (m_nodes[i].height < 0)
+		{
+			// free node in pool
+			continue;
+		}
+
+		if (m_nodes[i].IsLeaf())
+		{
+			m_nodes[i].parent = b2_nullNode;
+			nodes[count] = i;
+			++count;
+		}
+		else
+		{
+			FreeNode(i);
+		}
+	}
+
+	while (count > 1)
+	{
+		float minCost = b2_maxFloat;
+		int32 iMin = -1, jMin = -1;
+		for (int32 i = 0; i < count; ++i)
+		{
+			b2AABB aabbi = m_nodes[nodes[i]].aabb;
+
+			for (int32 j = i + 1; j < count; ++j)
+			{
+				b2AABB aabbj = m_nodes[nodes[j]].aabb;
+				b2AABB b;
+				b.Combine(aabbi, aabbj);
+				float cost = b.GetPerimeter();
+				if (cost < minCost)
+				{
+					iMin = i;
+					jMin = j;
+					minCost = cost;
+				}
+			}
+		}
+
+		int32 index1 = nodes[iMin];
+		int32 index2 = nodes[jMin];
+		b2TreeNode* child1 = m_nodes + index1;
+		b2TreeNode* child2 = m_nodes + index2;
+
+		int32 parentIndex = AllocateNode();
+		b2TreeNode* parent = m_nodes + parentIndex;
+		parent->child1 = index1;
+		parent->child2 = index2;
+		parent->height = 1 + b2Max(child1->height, child2->height);
+		parent->aabb.Combine(child1->aabb, child2->aabb);
+		parent->parent = b2_nullNode;
+
+		child1->parent = parentIndex;
+		child2->parent = parentIndex;
+
+		nodes[jMin] = nodes[count-1];
+		nodes[iMin] = parentIndex;
+		--count;
+	}
+
+	m_root = nodes[0];
+	b2Free(nodes);
+
+	Validate();
+}
+
+void b2DynamicTree::ShiftOrigin(const b2Vec2& newOrigin)
+{
+	// Build array of leaves. Free the rest.
+	for (int32 i = 0; i < m_nodeCapacity; ++i)
+	{
+		m_nodes[i].aabb.lowerBound -= newOrigin;
+		m_nodes[i].aabb.upperBound -= newOrigin;
+	}
+}

3rd/box2d/src/collision/b2_edge_shape.cpp

@@ -0,0 +1,158 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#include "box2d/b2_edge_shape.h"
+#include "box2d/b2_block_allocator.h"
+#include <new>
+
+void b2EdgeShape::SetOneSided(const b2Vec2& v0, const b2Vec2& v1, const b2Vec2& v2, const b2Vec2& v3)
+{
+	m_vertex0 = v0;
+	m_vertex1 = v1;
+	m_vertex2 = v2;
+	m_vertex3 = v3;
+	m_oneSided = true;
+}
+
+void b2EdgeShape::SetTwoSided(const b2Vec2& v1, const b2Vec2& v2)
+{
+	m_vertex1 = v1;
+	m_vertex2 = v2;
+	m_oneSided = false;
+}
+
+b2Shape* b2EdgeShape::Clone(b2BlockAllocator* allocator) const
+{
+	void* mem = allocator->Allocate(sizeof(b2EdgeShape));
+	b2EdgeShape* clone = new (mem) b2EdgeShape;
+	*clone = *this;
+	return clone;
+}
+
+int32 b2EdgeShape::GetChildCount() const
+{
+	return 1;
+}
+
+bool b2EdgeShape::TestPoint(const b2Transform& xf, const b2Vec2& p) const
+{
+	B2_NOT_USED(xf);
+	B2_NOT_USED(p);
+	return false;
+}
+
+// p = p1 + t * d
+// v = v1 + s * e
+// p1 + t * d = v1 + s * e
+// s * e - t * d = p1 - v1
+bool b2EdgeShape::RayCast(b2RayCastOutput* output, const b2RayCastInput& input,
+							const b2Transform& xf, int32 childIndex) const
+{
+	B2_NOT_USED(childIndex);
+
+	// Put the ray into the edge's frame of reference.
+	b2Vec2 p1 = b2MulT(xf.q, input.p1 - xf.p);
+	b2Vec2 p2 = b2MulT(xf.q, input.p2 - xf.p);
+	b2Vec2 d = p2 - p1;
+
+	b2Vec2 v1 = m_vertex1;
+	b2Vec2 v2 = m_vertex2;
+	b2Vec2 e = v2 - v1;
+
+	// Normal points to the right, looking from v1 at v2
+	b2Vec2 normal(e.y, -e.x);
+	normal.Normalize();
+
+	// q = p1 + t * d
+	// dot(normal, q - v1) = 0
+	// dot(normal, p1 - v1) + t * dot(normal, d) = 0
+	float numerator = b2Dot(normal, v1 - p1);
+	if (m_oneSided && numerator > 0.0f)
+	{
+		return false;
+	}
+
+	float denominator = b2Dot(normal, d);
+
+	if (denominator == 0.0f)
+	{
+		return false;
+	}
+
+	float t = numerator / denominator;
+	if (t < 0.0f || input.maxFraction < t)
+	{
+		return false;
+	}
+
+	b2Vec2 q = p1 + t * d;
+
+	// q = v1 + s * r
+	// s = dot(q - v1, r) / dot(r, r)
+	b2Vec2 r = v2 - v1;
+	float rr = b2Dot(r, r);
+	if (rr == 0.0f)
+	{
+		return false;
+	}
+
+	float s = b2Dot(q - v1, r) / rr;
+	if (s < 0.0f || 1.0f < s)
+	{
+		return false;
+	}
+
+	output->fraction = t;
+	if (numerator > 0.0f)
+	{
+		output->normal = -b2Mul(xf.q, normal);
+	}
+	else
+	{
+		output->normal = b2Mul(xf.q, normal);
+	}
+	return true;
+}
+
+void b2EdgeShape::ComputeAABB(b2AABB* aabb, const b2Transform& xf, int32 childIndex) const
+{
+	B2_NOT_USED(childIndex);
+
+	b2Vec2 v1 = b2Mul(xf, m_vertex1);
+	b2Vec2 v2 = b2Mul(xf, m_vertex2);
+
+	b2Vec2 lower = b2Min(v1, v2);
+	b2Vec2 upper = b2Max(v1, v2);
+
+	b2Vec2 r(m_radius, m_radius);
+	aabb->lowerBound = lower - r;
+	aabb->upperBound = upper + r;
+}
+
+void b2EdgeShape::ComputeMass(b2MassData* massData, float density) const
+{
+	B2_NOT_USED(density);
+
+	massData->mass = 0.0f;
+	massData->center = 0.5f * (m_vertex1 + m_vertex2);
+	massData->I = 0.0f;
+}

3rd/box2d/src/collision/b2_polygon_shape.cpp

@@ -0,0 +1,366 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#include "box2d/b2_polygon_shape.h"
+#include "box2d/b2_block_allocator.h"
+
+#include <new>
+
+b2PolygonShape::b2PolygonShape()
+{
+	m_type = e_polygon;
+	m_radius = b2_polygonRadius;
+	m_count = 0;
+	m_centroid.SetZero();
+}
+
+b2Shape* b2PolygonShape::Clone(b2BlockAllocator* allocator) const
+{
+	void* mem = allocator->Allocate(sizeof(b2PolygonShape));
+	b2PolygonShape* clone = new (mem) b2PolygonShape;
+	*clone = *this;
+	return clone;
+}
+
+void b2PolygonShape::SetAsBox(float hx, float hy)
+{
+	m_count = 4;
+	m_vertices[0].Set(-hx, -hy);
+	m_vertices[1].Set( hx, -hy);
+	m_vertices[2].Set( hx,  hy);
+	m_vertices[3].Set(-hx,  hy);
+	m_normals[0].Set(0.0f, -1.0f);
+	m_normals[1].Set(1.0f, 0.0f);
+	m_normals[2].Set(0.0f, 1.0f);
+	m_normals[3].Set(-1.0f, 0.0f);
+	m_centroid.SetZero();
+}
+
+void b2PolygonShape::SetAsBox(float hx, float hy, const b2Vec2& center, float angle)
+{
+	m_count = 4;
+	m_vertices[0].Set(-hx, -hy);
+	m_vertices[1].Set( hx, -hy);
+	m_vertices[2].Set( hx,  hy);
+	m_vertices[3].Set(-hx,  hy);
+	m_normals[0].Set(0.0f, -1.0f);
+	m_normals[1].Set(1.0f, 0.0f);
+	m_normals[2].Set(0.0f, 1.0f);
+	m_normals[3].Set(-1.0f, 0.0f);
+	m_centroid = center;
+
+	b2Transform xf;
+	xf.p = center;
+	xf.q.Set(angle);
+
+	// Transform vertices and normals.
+	for (int32 i = 0; i < m_count; ++i)
+	{
+		m_vertices[i] = b2Mul(xf, m_vertices[i]);
+		m_normals[i] = b2Mul(xf.q, m_normals[i]);
+	}
+}
+
+int32 b2PolygonShape::GetChildCount() const
+{
+	return 1;
+}
+
+static b2Vec2 ComputeCentroid(const b2Vec2* vs, int32 count)
+{
+	b2Assert(count >= 3);
+
+	b2Vec2 c(0.0f, 0.0f);
+	float area = 0.0f;
+
+	// Get a reference point for forming triangles.
+	// Use the first vertex to reduce round-off errors.
+	b2Vec2 s = vs[0];
+
+	const float inv3 = 1.0f / 3.0f;
+
+	for (int32 i = 0; i < count; ++i)
+	{
+		// Triangle vertices.
+		b2Vec2 p1 = vs[0] - s;
+		b2Vec2 p2 = vs[i] - s;
+		b2Vec2 p3 = i + 1 < count ? vs[i+1] - s : vs[0] - s;
+
+		b2Vec2 e1 = p2 - p1;
+		b2Vec2 e2 = p3 - p1;
+
+		float D = b2Cross(e1, e2);
+
+		float triangleArea = 0.5f * D;
+		area += triangleArea;
+
+		// Area weighted centroid
+		c += triangleArea * inv3 * (p1 + p2 + p3);
+	}
+
+	// Centroid
+	b2Assert(area > b2_epsilon);
+	c = (1.0f / area) * c + s;
+	return c;
+}
+
+bool b2PolygonShape::Set(const b2Vec2* vertices, int32 count)
+{
+	b2Hull hull = b2ComputeHull(vertices, count);
+
+	if (hull.count < 3)
+	{
+		return false;
+	}
+
+	Set(hull);
+
+	return true;
+}
+
+void b2PolygonShape::Set(const b2Hull& hull)
+{
+	b2Assert(hull.count >= 3);
+
+	m_count = hull.count;
+
+	// Copy vertices
+	for (int32 i = 0; i < hull.count; ++i)
+	{
+		m_vertices[i] = hull.points[i];
+	}
+
+	// Compute normals. Ensure the edges have non-zero length.
+	for (int32 i = 0; i < m_count; ++i)
+	{
+		int32 i1 = i;
+		int32 i2 = i + 1 < m_count ? i + 1 : 0;
+		b2Vec2 edge = m_vertices[i2] - m_vertices[i1];
+		b2Assert(edge.LengthSquared() > b2_epsilon * b2_epsilon);
+		m_normals[i] = b2Cross(edge, 1.0f);
+		m_normals[i].Normalize();
+	}
+
+	// Compute the polygon centroid.
+	m_centroid = ComputeCentroid(m_vertices, m_count);
+}
+
+bool b2PolygonShape::TestPoint(const b2Transform& xf, const b2Vec2& p) const
+{
+	b2Vec2 pLocal = b2MulT(xf.q, p - xf.p);
+
+	for (int32 i = 0; i < m_count; ++i)
+	{
+		float dot = b2Dot(m_normals[i], pLocal - m_vertices[i]);
+		if (dot > 0.0f)
+		{
+			return false;
+		}
+	}
+
+	return true;
+}
+
+bool b2PolygonShape::RayCast(b2RayCastOutput* output, const b2RayCastInput& input,
+								const b2Transform& xf, int32 childIndex) const
+{
+	B2_NOT_USED(childIndex);
+
+	// Put the ray into the polygon's frame of reference.
+	b2Vec2 p1 = b2MulT(xf.q, input.p1 - xf.p);
+	b2Vec2 p2 = b2MulT(xf.q, input.p2 - xf.p);
+	b2Vec2 d = p2 - p1;
+
+	float lower = 0.0f, upper = input.maxFraction;
+
+	int32 index = -1;
+
+	for (int32 i = 0; i < m_count; ++i)
+	{
+		// p = p1 + a * d
+		// dot(normal, p - v) = 0
+		// dot(normal, p1 - v) + a * dot(normal, d) = 0
+		float numerator = b2Dot(m_normals[i], m_vertices[i] - p1);
+		float denominator = b2Dot(m_normals[i], d);
+
+		if (denominator == 0.0f)
+		{	
+			if (numerator < 0.0f)
+			{
+				return false;
+			}
+		}
+		else
+		{
+			// Note: we want this predicate without division:
+			// lower < numerator / denominator, where denominator < 0
+			// Since denominator < 0, we have to flip the inequality:
+			// lower < numerator / denominator <==> denominator * lower > numerator.
+			if (denominator < 0.0f && numerator < lower * denominator)
+			{
+				// Increase lower.
+				// The segment enters this half-space.
+				lower = numerator / denominator;
+				index = i;
+			}
+			else if (denominator > 0.0f && numerator < upper * denominator)
+			{
+				// Decrease upper.
+				// The segment exits this half-space.
+				upper = numerator / denominator;
+			}
+		}
+
+		// The use of epsilon here causes the assert on lower to trip
+		// in some cases. Apparently the use of epsilon was to make edge
+		// shapes work, but now those are handled separately.
+		//if (upper < lower - b2_epsilon)
+		if (upper < lower)
+		{
+			return false;
+		}
+	}
+
+	b2Assert(0.0f <= lower && lower <= input.maxFraction);
+
+	if (index >= 0)
+	{
+		output->fraction = lower;
+		output->normal = b2Mul(xf.q, m_normals[index]);
+		return true;
+	}
+
+	return false;
+}
+
+void b2PolygonShape::ComputeAABB(b2AABB* aabb, const b2Transform& xf, int32 childIndex) const
+{
+	B2_NOT_USED(childIndex);
+
+	b2Vec2 lower = b2Mul(xf, m_vertices[0]);
+	b2Vec2 upper = lower;
+
+	for (int32 i = 1; i < m_count; ++i)
+	{
+		b2Vec2 v = b2Mul(xf, m_vertices[i]);
+		lower = b2Min(lower, v);
+		upper = b2Max(upper, v);
+	}
+
+	b2Vec2 r(m_radius, m_radius);
+	aabb->lowerBound = lower - r;
+	aabb->upperBound = upper + r;
+}
+
+void b2PolygonShape::ComputeMass(b2MassData* massData, float density) const
+{
+	// Polygon mass, centroid, and inertia.
+	// Let rho be the polygon density in mass per unit area.
+	// Then:
+	// mass = rho * int(dA)
+	// centroid.x = (1/mass) * rho * int(x * dA)
+	// centroid.y = (1/mass) * rho * int(y * dA)
+	// I = rho * int((x*x + y*y) * dA)
+	//
+	// We can compute these integrals by summing all the integrals
+	// for each triangle of the polygon. To evaluate the integral
+	// for a single triangle, we make a change of variables to
+	// the (u,v) coordinates of the triangle:
+	// x = x0 + e1x * u + e2x * v
+	// y = y0 + e1y * u + e2y * v
+	// where 0 <= u && 0 <= v && u + v <= 1.
+	//
+	// We integrate u from [0,1-v] and then v from [0,1].
+	// We also need to use the Jacobian of the transformation:
+	// D = cross(e1, e2)
+	//
+	// Simplification: triangle centroid = (1/3) * (p1 + p2 + p3)
+	//
+	// The rest of the derivation is handled by computer algebra.
+
+	b2Assert(m_count >= 3);
+
+	b2Vec2 center(0.0f, 0.0f);
+	float area = 0.0f;
+	float I = 0.0f;
+
+	// Get a reference point for forming triangles.
+	// Use the first vertex to reduce round-off errors.
+	b2Vec2 s = m_vertices[0];
+
+	const float k_inv3 = 1.0f / 3.0f;
+
+	for (int32 i = 0; i < m_count; ++i)
+	{
+		// Triangle vertices.
+		b2Vec2 e1 = m_vertices[i] - s;
+		b2Vec2 e2 = i + 1 < m_count ? m_vertices[i+1] - s : m_vertices[0] - s;
+
+		float D = b2Cross(e1, e2);
+
+		float triangleArea = 0.5f * D;
+		area += triangleArea;
+
+		// Area weighted centroid
+		center += triangleArea * k_inv3 * (e1 + e2);
+
+		float ex1 = e1.x, ey1 = e1.y;
+		float ex2 = e2.x, ey2 = e2.y;
+
+		float intx2 = ex1*ex1 + ex2*ex1 + ex2*ex2;
+		float inty2 = ey1*ey1 + ey2*ey1 + ey2*ey2;
+
+		I += (0.25f * k_inv3 * D) * (intx2 + inty2);
+	}
+
+	// Total mass
+	massData->mass = density * area;
+
+	// Center of mass
+	b2Assert(area > b2_epsilon);
+	center *= 1.0f / area;
+	massData->center = center + s;
+
+	// Inertia tensor relative to the local origin (point s).
+	massData->I = density * I;
+	
+	// Shift to center of mass then to original body origin.
+	massData->I += massData->mass * (b2Dot(massData->center, massData->center) - b2Dot(center, center));
+}
+
+bool b2PolygonShape::Validate() const
+{
+	if (m_count < 3 || b2_maxPolygonVertices < m_count)
+	{
+		return false;
+	}
+
+	b2Hull hull;
+	for (int32 i = 0; i < m_count; ++i)
+	{
+		hull.points[i] = m_vertices[i];
+	}
+
+	hull.count = m_count;
+
+	return b2ValidateHull(hull);
+}

3rd/box2d/src/collision/b2_time_of_impact.cpp

@@ -0,0 +1,490 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#include "box2d/b2_collision.h"
+#include "box2d/b2_distance.h"
+#include "box2d/b2_circle_shape.h"
+#include "box2d/b2_polygon_shape.h"
+#include "box2d/b2_time_of_impact.h"
+#include "box2d/b2_timer.h"
+
+#include <stdio.h>
+
+B2_API float b2_toiTime, b2_toiMaxTime;
+B2_API int32 b2_toiCalls, b2_toiIters, b2_toiMaxIters;
+B2_API int32 b2_toiRootIters, b2_toiMaxRootIters;
+
+//
+struct b2SeparationFunction
+{
+	enum Type
+	{
+		e_points,
+		e_faceA,
+		e_faceB
+	};
+
+	// TODO_ERIN might not need to return the separation
+
+	float Initialize(const b2SimplexCache* cache,
+		const b2DistanceProxy* proxyA, const b2Sweep& sweepA,
+		const b2DistanceProxy* proxyB, const b2Sweep& sweepB,
+		float t1)
+	{
+		m_proxyA = proxyA;
+		m_proxyB = proxyB;
+		int32 count = cache->count;
+		b2Assert(0 < count && count < 3);
+
+		m_sweepA = sweepA;
+		m_sweepB = sweepB;
+
+		b2Transform xfA, xfB;
+		m_sweepA.GetTransform(&xfA, t1);
+		m_sweepB.GetTransform(&xfB, t1);
+
+		if (count == 1)
+		{
+			m_type = e_points;
+			b2Vec2 localPointA = m_proxyA->GetVertex(cache->indexA[0]);
+			b2Vec2 localPointB = m_proxyB->GetVertex(cache->indexB[0]);
+			b2Vec2 pointA = b2Mul(xfA, localPointA);
+			b2Vec2 pointB = b2Mul(xfB, localPointB);
+			m_axis = pointB - pointA;
+			float s = m_axis.Normalize();
+			return s;
+		}
+		else if (cache->indexA[0] == cache->indexA[1])
+		{
+			// Two points on B and one on A.
+			m_type = e_faceB;
+			b2Vec2 localPointB1 = proxyB->GetVertex(cache->indexB[0]);
+			b2Vec2 localPointB2 = proxyB->GetVertex(cache->indexB[1]);
+
+			m_axis = b2Cross(localPointB2 - localPointB1, 1.0f);
+			m_axis.Normalize();
+			b2Vec2 normal = b2Mul(xfB.q, m_axis);
+
+			m_localPoint = 0.5f * (localPointB1 + localPointB2);
+			b2Vec2 pointB = b2Mul(xfB, m_localPoint);
+
+			b2Vec2 localPointA = proxyA->GetVertex(cache->indexA[0]);
+			b2Vec2 pointA = b2Mul(xfA, localPointA);
+
+			float s = b2Dot(pointA - pointB, normal);
+			if (s < 0.0f)
+			{
+				m_axis = -m_axis;
+				s = -s;
+			}
+			return s;
+		}
+		else
+		{
+			// Two points on A and one or two points on B.
+			m_type = e_faceA;
+			b2Vec2 localPointA1 = m_proxyA->GetVertex(cache->indexA[0]);
+			b2Vec2 localPointA2 = m_proxyA->GetVertex(cache->indexA[1]);
+			
+			m_axis = b2Cross(localPointA2 - localPointA1, 1.0f);
+			m_axis.Normalize();
+			b2Vec2 normal = b2Mul(xfA.q, m_axis);
+
+			m_localPoint = 0.5f * (localPointA1 + localPointA2);
+			b2Vec2 pointA = b2Mul(xfA, m_localPoint);
+
+			b2Vec2 localPointB = m_proxyB->GetVertex(cache->indexB[0]);
+			b2Vec2 pointB = b2Mul(xfB, localPointB);
+
+			float s = b2Dot(pointB - pointA, normal);
+			if (s < 0.0f)
+			{
+				m_axis = -m_axis;
+				s = -s;
+			}
+			return s;
+		}
+	}
+
+	//
+	float FindMinSeparation(int32* indexA, int32* indexB, float t) const
+	{
+		b2Transform xfA, xfB;
+		m_sweepA.GetTransform(&xfA, t);
+		m_sweepB.GetTransform(&xfB, t);
+
+		switch (m_type)
+		{
+		case e_points:
+			{
+				b2Vec2 axisA = b2MulT(xfA.q,  m_axis);
+				b2Vec2 axisB = b2MulT(xfB.q, -m_axis);
+
+				*indexA = m_proxyA->GetSupport(axisA);
+				*indexB = m_proxyB->GetSupport(axisB);
+
+				b2Vec2 localPointA = m_proxyA->GetVertex(*indexA);
+				b2Vec2 localPointB = m_proxyB->GetVertex(*indexB);
+				
+				b2Vec2 pointA = b2Mul(xfA, localPointA);
+				b2Vec2 pointB = b2Mul(xfB, localPointB);
+
+				float separation = b2Dot(pointB - pointA, m_axis);
+				return separation;
+			}
+
+		case e_faceA:
+			{
+				b2Vec2 normal = b2Mul(xfA.q, m_axis);
+				b2Vec2 pointA = b2Mul(xfA, m_localPoint);
+
+				b2Vec2 axisB = b2MulT(xfB.q, -normal);
+				
+				*indexA = -1;
+				*indexB = m_proxyB->GetSupport(axisB);
+
+				b2Vec2 localPointB = m_proxyB->GetVertex(*indexB);
+				b2Vec2 pointB = b2Mul(xfB, localPointB);
+
+				float separation = b2Dot(pointB - pointA, normal);
+				return separation;
+			}
+
+		case e_faceB:
+			{
+				b2Vec2 normal = b2Mul(xfB.q, m_axis);
+				b2Vec2 pointB = b2Mul(xfB, m_localPoint);
+
+				b2Vec2 axisA = b2MulT(xfA.q, -normal);
+
+				*indexB = -1;
+				*indexA = m_proxyA->GetSupport(axisA);
+
+				b2Vec2 localPointA = m_proxyA->GetVertex(*indexA);
+				b2Vec2 pointA = b2Mul(xfA, localPointA);
+
+				float separation = b2Dot(pointA - pointB, normal);
+				return separation;
+			}
+
+		default:
+			b2Assert(false);
+			*indexA = -1;
+			*indexB = -1;
+			return 0.0f;
+		}
+	}
+
+	//
+	float Evaluate(int32 indexA, int32 indexB, float t) const
+	{
+		b2Transform xfA, xfB;
+		m_sweepA.GetTransform(&xfA, t);
+		m_sweepB.GetTransform(&xfB, t);
+
+		switch (m_type)
+		{
+		case e_points:
+			{
+				b2Vec2 localPointA = m_proxyA->GetVertex(indexA);
+				b2Vec2 localPointB = m_proxyB->GetVertex(indexB);
+
+				b2Vec2 pointA = b2Mul(xfA, localPointA);
+				b2Vec2 pointB = b2Mul(xfB, localPointB);
+				float separation = b2Dot(pointB - pointA, m_axis);
+
+				return separation;
+			}
+
+		case e_faceA:
+			{
+				b2Vec2 normal = b2Mul(xfA.q, m_axis);
+				b2Vec2 pointA = b2Mul(xfA, m_localPoint);
+
+				b2Vec2 localPointB = m_proxyB->GetVertex(indexB);
+				b2Vec2 pointB = b2Mul(xfB, localPointB);
+
+				float separation = b2Dot(pointB - pointA, normal);
+				return separation;
+			}
+
+		case e_faceB:
+			{
+				b2Vec2 normal = b2Mul(xfB.q, m_axis);
+				b2Vec2 pointB = b2Mul(xfB, m_localPoint);
+
+				b2Vec2 localPointA = m_proxyA->GetVertex(indexA);
+				b2Vec2 pointA = b2Mul(xfA, localPointA);
+
+				float separation = b2Dot(pointA - pointB, normal);
+				return separation;
+			}
+
+		default:
+			b2Assert(false);
+			return 0.0f;
+		}
+	}
+
+	const b2DistanceProxy* m_proxyA;
+	const b2DistanceProxy* m_proxyB;
+	b2Sweep m_sweepA, m_sweepB;
+	Type m_type;
+	b2Vec2 m_localPoint;
+	b2Vec2 m_axis;
+};
+
+// CCD via the local separating axis method. This seeks progression
+// by computing the largest time at which separation is maintained.
+void b2TimeOfImpact(b2TOIOutput* output, const b2TOIInput* input)
+{
+	b2Timer timer;
+
+	++b2_toiCalls;
+
+	output->state = b2TOIOutput::e_unknown;
+	output->t = input->tMax;
+
+	const b2DistanceProxy* proxyA = &input->proxyA;
+	const b2DistanceProxy* proxyB = &input->proxyB;
+
+	b2Sweep sweepA = input->sweepA;
+	b2Sweep sweepB = input->sweepB;
+
+	// Large rotations can make the root finder fail, so we normalize the
+	// sweep angles.
+	sweepA.Normalize();
+	sweepB.Normalize();
+
+	float tMax = input->tMax;
+
+	float totalRadius = proxyA->m_radius + proxyB->m_radius;
+	float target = b2Max(b2_linearSlop, totalRadius - 3.0f * b2_linearSlop);
+	float tolerance = 0.25f * b2_linearSlop;
+	b2Assert(target > tolerance);
+
+	float t1 = 0.0f;
+	const int32 k_maxIterations = 20;	// TODO_ERIN b2Settings
+	int32 iter = 0;
+
+	// Prepare input for distance query.
+	b2SimplexCache cache;
+	cache.count = 0;
+	b2DistanceInput distanceInput;
+	distanceInput.proxyA = input->proxyA;
+	distanceInput.proxyB = input->proxyB;
+	distanceInput.useRadii = false;
+
+	// The outer loop progressively attempts to compute new separating axes.
+	// This loop terminates when an axis is repeated (no progress is made).
+	for(;;)
+	{
+		b2Transform xfA, xfB;
+		sweepA.GetTransform(&xfA, t1);
+		sweepB.GetTransform(&xfB, t1);
+
+		// Get the distance between shapes. We can also use the results
+		// to get a separating axis.
+		distanceInput.transformA = xfA;
+		distanceInput.transformB = xfB;
+		b2DistanceOutput distanceOutput;
+		b2Distance(&distanceOutput, &cache, &distanceInput);
+
+		// If the shapes are overlapped, we give up on continuous collision.
+		if (distanceOutput.distance <= 0.0f)
+		{
+			// Failure!
+			output->state = b2TOIOutput::e_overlapped;
+			output->t = 0.0f;
+			break;
+		}
+
+		if (distanceOutput.distance < target + tolerance)
+		{
+			// Victory!
+			output->state = b2TOIOutput::e_touching;
+			output->t = t1;
+			break;
+		}
+
+		// Initialize the separating axis.
+		b2SeparationFunction fcn;
+		fcn.Initialize(&cache, proxyA, sweepA, proxyB, sweepB, t1);
+#if 0
+		// Dump the curve seen by the root finder
+		{
+			const int32 N = 100;
+			float dx = 1.0f / N;
+			float xs[N+1];
+			float fs[N+1];
+
+			float x = 0.0f;
+
+			for (int32 i = 0; i <= N; ++i)
+			{
+				sweepA.GetTransform(&xfA, x);
+				sweepB.GetTransform(&xfB, x);
+				float f = fcn.Evaluate(xfA, xfB) - target;
+
+				printf("%g %g\n", x, f);
+
+				xs[i] = x;
+				fs[i] = f;
+
+				x += dx;
+			}
+		}
+#endif
+
+		// Compute the TOI on the separating axis. We do this by successively
+		// resolving the deepest point. This loop is bounded by the number of vertices.
+		bool done = false;
+		float t2 = tMax;
+		int32 pushBackIter = 0;
+		for (;;)
+		{
+			// Find the deepest point at t2. Store the witness point indices.
+			int32 indexA, indexB;
+			float s2 = fcn.FindMinSeparation(&indexA, &indexB, t2);
+
+			// Is the final configuration separated?
+			if (s2 > target + tolerance)
+			{
+				// Victory!
+				output->state = b2TOIOutput::e_separated;
+				output->t = tMax;
+				done = true;
+				break;
+			}
+
+			// Has the separation reached tolerance?
+			if (s2 > target - tolerance)
+			{
+				// Advance the sweeps
+				t1 = t2;
+				break;
+			}
+
+			// Compute the initial separation of the witness points.
+			float s1 = fcn.Evaluate(indexA, indexB, t1);
+
+			// Check for initial overlap. This might happen if the root finder
+			// runs out of iterations.
+			if (s1 < target - tolerance)
+			{
+				output->state = b2TOIOutput::e_failed;
+				output->t = t1;
+				done = true;
+				break;
+			}
+
+			// Check for touching
+			if (s1 <= target + tolerance)
+			{
+				// Victory! t1 should hold the TOI (could be 0.0).
+				output->state = b2TOIOutput::e_touching;
+				output->t = t1;
+				done = true;
+				break;
+			}
+
+			// Compute 1D root of: f(x) - target = 0
+			int32 rootIterCount = 0;
+			float a1 = t1, a2 = t2;
+			for (;;)
+			{
+				// Use a mix of the secant rule and bisection.
+				float t;
+				if (rootIterCount & 1)
+				{
+					// Secant rule to improve convergence.
+					t = a1 + (target - s1) * (a2 - a1) / (s2 - s1);
+				}
+				else
+				{
+					// Bisection to guarantee progress.
+					t = 0.5f * (a1 + a2);
+				}
+
+				++rootIterCount;
+				++b2_toiRootIters;
+
+				float s = fcn.Evaluate(indexA, indexB, t);
+
+				if (b2Abs(s - target) < tolerance)
+				{
+					// t2 holds a tentative value for t1
+					t2 = t;
+					break;
+				}
+
+				// Ensure we continue to bracket the root.
+				if (s > target)
+				{
+					a1 = t;
+					s1 = s;
+				}
+				else
+				{
+					a2 = t;
+					s2 = s;
+				}
+				
+				if (rootIterCount == 50)
+				{
+					break;
+				}
+			}
+
+			b2_toiMaxRootIters = b2Max(b2_toiMaxRootIters, rootIterCount);
+
+			++pushBackIter;
+
+			if (pushBackIter == b2_maxPolygonVertices)
+			{
+				break;
+			}
+		}
+
+		++iter;
+		++b2_toiIters;
+
+		if (done)
+		{
+			break;
+		}
+
+		if (iter == k_maxIterations)
+		{
+			// Root finder got stuck. Semi-victory.
+			output->state = b2TOIOutput::e_failed;
+			output->t = t1;
+			break;
+		}
+	}
+
+	b2_toiMaxIters = b2Max(b2_toiMaxIters, iter);
+
+	float time = timer.GetMilliseconds();
+	b2_toiMaxTime = b2Max(b2_toiMaxTime, time);
+	b2_toiTime += time;
+}

3rd/box2d/src/common/b2_block_allocator.cpp

@@ -0,0 +1,230 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#include "box2d/b2_block_allocator.h"
+#include <limits.h>
+#include <string.h>
+#include <stddef.h>
+
+static const int32 b2_chunkSize = 16 * 1024;
+static const int32 b2_maxBlockSize = 640;
+static const int32 b2_chunkArrayIncrement = 128;
+
+// These are the supported object sizes. Actual allocations are rounded up the next size.
+static const int32 b2_blockSizes[b2_blockSizeCount] =
+{
+	16,		// 0
+	32,		// 1
+	64,		// 2
+	96,		// 3
+	128,	// 4
+	160,	// 5
+	192,	// 6
+	224,	// 7
+	256,	// 8
+	320,	// 9
+	384,	// 10
+	448,	// 11
+	512,	// 12
+	640,	// 13
+};
+
+// This maps an arbitrary allocation size to a suitable slot in b2_blockSizes.
+struct b2SizeMap
+{
+	b2SizeMap()
+	{
+		int32 j = 0;
+		values[0] = 0;
+		for (int32 i = 1; i <= b2_maxBlockSize; ++i)
+		{
+			b2Assert(j < b2_blockSizeCount);
+			if (i <= b2_blockSizes[j])
+			{
+				values[i] = (uint8)j;
+			}
+			else
+			{
+				++j;
+				values[i] = (uint8)j;
+			}
+		}
+	}
+
+	uint8 values[b2_maxBlockSize + 1];
+};
+
+static const b2SizeMap b2_sizeMap;
+
+struct b2Chunk
+{
+	int32 blockSize;
+	b2Block* blocks;
+};
+
+struct b2Block
+{
+	b2Block* next;
+};
+
+b2BlockAllocator::b2BlockAllocator()
+{
+	b2Assert(b2_blockSizeCount < UCHAR_MAX);
+
+	m_chunkSpace = b2_chunkArrayIncrement;
+	m_chunkCount = 0;
+	m_chunks = (b2Chunk*)b2Alloc(m_chunkSpace * sizeof(b2Chunk));
+	
+	memset(m_chunks, 0, m_chunkSpace * sizeof(b2Chunk));
+	memset(m_freeLists, 0, sizeof(m_freeLists));
+}
+
+b2BlockAllocator::~b2BlockAllocator()
+{
+	for (int32 i = 0; i < m_chunkCount; ++i)
+	{
+		b2Free(m_chunks[i].blocks);
+	}
+
+	b2Free(m_chunks);
+}
+
+void* b2BlockAllocator::Allocate(int32 size)
+{
+	if (size == 0)
+	{
+		return nullptr;
+	}
+
+	b2Assert(0 < size);
+
+	if (size > b2_maxBlockSize)
+	{
+		return b2Alloc(size);
+	}
+
+	int32 index = b2_sizeMap.values[size];
+	b2Assert(0 <= index && index < b2_blockSizeCount);
+
+	if (m_freeLists[index])
+	{
+		b2Block* block = m_freeLists[index];
+		m_freeLists[index] = block->next;
+		return block;
+	}
+	else
+	{
+		if (m_chunkCount == m_chunkSpace)
+		{
+			b2Chunk* oldChunks = m_chunks;
+			m_chunkSpace += b2_chunkArrayIncrement;
+			m_chunks = (b2Chunk*)b2Alloc(m_chunkSpace * sizeof(b2Chunk));
+			memcpy(m_chunks, oldChunks, m_chunkCount * sizeof(b2Chunk));
+			memset(m_chunks + m_chunkCount, 0, b2_chunkArrayIncrement * sizeof(b2Chunk));
+			b2Free(oldChunks);
+		}
+
+		b2Chunk* chunk = m_chunks + m_chunkCount;
+		chunk->blocks = (b2Block*)b2Alloc(b2_chunkSize);
+#if defined(_DEBUG)
+		memset(chunk->blocks, 0xcd, b2_chunkSize);
+#endif
+		int32 blockSize = b2_blockSizes[index];
+		chunk->blockSize = blockSize;
+		int32 blockCount = b2_chunkSize / blockSize;
+		b2Assert(blockCount * blockSize <= b2_chunkSize);
+		for (int32 i = 0; i < blockCount - 1; ++i)
+		{
+			b2Block* block = (b2Block*)((int8*)chunk->blocks + blockSize * i);
+			b2Block* next = (b2Block*)((int8*)chunk->blocks + blockSize * (i + 1));
+			block->next = next;
+		}
+		b2Block* last = (b2Block*)((int8*)chunk->blocks + blockSize * (blockCount - 1));
+		last->next = nullptr;
+
+		m_freeLists[index] = chunk->blocks->next;
+		++m_chunkCount;
+
+		return chunk->blocks;
+	}
+}
+
+void b2BlockAllocator::Free(void* p, int32 size)
+{
+	if (size == 0)
+	{
+		return;
+	}
+
+	b2Assert(0 < size);
+
+	if (size > b2_maxBlockSize)
+	{
+		b2Free(p);
+		return;
+	}
+
+	int32 index = b2_sizeMap.values[size];
+	b2Assert(0 <= index && index < b2_blockSizeCount);
+
+#if defined(_DEBUG)
+	// Verify the memory address and size is valid.
+	int32 blockSize = b2_blockSizes[index];
+	bool found = false;
+	for (int32 i = 0; i < m_chunkCount; ++i)
+	{
+		b2Chunk* chunk = m_chunks + i;
+		if (chunk->blockSize != blockSize)
+		{
+			b2Assert(	(int8*)p + blockSize <= (int8*)chunk->blocks ||
+						(int8*)chunk->blocks + b2_chunkSize <= (int8*)p);
+		}
+		else
+		{
+			if ((int8*)chunk->blocks <= (int8*)p && (int8*)p + blockSize <= (int8*)chunk->blocks + b2_chunkSize)
+			{
+				found = true;
+			}
+		}
+	}
+
+	b2Assert(found);
+
+	memset(p, 0xfd, blockSize);
+#endif
+
+	b2Block* block = (b2Block*)p;
+	block->next = m_freeLists[index];
+	m_freeLists[index] = block;
+}
+
+void b2BlockAllocator::Clear()
+{
+	for (int32 i = 0; i < m_chunkCount; ++i)
+	{
+		b2Free(m_chunks[i].blocks);
+	}
+
+	m_chunkCount = 0;
+	memset(m_chunks, 0, m_chunkSpace * sizeof(b2Chunk));
+	memset(m_freeLists, 0, sizeof(m_freeLists));
+}

3rd/box2d/src/common/b2_draw.cpp

@@ -0,0 +1,47 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+#include "box2d/b2_draw.h"
+
+b2Draw::b2Draw()
+{
+	m_drawFlags = 0;
+}
+
+void b2Draw::SetFlags(uint32 flags)
+{
+	m_drawFlags = flags;
+}
+
+uint32 b2Draw::GetFlags() const
+{
+	return m_drawFlags;
+}
+
+void b2Draw::AppendFlags(uint32 flags)
+{
+	m_drawFlags |= flags;
+}
+
+void b2Draw::ClearFlags(uint32 flags)
+{
+	m_drawFlags &= ~flags;
+}

3rd/box2d/src/common/b2_math.cpp

@@ -0,0 +1,98 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#include "box2d/b2_math.h"
+
+const b2Vec2 b2Vec2_zero(0.0f, 0.0f);
+
+/// Solve A * x = b, where b is a column vector. This is more efficient
+/// than computing the inverse in one-shot cases.
+b2Vec3 b2Mat33::Solve33(const b2Vec3& b) const
+{
+	float det = b2Dot(ex, b2Cross(ey, ez));
+	if (det != 0.0f)
+	{
+		det = 1.0f / det;
+	}
+	b2Vec3 x;
+	x.x = det * b2Dot(b, b2Cross(ey, ez));
+	x.y = det * b2Dot(ex, b2Cross(b, ez));
+	x.z = det * b2Dot(ex, b2Cross(ey, b));
+	return x;
+}
+
+/// Solve A * x = b, where b is a column vector. This is more efficient
+/// than computing the inverse in one-shot cases.
+b2Vec2 b2Mat33::Solve22(const b2Vec2& b) const
+{
+	float a11 = ex.x, a12 = ey.x, a21 = ex.y, a22 = ey.y;
+	float det = a11 * a22 - a12 * a21;
+	if (det != 0.0f)
+	{
+		det = 1.0f / det;
+	}
+	b2Vec2 x;
+	x.x = det * (a22 * b.x - a12 * b.y);
+	x.y = det * (a11 * b.y - a21 * b.x);
+	return x;
+}
+
+///
+void b2Mat33::GetInverse22(b2Mat33* M) const
+{
+	float a = ex.x, b = ey.x, c = ex.y, d = ey.y;
+	float det = a * d - b * c;
+	if (det != 0.0f)
+	{
+		det = 1.0f / det;
+	}
+
+	M->ex.x =  det * d;	M->ey.x = -det * b; M->ex.z = 0.0f;
+	M->ex.y = -det * c;	M->ey.y =  det * a; M->ey.z = 0.0f;
+	M->ez.x = 0.0f; M->ez.y = 0.0f; M->ez.z = 0.0f;
+}
+
+/// Returns the zero matrix if singular.
+void b2Mat33::GetSymInverse33(b2Mat33* M) const
+{
+	float det = b2Dot(ex, b2Cross(ey, ez));
+	if (det != 0.0f)
+	{
+		det = 1.0f / det;
+	}
+
+	float a11 = ex.x, a12 = ey.x, a13 = ez.x;
+	float a22 = ey.y, a23 = ez.y;
+	float a33 = ez.z;
+
+	M->ex.x = det * (a22 * a33 - a23 * a23);
+	M->ex.y = det * (a13 * a23 - a12 * a33);
+	M->ex.z = det * (a12 * a23 - a13 * a22);
+
+	M->ey.x = M->ex.y;
+	M->ey.y = det * (a11 * a33 - a13 * a13);
+	M->ey.z = det * (a13 * a12 - a11 * a23);
+
+	M->ez.x = M->ex.z;
+	M->ez.y = M->ey.z;
+	M->ez.z = det * (a11 * a22 - a12 * a12);
+}

3rd/box2d/src/common/b2_settings.cpp

@@ -0,0 +1,74 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#define _CRT_SECURE_NO_WARNINGS
+
+#include "box2d/b2_settings.h"
+#include <stdio.h>
+#include <stdarg.h>
+#include <stdlib.h>
+
+b2Version b2_version = {2, 4, 1};
+
+// Memory allocators. Modify these to use your own allocator.
+void* b2Alloc_Default(int32 size)
+{
+	return malloc(size);
+}
+
+void b2Free_Default(void* mem)
+{
+	free(mem);
+}
+
+// You can modify this to use your logging facility.
+void b2Log_Default(const char* string, va_list args)
+{
+	vprintf(string, args);
+}
+
+FILE* b2_dumpFile = nullptr;
+
+void b2OpenDump(const char* fileName)
+{
+	b2Assert(b2_dumpFile == nullptr);
+	b2_dumpFile = fopen(fileName, "w");
+}
+
+void b2Dump(const char* string, ...)
+{
+	if (b2_dumpFile == nullptr)
+	{
+		return;
+	}
+
+	va_list args;
+	va_start(args, string);
+	vfprintf(b2_dumpFile, string, args);
+	va_end(args);
+}
+
+void b2CloseDump()
+{
+	fclose(b2_dumpFile);
+	b2_dumpFile = nullptr;
+}

3rd/box2d/src/common/b2_stack_allocator.cpp

@@ -0,0 +1,87 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#include "box2d/b2_stack_allocator.h"
+#include "box2d/b2_math.h"
+
+b2StackAllocator::b2StackAllocator()
+{
+	m_index = 0;
+	m_allocation = 0;
+	m_maxAllocation = 0;
+	m_entryCount = 0;
+}
+
+b2StackAllocator::~b2StackAllocator()
+{
+	b2Assert(m_index == 0);
+	b2Assert(m_entryCount == 0);
+}
+
+void* b2StackAllocator::Allocate(int32 size)
+{
+	b2Assert(m_entryCount < b2_maxStackEntries);
+
+	b2StackEntry* entry = m_entries + m_entryCount;
+	entry->size = size;
+	if (m_index + size > b2_stackSize)
+	{
+		entry->data = (char*)b2Alloc(size);
+		entry->usedMalloc = true;
+	}
+	else
+	{
+		entry->data = m_data + m_index;
+		entry->usedMalloc = false;
+		m_index += size;
+	}
+
+	m_allocation += size;
+	m_maxAllocation = b2Max(m_maxAllocation, m_allocation);
+	++m_entryCount;
+
+	return entry->data;
+}
+
+void b2StackAllocator::Free(void* p)
+{
+	b2Assert(m_entryCount > 0);
+	b2StackEntry* entry = m_entries + m_entryCount - 1;
+	b2Assert(p == entry->data);
+	if (entry->usedMalloc)
+	{
+		b2Free(p);
+	}
+	else
+	{
+		m_index -= entry->size;
+	}
+	m_allocation -= entry->size;
+	--m_entryCount;
+
+	p = nullptr;
+}
+
+int32 b2StackAllocator::GetMaxAllocation() const
+{
+	return m_maxAllocation;
+}

3rd/box2d/src/common/b2_timer.cpp

@@ -0,0 +1,125 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#include "box2d/b2_timer.h"
+
+#if defined(_WIN32)
+
+double b2Timer::s_invFrequency = 0.0;
+
+#ifndef WIN32_LEAN_AND_MEAN
+#define WIN32_LEAN_AND_MEAN
+#endif
+
+#include <windows.h>
+
+b2Timer::b2Timer()
+{
+	LARGE_INTEGER largeInteger;
+
+	if (s_invFrequency == 0.0)
+	{
+		QueryPerformanceFrequency(&largeInteger);
+		s_invFrequency = double(largeInteger.QuadPart);
+		if (s_invFrequency > 0.0)
+		{
+			s_invFrequency = 1000.0 / s_invFrequency;
+		}
+	}
+
+	QueryPerformanceCounter(&largeInteger);
+	m_start = double(largeInteger.QuadPart);
+}
+
+void b2Timer::Reset()
+{
+	LARGE_INTEGER largeInteger;
+	QueryPerformanceCounter(&largeInteger);
+	m_start = double(largeInteger.QuadPart);
+}
+
+float b2Timer::GetMilliseconds() const
+{
+	LARGE_INTEGER largeInteger;
+	QueryPerformanceCounter(&largeInteger);
+	double count = double(largeInteger.QuadPart);
+	float ms = float(s_invFrequency * (count - m_start));
+	return ms;
+}
+
+#elif defined(__linux__) || defined (__APPLE__)
+
+#include <sys/time.h>
+
+b2Timer::b2Timer()
+{
+    Reset();
+}
+
+void b2Timer::Reset()
+{
+    timeval t;
+    gettimeofday(&t, 0);
+    m_start_sec = t.tv_sec;
+    m_start_usec = t.tv_usec;
+}
+
+float b2Timer::GetMilliseconds() const
+{
+    timeval t;
+    gettimeofday(&t, 0);
+	time_t start_sec = m_start_sec;
+	suseconds_t start_usec = m_start_usec;
+	
+	// http://www.gnu.org/software/libc/manual/html_node/Elapsed-Time.html
+	if (t.tv_usec < start_usec)
+	{
+		int nsec = (start_usec - t.tv_usec) / 1000000 + 1;
+		start_usec -= 1000000 * nsec;
+		start_sec += nsec;
+	}
+	
+	if (t.tv_usec - start_usec > 1000000)
+	{
+		int nsec = (t.tv_usec - start_usec) / 1000000;
+		start_usec += 1000000 * nsec;
+		start_sec -= nsec;
+	}
+	return 1000.0f * (t.tv_sec - start_sec) + 0.001f * (t.tv_usec - start_usec);
+}
+
+#else
+
+b2Timer::b2Timer()
+{
+}
+
+void b2Timer::Reset()
+{
+}
+
+float b2Timer::GetMilliseconds() const
+{
+	return 0.0f;
+}
+
+#endif

3rd/box2d/src/dynamics/b2_body.cpp

@@ -0,0 +1,570 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#include "box2d/b2_body.h"
+#include "box2d/b2_contact.h"
+#include "box2d/b2_fixture.h"
+#include "box2d/b2_joint.h"
+#include "box2d/b2_world.h"
+
+#include <new>
+
+b2Body::b2Body(const b2BodyDef* bd, b2World* world)
+{
+	b2Assert(bd->position.IsValid());
+	b2Assert(bd->linearVelocity.IsValid());
+	b2Assert(b2IsValid(bd->angle));
+	b2Assert(b2IsValid(bd->angularVelocity));
+	b2Assert(b2IsValid(bd->angularDamping) && bd->angularDamping >= 0.0f);
+	b2Assert(b2IsValid(bd->linearDamping) && bd->linearDamping >= 0.0f);
+
+	m_flags = 0;
+
+	if (bd->bullet)
+	{
+		m_flags |= e_bulletFlag;
+	}
+	if (bd->fixedRotation)
+	{
+		m_flags |= e_fixedRotationFlag;
+	}
+	if (bd->allowSleep)
+	{
+		m_flags |= e_autoSleepFlag;
+	}
+	if (bd->awake && bd->type != b2_staticBody)
+	{
+		m_flags |= e_awakeFlag;
+	}
+	if (bd->enabled)
+	{
+		m_flags |= e_enabledFlag;
+	}
+
+	m_world = world;
+
+	m_xf.p = bd->position;
+	m_xf.q.Set(bd->angle);
+
+	m_sweep.localCenter.SetZero();
+	m_sweep.c0 = m_xf.p;
+	m_sweep.c = m_xf.p;
+	m_sweep.a0 = bd->angle;
+	m_sweep.a = bd->angle;
+	m_sweep.alpha0 = 0.0f;
+
+	m_jointList = nullptr;
+	m_contactList = nullptr;
+	m_prev = nullptr;
+	m_next = nullptr;
+
+	m_linearVelocity = bd->linearVelocity;
+	m_angularVelocity = bd->angularVelocity;
+
+	m_linearDamping = bd->linearDamping;
+	m_angularDamping = bd->angularDamping;
+	m_gravityScale = bd->gravityScale;
+
+	m_force.SetZero();
+	m_torque = 0.0f;
+
+	m_sleepTime = 0.0f;
+
+	m_type = bd->type;
+
+	m_mass = 0.0f;
+	m_invMass = 0.0f;
+
+	m_I = 0.0f;
+	m_invI = 0.0f;
+
+	m_userData = bd->userData;
+
+	m_fixtureList = nullptr;
+	m_fixtureCount = 0;
+}
+
+b2Body::~b2Body()
+{
+	// shapes and joints are destroyed in b2World::Destroy
+}
+
+void b2Body::SetType(b2BodyType type)
+{
+	b2Assert(m_world->IsLocked() == false);
+	if (m_world->IsLocked() == true)
+	{
+		return;
+	}
+
+	if (m_type == type)
+	{
+		return;
+	}
+
+	m_type = type;
+
+	ResetMassData();
+
+	if (m_type == b2_staticBody)
+	{
+		m_linearVelocity.SetZero();
+		m_angularVelocity = 0.0f;
+		m_sweep.a0 = m_sweep.a;
+		m_sweep.c0 = m_sweep.c;
+		m_flags &= ~e_awakeFlag;
+		SynchronizeFixtures();
+	}
+
+	SetAwake(true);
+
+	m_force.SetZero();
+	m_torque = 0.0f;
+
+	// Delete the attached contacts.
+	b2ContactEdge* ce = m_contactList;
+	while (ce)
+	{
+		b2ContactEdge* ce0 = ce;
+		ce = ce->next;
+		m_world->m_contactManager.Destroy(ce0->contact);
+	}
+	m_contactList = nullptr;
+
+	// Touch the proxies so that new contacts will be created (when appropriate)
+	b2BroadPhase* broadPhase = &m_world->m_contactManager.m_broadPhase;
+	for (b2Fixture* f = m_fixtureList; f; f = f->m_next)
+	{
+		int32 proxyCount = f->m_proxyCount;
+		for (int32 i = 0; i < proxyCount; ++i)
+		{
+			broadPhase->TouchProxy(f->m_proxies[i].proxyId);
+		}
+	}
+}
+
+b2Fixture* b2Body::CreateFixture(const b2FixtureDef* def)
+{
+	b2Assert(m_world->IsLocked() == false);
+	if (m_world->IsLocked() == true)
+	{
+		return nullptr;
+	}
+
+	b2BlockAllocator* allocator = &m_world->m_blockAllocator;
+
+	void* memory = allocator->Allocate(sizeof(b2Fixture));
+	b2Fixture* fixture = new (memory) b2Fixture;
+	fixture->Create(allocator, this, def);
+
+	if (m_flags & e_enabledFlag)
+	{
+		b2BroadPhase* broadPhase = &m_world->m_contactManager.m_broadPhase;
+		fixture->CreateProxies(broadPhase, m_xf);
+	}
+
+	fixture->m_next = m_fixtureList;
+	m_fixtureList = fixture;
+	++m_fixtureCount;
+
+	fixture->m_body = this;
+
+	// Adjust mass properties if needed.
+	if (fixture->m_density > 0.0f)
+	{
+		ResetMassData();
+	}
+
+	// Let the world know we have a new fixture. This will cause new contacts
+	// to be created at the beginning of the next time step.
+	m_world->m_newContacts = true;
+
+	return fixture;
+}
+
+b2Fixture* b2Body::CreateFixture(const b2Shape* shape, float density)
+{
+	b2FixtureDef def;
+	def.shape = shape;
+	def.density = density;
+
+	return CreateFixture(&def);
+}
+
+void b2Body::DestroyFixture(b2Fixture* fixture)
+{
+	if (fixture == NULL)
+	{
+		return;
+	}
+
+	b2Assert(m_world->IsLocked() == false);
+	if (m_world->IsLocked() == true)
+	{
+		return;
+	}
+
+	b2Assert(fixture->m_body == this);
+
+	// Remove the fixture from this body's singly linked list.
+	b2Assert(m_fixtureCount > 0);
+	b2Fixture** node = &m_fixtureList;
+	bool found = false;
+	while (*node != nullptr)
+	{
+		if (*node == fixture)
+		{
+			*node = fixture->m_next;
+			found = true;
+			break;
+		}
+
+		node = &(*node)->m_next;
+	}
+
+	// You tried to remove a shape that is not attached to this body.
+	b2Assert(found);
+
+	const float density = fixture->m_density;
+
+	// Destroy any contacts associated with the fixture.
+	b2ContactEdge* edge = m_contactList;
+	while (edge)
+	{
+		b2Contact* c = edge->contact;
+		edge = edge->next;
+
+		b2Fixture* fixtureA = c->GetFixtureA();
+		b2Fixture* fixtureB = c->GetFixtureB();
+
+		if (fixture == fixtureA || fixture == fixtureB)
+		{
+			// This destroys the contact and removes it from
+			// this body's contact list.
+			m_world->m_contactManager.Destroy(c);
+		}
+	}
+
+	b2BlockAllocator* allocator = &m_world->m_blockAllocator;
+
+	if (m_flags & e_enabledFlag)
+	{
+		b2BroadPhase* broadPhase = &m_world->m_contactManager.m_broadPhase;
+		fixture->DestroyProxies(broadPhase);
+	}
+
+	fixture->m_body = nullptr;
+	fixture->m_next = nullptr;
+	fixture->Destroy(allocator);
+	fixture->~b2Fixture();
+	allocator->Free(fixture, sizeof(b2Fixture));
+
+	--m_fixtureCount;
+
+	// Reset the mass data
+	if (density > 0.0f)
+	{
+		ResetMassData();
+	}
+}
+
+void b2Body::ResetMassData()
+{
+	// Compute mass data from shapes. Each shape has its own density.
+	m_mass = 0.0f;
+	m_invMass = 0.0f;
+	m_I = 0.0f;
+	m_invI = 0.0f;
+	m_sweep.localCenter.SetZero();
+
+	// Static and kinematic bodies have zero mass.
+	if (m_type == b2_staticBody || m_type == b2_kinematicBody)
+	{
+		m_sweep.c0 = m_xf.p;
+		m_sweep.c = m_xf.p;
+		m_sweep.a0 = m_sweep.a;
+		return;
+	}
+
+	b2Assert(m_type == b2_dynamicBody);
+
+	// Accumulate mass over all fixtures.
+	b2Vec2 localCenter = b2Vec2_zero;
+	for (b2Fixture* f = m_fixtureList; f; f = f->m_next)
+	{
+		if (f->m_density == 0.0f)
+		{
+			continue;
+		}
+
+		b2MassData massData;
+		f->GetMassData(&massData);
+		m_mass += massData.mass;
+		localCenter += massData.mass * massData.center;
+		m_I += massData.I;
+	}
+
+	// Compute center of mass.
+	if (m_mass > 0.0f)
+	{
+		m_invMass = 1.0f / m_mass;
+		localCenter *= m_invMass;
+	}
+
+	if (m_I > 0.0f && (m_flags & e_fixedRotationFlag) == 0)
+	{
+		// Center the inertia about the center of mass.
+		m_I -= m_mass * b2Dot(localCenter, localCenter);
+		b2Assert(m_I > 0.0f);
+		m_invI = 1.0f / m_I;
+
+	}
+	else
+	{
+		m_I = 0.0f;
+		m_invI = 0.0f;
+	}
+
+	// Move center of mass.
+	b2Vec2 oldCenter = m_sweep.c;
+	m_sweep.localCenter = localCenter;
+	m_sweep.c0 = m_sweep.c = b2Mul(m_xf, m_sweep.localCenter);
+
+	// Update center of mass velocity.
+	m_linearVelocity += b2Cross(m_angularVelocity, m_sweep.c - oldCenter);
+}
+
+void b2Body::SetMassData(const b2MassData* massData)
+{
+	b2Assert(m_world->IsLocked() == false);
+	if (m_world->IsLocked() == true)
+	{
+		return;
+	}
+
+	if (m_type != b2_dynamicBody)
+	{
+		return;
+	}
+
+	m_invMass = 0.0f;
+	m_I = 0.0f;
+	m_invI = 0.0f;
+
+	m_mass = massData->mass;
+	if (m_mass <= 0.0f)
+	{
+		m_mass = 1.0f;
+	}
+
+	m_invMass = 1.0f / m_mass;
+
+	if (massData->I > 0.0f && (m_flags & b2Body::e_fixedRotationFlag) == 0)
+	{
+		m_I = massData->I - m_mass * b2Dot(massData->center, massData->center);
+		b2Assert(m_I > 0.0f);
+		m_invI = 1.0f / m_I;
+	}
+
+	// Move center of mass.
+	b2Vec2 oldCenter = m_sweep.c;
+	m_sweep.localCenter =  massData->center;
+	m_sweep.c0 = m_sweep.c = b2Mul(m_xf, m_sweep.localCenter);
+
+	// Update center of mass velocity.
+	m_linearVelocity += b2Cross(m_angularVelocity, m_sweep.c - oldCenter);
+}
+
+bool b2Body::ShouldCollide(const b2Body* other) const
+{
+	// At least one body should be dynamic.
+	if (m_type != b2_dynamicBody && other->m_type != b2_dynamicBody)
+	{
+		return false;
+	}
+
+	// Does a joint prevent collision?
+	for (b2JointEdge* jn = m_jointList; jn; jn = jn->next)
+	{
+		if (jn->other == other)
+		{
+			if (jn->joint->m_collideConnected == false)
+			{
+				return false;
+			}
+		}
+	}
+
+	return true;
+}
+
+void b2Body::SetTransform(const b2Vec2& position, float angle)
+{
+	b2Assert(m_world->IsLocked() == false);
+	if (m_world->IsLocked() == true)
+	{
+		return;
+	}
+
+	m_xf.q.Set(angle);
+	m_xf.p = position;
+
+	m_sweep.c = b2Mul(m_xf, m_sweep.localCenter);
+	m_sweep.a = angle;
+
+	m_sweep.c0 = m_sweep.c;
+	m_sweep.a0 = angle;
+
+	b2BroadPhase* broadPhase = &m_world->m_contactManager.m_broadPhase;
+	for (b2Fixture* f = m_fixtureList; f; f = f->m_next)
+	{
+		f->Synchronize(broadPhase, m_xf, m_xf);
+	}
+
+	// Check for new contacts the next step
+	m_world->m_newContacts = true;
+}
+
+void b2Body::SynchronizeFixtures()
+{
+	b2BroadPhase* broadPhase = &m_world->m_contactManager.m_broadPhase;
+
+	if (m_flags & b2Body::e_awakeFlag)
+	{
+		b2Transform xf1;
+		xf1.q.Set(m_sweep.a0);
+		xf1.p = m_sweep.c0 - b2Mul(xf1.q, m_sweep.localCenter);
+
+		for (b2Fixture* f = m_fixtureList; f; f = f->m_next)
+		{
+			f->Synchronize(broadPhase, xf1, m_xf);
+		}
+	}
+	else
+	{
+		for (b2Fixture* f = m_fixtureList; f; f = f->m_next)
+		{
+			f->Synchronize(broadPhase, m_xf, m_xf);
+		}
+	}
+}
+
+void b2Body::SetEnabled(bool flag)
+{
+	b2Assert(m_world->IsLocked() == false);
+
+	if (flag == IsEnabled())
+	{
+		return;
+	}
+
+	if (flag)
+	{
+		m_flags |= e_enabledFlag;
+
+		// Create all proxies.
+		b2BroadPhase* broadPhase = &m_world->m_contactManager.m_broadPhase;
+		for (b2Fixture* f = m_fixtureList; f; f = f->m_next)
+		{
+			f->CreateProxies(broadPhase, m_xf);
+		}
+
+		// Contacts are created at the beginning of the next
+		m_world->m_newContacts = true;
+	}
+	else
+	{
+		m_flags &= ~e_enabledFlag;
+
+		// Destroy all proxies.
+		b2BroadPhase* broadPhase = &m_world->m_contactManager.m_broadPhase;
+		for (b2Fixture* f = m_fixtureList; f; f = f->m_next)
+		{
+			f->DestroyProxies(broadPhase);
+		}
+
+		// Destroy the attached contacts.
+		b2ContactEdge* ce = m_contactList;
+		while (ce)
+		{
+			b2ContactEdge* ce0 = ce;
+			ce = ce->next;
+			m_world->m_contactManager.Destroy(ce0->contact);
+		}
+		m_contactList = nullptr;
+	}
+}
+
+void b2Body::SetFixedRotation(bool flag)
+{
+	bool status = (m_flags & e_fixedRotationFlag) == e_fixedRotationFlag;
+	if (status == flag)
+	{
+		return;
+	}
+
+	if (flag)
+	{
+		m_flags |= e_fixedRotationFlag;
+	}
+	else
+	{
+		m_flags &= ~e_fixedRotationFlag;
+	}
+
+	m_angularVelocity = 0.0f;
+
+	ResetMassData();
+}
+
+void b2Body::Dump()
+{
+	int32 bodyIndex = m_islandIndex;
+
+	// %.9g is sufficient to save and load the same value using text
+	// FLT_DECIMAL_DIG == 9
+
+	b2Dump("{\n");
+	b2Dump("  b2BodyDef bd;\n");
+	b2Dump("  bd.type = b2BodyType(%d);\n", m_type);
+	b2Dump("  bd.position.Set(%.9g, %.9g);\n", m_xf.p.x, m_xf.p.y);
+	b2Dump("  bd.angle = %.9g;\n", m_sweep.a);
+	b2Dump("  bd.linearVelocity.Set(%.9g, %.9g);\n", m_linearVelocity.x, m_linearVelocity.y);
+	b2Dump("  bd.angularVelocity = %.9g;\n", m_angularVelocity);
+	b2Dump("  bd.linearDamping = %.9g;\n", m_linearDamping);
+	b2Dump("  bd.angularDamping = %.9g;\n", m_angularDamping);
+	b2Dump("  bd.allowSleep = bool(%d);\n", m_flags & e_autoSleepFlag);
+	b2Dump("  bd.awake = bool(%d);\n", m_flags & e_awakeFlag);
+	b2Dump("  bd.fixedRotation = bool(%d);\n", m_flags & e_fixedRotationFlag);
+	b2Dump("  bd.bullet = bool(%d);\n", m_flags & e_bulletFlag);
+	b2Dump("  bd.enabled = bool(%d);\n", m_flags & e_enabledFlag);
+	b2Dump("  bd.gravityScale = %.9g;\n", m_gravityScale);
+	b2Dump("  bodies[%d] = m_world->CreateBody(&bd);\n", m_islandIndex);
+	b2Dump("\n");
+	for (b2Fixture* f = m_fixtureList; f; f = f->m_next)
+	{
+		b2Dump("  {\n");
+		f->Dump(bodyIndex);
+		b2Dump("  }\n");
+	}
+	b2Dump("}\n");
+}

3rd/box2d/src/dynamics/b2_chain_circle_contact.cpp

@@ -0,0 +1,57 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#include "b2_chain_circle_contact.h"
+#include "box2d/b2_block_allocator.h"
+#include "box2d/b2_fixture.h"
+#include "box2d/b2_chain_shape.h"
+#include "box2d/b2_edge_shape.h"
+
+#include <new>
+
+b2Contact* b2ChainAndCircleContact::Create(b2Fixture* fixtureA, int32 indexA, b2Fixture* fixtureB, int32 indexB, b2BlockAllocator* allocator)
+{
+	void* mem = allocator->Allocate(sizeof(b2ChainAndCircleContact));
+	return new (mem) b2ChainAndCircleContact(fixtureA, indexA, fixtureB, indexB);
+}
+
+void b2ChainAndCircleContact::Destroy(b2Contact* contact, b2BlockAllocator* allocator)
+{
+	((b2ChainAndCircleContact*)contact)->~b2ChainAndCircleContact();
+	allocator->Free(contact, sizeof(b2ChainAndCircleContact));
+}
+
+b2ChainAndCircleContact::b2ChainAndCircleContact(b2Fixture* fixtureA, int32 indexA, b2Fixture* fixtureB, int32 indexB)
+: b2Contact(fixtureA, indexA, fixtureB, indexB)
+{
+	b2Assert(m_fixtureA->GetType() == b2Shape::e_chain);
+	b2Assert(m_fixtureB->GetType() == b2Shape::e_circle);
+}
+
+void b2ChainAndCircleContact::Evaluate(b2Manifold* manifold, const b2Transform& xfA, const b2Transform& xfB)
+{
+	b2ChainShape* chain = (b2ChainShape*)m_fixtureA->GetShape();
+	b2EdgeShape edge;
+	chain->GetChildEdge(&edge, m_indexA);
+	b2CollideEdgeAndCircle(	manifold, &edge, xfA,
+							(b2CircleShape*)m_fixtureB->GetShape(), xfB);
+}

3rd/box2d/src/dynamics/b2_chain_circle_contact.h

@@ -0,0 +1,43 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#ifndef B2_CHAIN_AND_CIRCLE_CONTACT_H
+#define B2_CHAIN_AND_CIRCLE_CONTACT_H
+
+#include "box2d/b2_contact.h"
+
+class b2BlockAllocator;
+
+class b2ChainAndCircleContact : public b2Contact
+{
+public:
+	static b2Contact* Create(	b2Fixture* fixtureA, int32 indexA,
+								b2Fixture* fixtureB, int32 indexB, b2BlockAllocator* allocator);
+	static void Destroy(b2Contact* contact, b2BlockAllocator* allocator);
+
+	b2ChainAndCircleContact(b2Fixture* fixtureA, int32 indexA, b2Fixture* fixtureB, int32 indexB);
+	~b2ChainAndCircleContact() {}
+
+	void Evaluate(b2Manifold* manifold, const b2Transform& xfA, const b2Transform& xfB) override;
+};
+
+#endif

3rd/box2d/src/dynamics/b2_chain_polygon_contact.cpp

@@ -0,0 +1,57 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#include "b2_chain_polygon_contact.h"
+#include "box2d/b2_block_allocator.h"
+#include "box2d/b2_fixture.h"
+#include "box2d/b2_chain_shape.h"
+#include "box2d/b2_edge_shape.h"
+
+#include <new>
+
+b2Contact* b2ChainAndPolygonContact::Create(b2Fixture* fixtureA, int32 indexA, b2Fixture* fixtureB, int32 indexB, b2BlockAllocator* allocator)
+{
+	void* mem = allocator->Allocate(sizeof(b2ChainAndPolygonContact));
+	return new (mem) b2ChainAndPolygonContact(fixtureA, indexA, fixtureB, indexB);
+}
+
+void b2ChainAndPolygonContact::Destroy(b2Contact* contact, b2BlockAllocator* allocator)
+{
+	((b2ChainAndPolygonContact*)contact)->~b2ChainAndPolygonContact();
+	allocator->Free(contact, sizeof(b2ChainAndPolygonContact));
+}
+
+b2ChainAndPolygonContact::b2ChainAndPolygonContact(b2Fixture* fixtureA, int32 indexA, b2Fixture* fixtureB, int32 indexB)
+: b2Contact(fixtureA, indexA, fixtureB, indexB)
+{
+	b2Assert(m_fixtureA->GetType() == b2Shape::e_chain);
+	b2Assert(m_fixtureB->GetType() == b2Shape::e_polygon);
+}
+
+void b2ChainAndPolygonContact::Evaluate(b2Manifold* manifold, const b2Transform& xfA, const b2Transform& xfB)
+{
+	b2ChainShape* chain = (b2ChainShape*)m_fixtureA->GetShape();
+	b2EdgeShape edge;
+	chain->GetChildEdge(&edge, m_indexA);
+	b2CollideEdgeAndPolygon(	manifold, &edge, xfA,
+								(b2PolygonShape*)m_fixtureB->GetShape(), xfB);
+}

3rd/box2d/src/dynamics/b2_chain_polygon_contact.h

@@ -0,0 +1,43 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#ifndef B2_CHAIN_AND_POLYGON_CONTACT_H
+#define B2_CHAIN_AND_POLYGON_CONTACT_H
+
+#include "box2d/b2_contact.h"
+
+class b2BlockAllocator;
+
+class b2ChainAndPolygonContact : public b2Contact
+{
+public:
+	static b2Contact* Create(	b2Fixture* fixtureA, int32 indexA,
+								b2Fixture* fixtureB, int32 indexB, b2BlockAllocator* allocator);
+	static void Destroy(b2Contact* contact, b2BlockAllocator* allocator);
+
+	b2ChainAndPolygonContact(b2Fixture* fixtureA, int32 indexA, b2Fixture* fixtureB, int32 indexB);
+	~b2ChainAndPolygonContact() {}
+
+	void Evaluate(b2Manifold* manifold, const b2Transform& xfA, const b2Transform& xfB) override;
+};
+
+#endif

3rd/box2d/src/dynamics/b2_circle_contact.cpp

@@ -0,0 +1,56 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#include "b2_circle_contact.h"
+#include "box2d/b2_block_allocator.h"
+#include "box2d/b2_body.h"
+#include "box2d/b2_fixture.h"
+#include "box2d/b2_time_of_impact.h"
+#include "box2d/b2_world_callbacks.h"
+
+#include <new>
+
+b2Contact* b2CircleContact::Create(b2Fixture* fixtureA, int32, b2Fixture* fixtureB, int32, b2BlockAllocator* allocator)
+{
+	void* mem = allocator->Allocate(sizeof(b2CircleContact));
+	return new (mem) b2CircleContact(fixtureA, fixtureB);
+}
+
+void b2CircleContact::Destroy(b2Contact* contact, b2BlockAllocator* allocator)
+{
+	((b2CircleContact*)contact)->~b2CircleContact();
+	allocator->Free(contact, sizeof(b2CircleContact));
+}
+
+b2CircleContact::b2CircleContact(b2Fixture* fixtureA, b2Fixture* fixtureB)
+	: b2Contact(fixtureA, 0, fixtureB, 0)
+{
+	b2Assert(m_fixtureA->GetType() == b2Shape::e_circle);
+	b2Assert(m_fixtureB->GetType() == b2Shape::e_circle);
+}
+
+void b2CircleContact::Evaluate(b2Manifold* manifold, const b2Transform& xfA, const b2Transform& xfB)
+{
+	b2CollideCircles(manifold,
+					(b2CircleShape*)m_fixtureA->GetShape(), xfA,
+					(b2CircleShape*)m_fixtureB->GetShape(), xfB);
+}

3rd/box2d/src/dynamics/b2_circle_contact.h

@@ -0,0 +1,43 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#ifndef B2_CIRCLE_CONTACT_H
+#define B2_CIRCLE_CONTACT_H
+
+#include "box2d/b2_contact.h"
+
+class b2BlockAllocator;
+
+class b2CircleContact : public b2Contact
+{
+public:
+	static b2Contact* Create(	b2Fixture* fixtureA, int32 indexA,
+								b2Fixture* fixtureB, int32 indexB, b2BlockAllocator* allocator);
+	static void Destroy(b2Contact* contact, b2BlockAllocator* allocator);
+
+	b2CircleContact(b2Fixture* fixtureA, b2Fixture* fixtureB);
+	~b2CircleContact() {}
+
+	void Evaluate(b2Manifold* manifold, const b2Transform& xfA, const b2Transform& xfB) override;
+};
+
+#endif

3rd/box2d/src/dynamics/b2_contact.cpp

@@ -0,0 +1,252 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#include "b2_chain_circle_contact.h"
+#include "b2_chain_polygon_contact.h"
+#include "b2_circle_contact.h"
+#include "b2_contact_solver.h"
+#include "b2_edge_circle_contact.h"
+#include "b2_edge_polygon_contact.h"
+#include "b2_polygon_circle_contact.h"
+#include "b2_polygon_contact.h"
+
+#include "box2d/b2_contact.h"
+#include "box2d/b2_block_allocator.h"
+#include "box2d/b2_body.h"
+#include "box2d/b2_collision.h"
+#include "box2d/b2_fixture.h"
+#include "box2d/b2_shape.h"
+#include "box2d/b2_time_of_impact.h"
+#include "box2d/b2_world.h"
+
+b2ContactRegister b2Contact::s_registers[b2Shape::e_typeCount][b2Shape::e_typeCount];
+bool b2Contact::s_initialized = false;
+
+void b2Contact::InitializeRegisters()
+{
+	AddType(b2CircleContact::Create, b2CircleContact::Destroy, b2Shape::e_circle, b2Shape::e_circle);
+	AddType(b2PolygonAndCircleContact::Create, b2PolygonAndCircleContact::Destroy, b2Shape::e_polygon, b2Shape::e_circle);
+	AddType(b2PolygonContact::Create, b2PolygonContact::Destroy, b2Shape::e_polygon, b2Shape::e_polygon);
+	AddType(b2EdgeAndCircleContact::Create, b2EdgeAndCircleContact::Destroy, b2Shape::e_edge, b2Shape::e_circle);
+	AddType(b2EdgeAndPolygonContact::Create, b2EdgeAndPolygonContact::Destroy, b2Shape::e_edge, b2Shape::e_polygon);
+	AddType(b2ChainAndCircleContact::Create, b2ChainAndCircleContact::Destroy, b2Shape::e_chain, b2Shape::e_circle);
+	AddType(b2ChainAndPolygonContact::Create, b2ChainAndPolygonContact::Destroy, b2Shape::e_chain, b2Shape::e_polygon);
+}
+
+void b2Contact::AddType(b2ContactCreateFcn* createFcn, b2ContactDestroyFcn* destoryFcn,
+						b2Shape::Type type1, b2Shape::Type type2)
+{
+	b2Assert(0 <= type1 && type1 < b2Shape::e_typeCount);
+	b2Assert(0 <= type2 && type2 < b2Shape::e_typeCount);
+	
+	s_registers[type1][type2].createFcn = createFcn;
+	s_registers[type1][type2].destroyFcn = destoryFcn;
+	s_registers[type1][type2].primary = true;
+
+	if (type1 != type2)
+	{
+		s_registers[type2][type1].createFcn = createFcn;
+		s_registers[type2][type1].destroyFcn = destoryFcn;
+		s_registers[type2][type1].primary = false;
+	}
+}
+
+b2Contact* b2Contact::Create(b2Fixture* fixtureA, int32 indexA, b2Fixture* fixtureB, int32 indexB, b2BlockAllocator* allocator)
+{
+	if (s_initialized == false)
+	{
+		InitializeRegisters();
+		s_initialized = true;
+	}
+
+	b2Shape::Type type1 = fixtureA->GetType();
+	b2Shape::Type type2 = fixtureB->GetType();
+
+	b2Assert(0 <= type1 && type1 < b2Shape::e_typeCount);
+	b2Assert(0 <= type2 && type2 < b2Shape::e_typeCount);
+	
+	b2ContactCreateFcn* createFcn = s_registers[type1][type2].createFcn;
+	if (createFcn)
+	{
+		if (s_registers[type1][type2].primary)
+		{
+			return createFcn(fixtureA, indexA, fixtureB, indexB, allocator);
+		}
+		else
+		{
+			return createFcn(fixtureB, indexB, fixtureA, indexA, allocator);
+		}
+	}
+	else
+	{
+		return nullptr;
+	}
+}
+
+void b2Contact::Destroy(b2Contact* contact, b2BlockAllocator* allocator)
+{
+	b2Assert(s_initialized == true);
+
+	b2Fixture* fixtureA = contact->m_fixtureA;
+	b2Fixture* fixtureB = contact->m_fixtureB;
+
+	if (contact->m_manifold.pointCount > 0 &&
+		fixtureA->IsSensor() == false &&
+		fixtureB->IsSensor() == false)
+	{
+		fixtureA->GetBody()->SetAwake(true);
+		fixtureB->GetBody()->SetAwake(true);
+	}
+
+	b2Shape::Type typeA = fixtureA->GetType();
+	b2Shape::Type typeB = fixtureB->GetType();
+
+	b2Assert(0 <= typeA && typeA < b2Shape::e_typeCount);
+	b2Assert(0 <= typeB && typeB < b2Shape::e_typeCount);
+
+	b2ContactDestroyFcn* destroyFcn = s_registers[typeA][typeB].destroyFcn;
+	destroyFcn(contact, allocator);
+}
+
+b2Contact::b2Contact(b2Fixture* fA, int32 indexA, b2Fixture* fB, int32 indexB)
+{
+	m_flags = e_enabledFlag;
+
+	m_fixtureA = fA;
+	m_fixtureB = fB;
+
+	m_indexA = indexA;
+	m_indexB = indexB;
+
+	m_manifold.pointCount = 0;
+
+	m_prev = nullptr;
+	m_next = nullptr;
+
+	m_nodeA.contact = nullptr;
+	m_nodeA.prev = nullptr;
+	m_nodeA.next = nullptr;
+	m_nodeA.other = nullptr;
+
+	m_nodeB.contact = nullptr;
+	m_nodeB.prev = nullptr;
+	m_nodeB.next = nullptr;
+	m_nodeB.other = nullptr;
+
+	m_toiCount = 0;
+
+	m_friction = b2MixFriction(m_fixtureA->m_friction, m_fixtureB->m_friction);
+	m_restitution = b2MixRestitution(m_fixtureA->m_restitution, m_fixtureB->m_restitution);
+	m_restitutionThreshold = b2MixRestitutionThreshold(m_fixtureA->m_restitutionThreshold, m_fixtureB->m_restitutionThreshold);
+
+	m_tangentSpeed = 0.0f;
+}
+
+// Update the contact manifold and touching status.
+// Note: do not assume the fixture AABBs are overlapping or are valid.
+void b2Contact::Update(b2ContactListener* listener)
+{
+	b2Manifold oldManifold = m_manifold;
+
+	// Re-enable this contact.
+	m_flags |= e_enabledFlag;
+
+	bool touching = false;
+	bool wasTouching = (m_flags & e_touchingFlag) == e_touchingFlag;
+
+	bool sensorA = m_fixtureA->IsSensor();
+	bool sensorB = m_fixtureB->IsSensor();
+	bool sensor = sensorA || sensorB;
+
+	b2Body* bodyA = m_fixtureA->GetBody();
+	b2Body* bodyB = m_fixtureB->GetBody();
+	const b2Transform& xfA = bodyA->GetTransform();
+	const b2Transform& xfB = bodyB->GetTransform();
+
+	// Is this contact a sensor?
+	if (sensor)
+	{
+		const b2Shape* shapeA = m_fixtureA->GetShape();
+		const b2Shape* shapeB = m_fixtureB->GetShape();
+		touching = b2TestOverlap(shapeA, m_indexA, shapeB, m_indexB, xfA, xfB);
+
+		// Sensors don't generate manifolds.
+		m_manifold.pointCount = 0;
+	}
+	else
+	{
+		Evaluate(&m_manifold, xfA, xfB);
+		touching = m_manifold.pointCount > 0;
+
+		// Match old contact ids to new contact ids and copy the
+		// stored impulses to warm start the solver.
+		for (int32 i = 0; i < m_manifold.pointCount; ++i)
+		{
+			b2ManifoldPoint* mp2 = m_manifold.points + i;
+			mp2->normalImpulse = 0.0f;
+			mp2->tangentImpulse = 0.0f;
+			b2ContactID id2 = mp2->id;
+
+			for (int32 j = 0; j < oldManifold.pointCount; ++j)
+			{
+				b2ManifoldPoint* mp1 = oldManifold.points + j;
+
+				if (mp1->id.key == id2.key)
+				{
+					mp2->normalImpulse = mp1->normalImpulse;
+					mp2->tangentImpulse = mp1->tangentImpulse;
+					break;
+				}
+			}
+		}
+
+		if (touching != wasTouching)
+		{
+			bodyA->SetAwake(true);
+			bodyB->SetAwake(true);
+		}
+	}
+
+	if (touching)
+	{
+		m_flags |= e_touchingFlag;
+	}
+	else
+	{
+		m_flags &= ~e_touchingFlag;
+	}
+
+	if (wasTouching == false && touching == true && listener)
+	{
+		listener->BeginContact(this);
+	}
+
+	if (wasTouching == true && touching == false && listener)
+	{
+		listener->EndContact(this);
+	}
+
+	if (sensor == false && touching && listener)
+	{
+		listener->PreSolve(this, &oldManifold);
+	}
+}

3rd/box2d/src/dynamics/b2_contact_manager.cpp

@@ -0,0 +1,293 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#include "box2d/b2_body.h"
+#include "box2d/b2_contact.h"
+#include "box2d/b2_contact_manager.h"
+#include "box2d/b2_fixture.h"
+#include "box2d/b2_world_callbacks.h"
+
+b2ContactFilter b2_defaultFilter;
+b2ContactListener b2_defaultListener;
+
+b2ContactManager::b2ContactManager()
+{
+	m_contactList = nullptr;
+	m_contactCount = 0;
+	m_contactFilter = &b2_defaultFilter;
+	m_contactListener = &b2_defaultListener;
+	m_allocator = nullptr;
+}
+
+void b2ContactManager::Destroy(b2Contact* c)
+{
+	b2Fixture* fixtureA = c->GetFixtureA();
+	b2Fixture* fixtureB = c->GetFixtureB();
+	b2Body* bodyA = fixtureA->GetBody();
+	b2Body* bodyB = fixtureB->GetBody();
+
+	if (m_contactListener && c->IsTouching())
+	{
+		m_contactListener->EndContact(c);
+	}
+
+	// Remove from the world.
+	if (c->m_prev)
+	{
+		c->m_prev->m_next = c->m_next;
+	}
+
+	if (c->m_next)
+	{
+		c->m_next->m_prev = c->m_prev;
+	}
+
+	if (c == m_contactList)
+	{
+		m_contactList = c->m_next;
+	}
+
+	// Remove from body 1
+	if (c->m_nodeA.prev)
+	{
+		c->m_nodeA.prev->next = c->m_nodeA.next;
+	}
+
+	if (c->m_nodeA.next)
+	{
+		c->m_nodeA.next->prev = c->m_nodeA.prev;
+	}
+
+	if (&c->m_nodeA == bodyA->m_contactList)
+	{
+		bodyA->m_contactList = c->m_nodeA.next;
+	}
+
+	// Remove from body 2
+	if (c->m_nodeB.prev)
+	{
+		c->m_nodeB.prev->next = c->m_nodeB.next;
+	}
+
+	if (c->m_nodeB.next)
+	{
+		c->m_nodeB.next->prev = c->m_nodeB.prev;
+	}
+
+	if (&c->m_nodeB == bodyB->m_contactList)
+	{
+		bodyB->m_contactList = c->m_nodeB.next;
+	}
+
+	// Call the factory.
+	b2Contact::Destroy(c, m_allocator);
+	--m_contactCount;
+}
+
+// This is the top level collision call for the time step. Here
+// all the narrow phase collision is processed for the world
+// contact list.
+void b2ContactManager::Collide()
+{
+	// Update awake contacts.
+	b2Contact* c = m_contactList;
+	while (c)
+	{
+		b2Fixture* fixtureA = c->GetFixtureA();
+		b2Fixture* fixtureB = c->GetFixtureB();
+		int32 indexA = c->GetChildIndexA();
+		int32 indexB = c->GetChildIndexB();
+		b2Body* bodyA = fixtureA->GetBody();
+		b2Body* bodyB = fixtureB->GetBody();
+		 
+		// Is this contact flagged for filtering?
+		if (c->m_flags & b2Contact::e_filterFlag)
+		{
+			// Should these bodies collide?
+			if (bodyB->ShouldCollide(bodyA) == false)
+			{
+				b2Contact* cNuke = c;
+				c = cNuke->GetNext();
+				Destroy(cNuke);
+				continue;
+			}
+
+			// Check user filtering.
+			if (m_contactFilter && m_contactFilter->ShouldCollide(fixtureA, fixtureB) == false)
+			{
+				b2Contact* cNuke = c;
+				c = cNuke->GetNext();
+				Destroy(cNuke);
+				continue;
+			}
+
+			// Clear the filtering flag.
+			c->m_flags &= ~b2Contact::e_filterFlag;
+		}
+
+		bool activeA = bodyA->IsAwake() && bodyA->m_type != b2_staticBody;
+		bool activeB = bodyB->IsAwake() && bodyB->m_type != b2_staticBody;
+
+		// At least one body must be awake and it must be dynamic or kinematic.
+		if (activeA == false && activeB == false)
+		{
+			c = c->GetNext();
+			continue;
+		}
+
+		int32 proxyIdA = fixtureA->m_proxies[indexA].proxyId;
+		int32 proxyIdB = fixtureB->m_proxies[indexB].proxyId;
+		bool overlap = m_broadPhase.TestOverlap(proxyIdA, proxyIdB);
+
+		// Here we destroy contacts that cease to overlap in the broad-phase.
+		if (overlap == false)
+		{
+			b2Contact* cNuke = c;
+			c = cNuke->GetNext();
+			Destroy(cNuke);
+			continue;
+		}
+
+		// The contact persists.
+		c->Update(m_contactListener);
+		c = c->GetNext();
+	}
+}
+
+void b2ContactManager::FindNewContacts()
+{
+	m_broadPhase.UpdatePairs(this);
+}
+
+void b2ContactManager::AddPair(void* proxyUserDataA, void* proxyUserDataB)
+{
+	b2FixtureProxy* proxyA = (b2FixtureProxy*)proxyUserDataA;
+	b2FixtureProxy* proxyB = (b2FixtureProxy*)proxyUserDataB;
+
+	b2Fixture* fixtureA = proxyA->fixture;
+	b2Fixture* fixtureB = proxyB->fixture;
+
+	int32 indexA = proxyA->childIndex;
+	int32 indexB = proxyB->childIndex;
+
+	b2Body* bodyA = fixtureA->GetBody();
+	b2Body* bodyB = fixtureB->GetBody();
+
+	// Are the fixtures on the same body?
+	if (bodyA == bodyB)
+	{
+		return;
+	}
+
+	// TODO_ERIN use a hash table to remove a potential bottleneck when both
+	// bodies have a lot of contacts.
+	// Does a contact already exist?
+	b2ContactEdge* edge = bodyB->GetContactList();
+	while (edge)
+	{
+		if (edge->other == bodyA)
+		{
+			b2Fixture* fA = edge->contact->GetFixtureA();
+			b2Fixture* fB = edge->contact->GetFixtureB();
+			int32 iA = edge->contact->GetChildIndexA();
+			int32 iB = edge->contact->GetChildIndexB();
+
+			if (fA == fixtureA && fB == fixtureB && iA == indexA && iB == indexB)
+			{
+				// A contact already exists.
+				return;
+			}
+
+			if (fA == fixtureB && fB == fixtureA && iA == indexB && iB == indexA)
+			{
+				// A contact already exists.
+				return;
+			}
+		}
+
+		edge = edge->next;
+	}
+
+	// Does a joint override collision? Is at least one body dynamic?
+	if (bodyB->ShouldCollide(bodyA) == false)
+	{
+		return;
+	}
+
+	// Check user filtering.
+	if (m_contactFilter && m_contactFilter->ShouldCollide(fixtureA, fixtureB) == false)
+	{
+		return;
+	}
+
+	// Call the factory.
+	b2Contact* c = b2Contact::Create(fixtureA, indexA, fixtureB, indexB, m_allocator);
+	if (c == nullptr)
+	{
+		return;
+	}
+
+	// Contact creation may swap fixtures.
+	fixtureA = c->GetFixtureA();
+	fixtureB = c->GetFixtureB();
+	indexA = c->GetChildIndexA();
+	indexB = c->GetChildIndexB();
+	bodyA = fixtureA->GetBody();
+	bodyB = fixtureB->GetBody();
+
+	// Insert into the world.
+	c->m_prev = nullptr;
+	c->m_next = m_contactList;
+	if (m_contactList != nullptr)
+	{
+		m_contactList->m_prev = c;
+	}
+	m_contactList = c;
+
+	// Connect to island graph.
+
+	// Connect to body A
+	c->m_nodeA.contact = c;
+	c->m_nodeA.other = bodyB;
+
+	c->m_nodeA.prev = nullptr;
+	c->m_nodeA.next = bodyA->m_contactList;
+	if (bodyA->m_contactList != nullptr)
+	{
+		bodyA->m_contactList->prev = &c->m_nodeA;
+	}
+	bodyA->m_contactList = &c->m_nodeA;
+
+	// Connect to body B
+	c->m_nodeB.contact = c;
+	c->m_nodeB.other = bodyA;
+
+	c->m_nodeB.prev = nullptr;
+	c->m_nodeB.next = bodyB->m_contactList;
+	if (bodyB->m_contactList != nullptr)
+	{
+		bodyB->m_contactList->prev = &c->m_nodeB;
+	}
+	bodyB->m_contactList = &c->m_nodeB;
+
+	++m_contactCount;
+}

3rd/box2d/src/dynamics/b2_contact_solver.cpp

@@ -0,0 +1,843 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#include "b2_contact_solver.h"
+
+#include "box2d/b2_body.h"
+#include "box2d/b2_contact.h"
+#include "box2d/b2_fixture.h"
+#include "box2d/b2_stack_allocator.h"
+#include "box2d/b2_world.h"
+
+// Solver debugging is normally disabled because the block solver sometimes has to deal with a poorly conditioned effective mass matrix.
+#define B2_DEBUG_SOLVER 0
+
+B2_API bool g_blockSolve = true;
+
+struct b2ContactPositionConstraint
+{
+	b2Vec2 localPoints[b2_maxManifoldPoints];
+	b2Vec2 localNormal;
+	b2Vec2 localPoint;
+	int32 indexA;
+	int32 indexB;
+	float invMassA, invMassB;
+	b2Vec2 localCenterA, localCenterB;
+	float invIA, invIB;
+	b2Manifold::Type type;
+	float radiusA, radiusB;
+	int32 pointCount;
+};
+
+b2ContactSolver::b2ContactSolver(b2ContactSolverDef* def)
+{
+	m_step = def->step;
+	m_allocator = def->allocator;
+	m_count = def->count;
+	m_positionConstraints = (b2ContactPositionConstraint*)m_allocator->Allocate(m_count * sizeof(b2ContactPositionConstraint));
+	m_velocityConstraints = (b2ContactVelocityConstraint*)m_allocator->Allocate(m_count * sizeof(b2ContactVelocityConstraint));
+	m_positions = def->positions;
+	m_velocities = def->velocities;
+	m_contacts = def->contacts;
+
+	// Initialize position independent portions of the constraints.
+	for (int32 i = 0; i < m_count; ++i)
+	{
+		b2Contact* contact = m_contacts[i];
+
+		b2Fixture* fixtureA = contact->m_fixtureA;
+		b2Fixture* fixtureB = contact->m_fixtureB;
+		b2Shape* shapeA = fixtureA->GetShape();
+		b2Shape* shapeB = fixtureB->GetShape();
+		float radiusA = shapeA->m_radius;
+		float radiusB = shapeB->m_radius;
+		b2Body* bodyA = fixtureA->GetBody();
+		b2Body* bodyB = fixtureB->GetBody();
+		b2Manifold* manifold = contact->GetManifold();
+
+		int32 pointCount = manifold->pointCount;
+		b2Assert(pointCount > 0);
+
+		b2ContactVelocityConstraint* vc = m_velocityConstraints + i;
+		vc->friction = contact->m_friction;
+		vc->restitution = contact->m_restitution;
+		vc->threshold = contact->m_restitutionThreshold;
+		vc->tangentSpeed = contact->m_tangentSpeed;
+		vc->indexA = bodyA->m_islandIndex;
+		vc->indexB = bodyB->m_islandIndex;
+		vc->invMassA = bodyA->m_invMass;
+		vc->invMassB = bodyB->m_invMass;
+		vc->invIA = bodyA->m_invI;
+		vc->invIB = bodyB->m_invI;
+		vc->contactIndex = i;
+		vc->pointCount = pointCount;
+		vc->K.SetZero();
+		vc->normalMass.SetZero();
+
+		b2ContactPositionConstraint* pc = m_positionConstraints + i;
+		pc->indexA = bodyA->m_islandIndex;
+		pc->indexB = bodyB->m_islandIndex;
+		pc->invMassA = bodyA->m_invMass;
+		pc->invMassB = bodyB->m_invMass;
+		pc->localCenterA = bodyA->m_sweep.localCenter;
+		pc->localCenterB = bodyB->m_sweep.localCenter;
+		pc->invIA = bodyA->m_invI;
+		pc->invIB = bodyB->m_invI;
+		pc->localNormal = manifold->localNormal;
+		pc->localPoint = manifold->localPoint;
+		pc->pointCount = pointCount;
+		pc->radiusA = radiusA;
+		pc->radiusB = radiusB;
+		pc->type = manifold->type;
+
+		for (int32 j = 0; j < pointCount; ++j)
+		{
+			b2ManifoldPoint* cp = manifold->points + j;
+			b2VelocityConstraintPoint* vcp = vc->points + j;
+	
+			if (m_step.warmStarting)
+			{
+				vcp->normalImpulse = m_step.dtRatio * cp->normalImpulse;
+				vcp->tangentImpulse = m_step.dtRatio * cp->tangentImpulse;
+			}
+			else
+			{
+				vcp->normalImpulse = 0.0f;
+				vcp->tangentImpulse = 0.0f;
+			}
+
+			vcp->rA.SetZero();
+			vcp->rB.SetZero();
+			vcp->normalMass = 0.0f;
+			vcp->tangentMass = 0.0f;
+			vcp->velocityBias = 0.0f;
+
+			pc->localPoints[j] = cp->localPoint;
+		}
+	}
+}
+
+b2ContactSolver::~b2ContactSolver()
+{
+	m_allocator->Free(m_velocityConstraints);
+	m_allocator->Free(m_positionConstraints);
+}
+
+// Initialize position dependent portions of the velocity constraints.
+void b2ContactSolver::InitializeVelocityConstraints()
+{
+	for (int32 i = 0; i < m_count; ++i)
+	{
+		b2ContactVelocityConstraint* vc = m_velocityConstraints + i;
+		b2ContactPositionConstraint* pc = m_positionConstraints + i;
+
+		float radiusA = pc->radiusA;
+		float radiusB = pc->radiusB;
+		b2Manifold* manifold = m_contacts[vc->contactIndex]->GetManifold();
+
+		int32 indexA = vc->indexA;
+		int32 indexB = vc->indexB;
+
+		float mA = vc->invMassA;
+		float mB = vc->invMassB;
+		float iA = vc->invIA;
+		float iB = vc->invIB;
+		b2Vec2 localCenterA = pc->localCenterA;
+		b2Vec2 localCenterB = pc->localCenterB;
+
+		b2Vec2 cA = m_positions[indexA].c;
+		float aA = m_positions[indexA].a;
+		b2Vec2 vA = m_velocities[indexA].v;
+		float wA = m_velocities[indexA].w;
+
+		b2Vec2 cB = m_positions[indexB].c;
+		float aB = m_positions[indexB].a;
+		b2Vec2 vB = m_velocities[indexB].v;
+		float wB = m_velocities[indexB].w;
+
+		b2Assert(manifold->pointCount > 0);
+
+		b2Transform xfA, xfB;
+		xfA.q.Set(aA);
+		xfB.q.Set(aB);
+		xfA.p = cA - b2Mul(xfA.q, localCenterA);
+		xfB.p = cB - b2Mul(xfB.q, localCenterB);
+
+		b2WorldManifold worldManifold;
+		worldManifold.Initialize(manifold, xfA, radiusA, xfB, radiusB);
+
+		vc->normal = worldManifold.normal;
+
+		int32 pointCount = vc->pointCount;
+		for (int32 j = 0; j < pointCount; ++j)
+		{
+			b2VelocityConstraintPoint* vcp = vc->points + j;
+
+			vcp->rA = worldManifold.points[j] - cA;
+			vcp->rB = worldManifold.points[j] - cB;
+
+			float rnA = b2Cross(vcp->rA, vc->normal);
+			float rnB = b2Cross(vcp->rB, vc->normal);
+
+			float kNormal = mA + mB + iA * rnA * rnA + iB * rnB * rnB;
+
+			vcp->normalMass = kNormal > 0.0f ? 1.0f / kNormal : 0.0f;
+
+			b2Vec2 tangent = b2Cross(vc->normal, 1.0f);
+
+			float rtA = b2Cross(vcp->rA, tangent);
+			float rtB = b2Cross(vcp->rB, tangent);
+
+			float kTangent = mA + mB + iA * rtA * rtA + iB * rtB * rtB;
+
+			vcp->tangentMass = kTangent > 0.0f ? 1.0f /  kTangent : 0.0f;
+
+			// Setup a velocity bias for restitution.
+			vcp->velocityBias = 0.0f;
+			float vRel = b2Dot(vc->normal, vB + b2Cross(wB, vcp->rB) - vA - b2Cross(wA, vcp->rA));
+			if (vRel < -vc->threshold)
+			{
+				vcp->velocityBias = -vc->restitution * vRel;
+			}
+		}
+
+		// If we have two points, then prepare the block solver.
+		if (vc->pointCount == 2 && g_blockSolve)
+		{
+			b2VelocityConstraintPoint* vcp1 = vc->points + 0;
+			b2VelocityConstraintPoint* vcp2 = vc->points + 1;
+
+			float rn1A = b2Cross(vcp1->rA, vc->normal);
+			float rn1B = b2Cross(vcp1->rB, vc->normal);
+			float rn2A = b2Cross(vcp2->rA, vc->normal);
+			float rn2B = b2Cross(vcp2->rB, vc->normal);
+
+			float k11 = mA + mB + iA * rn1A * rn1A + iB * rn1B * rn1B;
+			float k22 = mA + mB + iA * rn2A * rn2A + iB * rn2B * rn2B;
+			float k12 = mA + mB + iA * rn1A * rn2A + iB * rn1B * rn2B;
+
+			// Ensure a reasonable condition number.
+			const float k_maxConditionNumber = 1000.0f;
+			if (k11 * k11 < k_maxConditionNumber * (k11 * k22 - k12 * k12))
+			{
+				// K is safe to invert.
+				vc->K.ex.Set(k11, k12);
+				vc->K.ey.Set(k12, k22);
+				vc->normalMass = vc->K.GetInverse();
+			}
+			else
+			{
+				// The constraints are redundant, just use one.
+				// TODO_ERIN use deepest?
+				vc->pointCount = 1;
+			}
+		}
+	}
+}
+
+void b2ContactSolver::WarmStart()
+{
+	// Warm start.
+	for (int32 i = 0; i < m_count; ++i)
+	{
+		b2ContactVelocityConstraint* vc = m_velocityConstraints + i;
+
+		int32 indexA = vc->indexA;
+		int32 indexB = vc->indexB;
+		float mA = vc->invMassA;
+		float iA = vc->invIA;
+		float mB = vc->invMassB;
+		float iB = vc->invIB;
+		int32 pointCount = vc->pointCount;
+
+		b2Vec2 vA = m_velocities[indexA].v;
+		float wA = m_velocities[indexA].w;
+		b2Vec2 vB = m_velocities[indexB].v;
+		float wB = m_velocities[indexB].w;
+
+		b2Vec2 normal = vc->normal;
+		b2Vec2 tangent = b2Cross(normal, 1.0f);
+
+		for (int32 j = 0; j < pointCount; ++j)
+		{
+			b2VelocityConstraintPoint* vcp = vc->points + j;
+			b2Vec2 P = vcp->normalImpulse * normal + vcp->tangentImpulse * tangent;
+			wA -= iA * b2Cross(vcp->rA, P);
+			vA -= mA * P;
+			wB += iB * b2Cross(vcp->rB, P);
+			vB += mB * P;
+		}
+
+		m_velocities[indexA].v = vA;
+		m_velocities[indexA].w = wA;
+		m_velocities[indexB].v = vB;
+		m_velocities[indexB].w = wB;
+	}
+}
+
+void b2ContactSolver::SolveVelocityConstraints()
+{
+	for (int32 i = 0; i < m_count; ++i)
+	{
+		b2ContactVelocityConstraint* vc = m_velocityConstraints + i;
+
+		int32 indexA = vc->indexA;
+		int32 indexB = vc->indexB;
+		float mA = vc->invMassA;
+		float iA = vc->invIA;
+		float mB = vc->invMassB;
+		float iB = vc->invIB;
+		int32 pointCount = vc->pointCount;
+
+		b2Vec2 vA = m_velocities[indexA].v;
+		float wA = m_velocities[indexA].w;
+		b2Vec2 vB = m_velocities[indexB].v;
+		float wB = m_velocities[indexB].w;
+
+		b2Vec2 normal = vc->normal;
+		b2Vec2 tangent = b2Cross(normal, 1.0f);
+		float friction = vc->friction;
+
+		b2Assert(pointCount == 1 || pointCount == 2);
+
+		// Solve tangent constraints first because non-penetration is more important
+		// than friction.
+		for (int32 j = 0; j < pointCount; ++j)
+		{
+			b2VelocityConstraintPoint* vcp = vc->points + j;
+
+			// Relative velocity at contact
+			b2Vec2 dv = vB + b2Cross(wB, vcp->rB) - vA - b2Cross(wA, vcp->rA);
+
+			// Compute tangent force
+			float vt = b2Dot(dv, tangent) - vc->tangentSpeed;
+			float lambda = vcp->tangentMass * (-vt);
+
+			// b2Clamp the accumulated force
+			float maxFriction = friction * vcp->normalImpulse;
+			float newImpulse = b2Clamp(vcp->tangentImpulse + lambda, -maxFriction, maxFriction);
+			lambda = newImpulse - vcp->tangentImpulse;
+			vcp->tangentImpulse = newImpulse;
+
+			// Apply contact impulse
+			b2Vec2 P = lambda * tangent;
+
+			vA -= mA * P;
+			wA -= iA * b2Cross(vcp->rA, P);
+
+			vB += mB * P;
+			wB += iB * b2Cross(vcp->rB, P);
+		}
+
+		// Solve normal constraints
+		if (pointCount == 1 || g_blockSolve == false)
+		{
+			for (int32 j = 0; j < pointCount; ++j)
+			{
+				b2VelocityConstraintPoint* vcp = vc->points + j;
+
+				// Relative velocity at contact
+				b2Vec2 dv = vB + b2Cross(wB, vcp->rB) - vA - b2Cross(wA, vcp->rA);
+
+				// Compute normal impulse
+				float vn = b2Dot(dv, normal);
+				float lambda = -vcp->normalMass * (vn - vcp->velocityBias);
+
+				// b2Clamp the accumulated impulse
+				float newImpulse = b2Max(vcp->normalImpulse + lambda, 0.0f);
+				lambda = newImpulse - vcp->normalImpulse;
+				vcp->normalImpulse = newImpulse;
+
+				// Apply contact impulse
+				b2Vec2 P = lambda * normal;
+				vA -= mA * P;
+				wA -= iA * b2Cross(vcp->rA, P);
+
+				vB += mB * P;
+				wB += iB * b2Cross(vcp->rB, P);
+			}
+		}
+		else
+		{
+			// Block solver developed in collaboration with Dirk Gregorius (back in 01/07 on Box2D_Lite).
+			// Build the mini LCP for this contact patch
+			//
+			// vn = A * x + b, vn >= 0, x >= 0 and vn_i * x_i = 0 with i = 1..2
+			//
+			// A = J * W * JT and J = ( -n, -r1 x n, n, r2 x n )
+			// b = vn0 - velocityBias
+			//
+			// The system is solved using the "Total enumeration method" (s. Murty). The complementary constraint vn_i * x_i
+			// implies that we must have in any solution either vn_i = 0 or x_i = 0. So for the 2D contact problem the cases
+			// vn1 = 0 and vn2 = 0, x1 = 0 and x2 = 0, x1 = 0 and vn2 = 0, x2 = 0 and vn1 = 0 need to be tested. The first valid
+			// solution that satisfies the problem is chosen.
+			// 
+			// In order to account of the accumulated impulse 'a' (because of the iterative nature of the solver which only requires
+			// that the accumulated impulse is clamped and not the incremental impulse) we change the impulse variable (x_i).
+			//
+			// Substitute:
+			// 
+			// x = a + d
+			// 
+			// a := old total impulse
+			// x := new total impulse
+			// d := incremental impulse 
+			//
+			// For the current iteration we extend the formula for the incremental impulse
+			// to compute the new total impulse:
+			//
+			// vn = A * d + b
+			//    = A * (x - a) + b
+			//    = A * x + b - A * a
+			//    = A * x + b'
+			// b' = b - A * a;
+
+			b2VelocityConstraintPoint* cp1 = vc->points + 0;
+			b2VelocityConstraintPoint* cp2 = vc->points + 1;
+
+			b2Vec2 a(cp1->normalImpulse, cp2->normalImpulse);
+			b2Assert(a.x >= 0.0f && a.y >= 0.0f);
+
+			// Relative velocity at contact
+			b2Vec2 dv1 = vB + b2Cross(wB, cp1->rB) - vA - b2Cross(wA, cp1->rA);
+			b2Vec2 dv2 = vB + b2Cross(wB, cp2->rB) - vA - b2Cross(wA, cp2->rA);
+
+			// Compute normal velocity
+			float vn1 = b2Dot(dv1, normal);
+			float vn2 = b2Dot(dv2, normal);
+
+			b2Vec2 b;
+			b.x = vn1 - cp1->velocityBias;
+			b.y = vn2 - cp2->velocityBias;
+
+			// Compute b'
+			b -= b2Mul(vc->K, a);
+
+			const float k_errorTol = 1e-3f;
+			B2_NOT_USED(k_errorTol);
+
+			for (;;)
+			{
+				//
+				// Case 1: vn = 0
+				//
+				// 0 = A * x + b'
+				//
+				// Solve for x:
+				//
+				// x = - inv(A) * b'
+				//
+				b2Vec2 x = - b2Mul(vc->normalMass, b);
+
+				if (x.x >= 0.0f && x.y >= 0.0f)
+				{
+					// Get the incremental impulse
+					b2Vec2 d = x - a;
+
+					// Apply incremental impulse
+					b2Vec2 P1 = d.x * normal;
+					b2Vec2 P2 = d.y * normal;
+					vA -= mA * (P1 + P2);
+					wA -= iA * (b2Cross(cp1->rA, P1) + b2Cross(cp2->rA, P2));
+
+					vB += mB * (P1 + P2);
+					wB += iB * (b2Cross(cp1->rB, P1) + b2Cross(cp2->rB, P2));
+
+					// Accumulate
+					cp1->normalImpulse = x.x;
+					cp2->normalImpulse = x.y;
+
+#if B2_DEBUG_SOLVER == 1
+					// Postconditions
+					dv1 = vB + b2Cross(wB, cp1->rB) - vA - b2Cross(wA, cp1->rA);
+					dv2 = vB + b2Cross(wB, cp2->rB) - vA - b2Cross(wA, cp2->rA);
+
+					// Compute normal velocity
+					vn1 = b2Dot(dv1, normal);
+					vn2 = b2Dot(dv2, normal);
+
+					b2Assert(b2Abs(vn1 - cp1->velocityBias) < k_errorTol);
+					b2Assert(b2Abs(vn2 - cp2->velocityBias) < k_errorTol);
+#endif
+					break;
+				}
+
+				//
+				// Case 2: vn1 = 0 and x2 = 0
+				//
+				//   0 = a11 * x1 + a12 * 0 + b1' 
+				// vn2 = a21 * x1 + a22 * 0 + b2'
+				//
+				x.x = - cp1->normalMass * b.x;
+				x.y = 0.0f;
+				vn1 = 0.0f;
+				vn2 = vc->K.ex.y * x.x + b.y;
+				if (x.x >= 0.0f && vn2 >= 0.0f)
+				{
+					// Get the incremental impulse
+					b2Vec2 d = x - a;
+
+					// Apply incremental impulse
+					b2Vec2 P1 = d.x * normal;
+					b2Vec2 P2 = d.y * normal;
+					vA -= mA * (P1 + P2);
+					wA -= iA * (b2Cross(cp1->rA, P1) + b2Cross(cp2->rA, P2));
+
+					vB += mB * (P1 + P2);
+					wB += iB * (b2Cross(cp1->rB, P1) + b2Cross(cp2->rB, P2));
+
+					// Accumulate
+					cp1->normalImpulse = x.x;
+					cp2->normalImpulse = x.y;
+
+#if B2_DEBUG_SOLVER == 1
+					// Postconditions
+					dv1 = vB + b2Cross(wB, cp1->rB) - vA - b2Cross(wA, cp1->rA);
+
+					// Compute normal velocity
+					vn1 = b2Dot(dv1, normal);
+
+					b2Assert(b2Abs(vn1 - cp1->velocityBias) < k_errorTol);
+#endif
+					break;
+				}
+
+
+				//
+				// Case 3: vn2 = 0 and x1 = 0
+				//
+				// vn1 = a11 * 0 + a12 * x2 + b1' 
+				//   0 = a21 * 0 + a22 * x2 + b2'
+				//
+				x.x = 0.0f;
+				x.y = - cp2->normalMass * b.y;
+				vn1 = vc->K.ey.x * x.y + b.x;
+				vn2 = 0.0f;
+
+				if (x.y >= 0.0f && vn1 >= 0.0f)
+				{
+					// Resubstitute for the incremental impulse
+					b2Vec2 d = x - a;
+
+					// Apply incremental impulse
+					b2Vec2 P1 = d.x * normal;
+					b2Vec2 P2 = d.y * normal;
+					vA -= mA * (P1 + P2);
+					wA -= iA * (b2Cross(cp1->rA, P1) + b2Cross(cp2->rA, P2));
+
+					vB += mB * (P1 + P2);
+					wB += iB * (b2Cross(cp1->rB, P1) + b2Cross(cp2->rB, P2));
+
+					// Accumulate
+					cp1->normalImpulse = x.x;
+					cp2->normalImpulse = x.y;
+
+#if B2_DEBUG_SOLVER == 1
+					// Postconditions
+					dv2 = vB + b2Cross(wB, cp2->rB) - vA - b2Cross(wA, cp2->rA);
+
+					// Compute normal velocity
+					vn2 = b2Dot(dv2, normal);
+
+					b2Assert(b2Abs(vn2 - cp2->velocityBias) < k_errorTol);
+#endif
+					break;
+				}
+
+				//
+				// Case 4: x1 = 0 and x2 = 0
+				// 
+				// vn1 = b1
+				// vn2 = b2;
+				x.x = 0.0f;
+				x.y = 0.0f;
+				vn1 = b.x;
+				vn2 = b.y;
+
+				if (vn1 >= 0.0f && vn2 >= 0.0f )
+				{
+					// Resubstitute for the incremental impulse
+					b2Vec2 d = x - a;
+
+					// Apply incremental impulse
+					b2Vec2 P1 = d.x * normal;
+					b2Vec2 P2 = d.y * normal;
+					vA -= mA * (P1 + P2);
+					wA -= iA * (b2Cross(cp1->rA, P1) + b2Cross(cp2->rA, P2));
+
+					vB += mB * (P1 + P2);
+					wB += iB * (b2Cross(cp1->rB, P1) + b2Cross(cp2->rB, P2));
+
+					// Accumulate
+					cp1->normalImpulse = x.x;
+					cp2->normalImpulse = x.y;
+
+					break;
+				}
+
+				// No solution, give up. This is hit sometimes, but it doesn't seem to matter.
+				break;
+			}
+		}
+
+		m_velocities[indexA].v = vA;
+		m_velocities[indexA].w = wA;
+		m_velocities[indexB].v = vB;
+		m_velocities[indexB].w = wB;
+	}
+}
+
+void b2ContactSolver::StoreImpulses()
+{
+	for (int32 i = 0; i < m_count; ++i)
+	{
+		b2ContactVelocityConstraint* vc = m_velocityConstraints + i;
+		b2Manifold* manifold = m_contacts[vc->contactIndex]->GetManifold();
+
+		for (int32 j = 0; j < vc->pointCount; ++j)
+		{
+			manifold->points[j].normalImpulse = vc->points[j].normalImpulse;
+			manifold->points[j].tangentImpulse = vc->points[j].tangentImpulse;
+		}
+	}
+}
+
+struct b2PositionSolverManifold
+{
+	void Initialize(b2ContactPositionConstraint* pc, const b2Transform& xfA, const b2Transform& xfB, int32 index)
+	{
+		b2Assert(pc->pointCount > 0);
+
+		switch (pc->type)
+		{
+		case b2Manifold::e_circles:
+			{
+				b2Vec2 pointA = b2Mul(xfA, pc->localPoint);
+				b2Vec2 pointB = b2Mul(xfB, pc->localPoints[0]);
+				normal = pointB - pointA;
+				normal.Normalize();
+				point = 0.5f * (pointA + pointB);
+				separation = b2Dot(pointB - pointA, normal) - pc->radiusA - pc->radiusB;
+			}
+			break;
+
+		case b2Manifold::e_faceA:
+			{
+				normal = b2Mul(xfA.q, pc->localNormal);
+				b2Vec2 planePoint = b2Mul(xfA, pc->localPoint);
+
+				b2Vec2 clipPoint = b2Mul(xfB, pc->localPoints[index]);
+				separation = b2Dot(clipPoint - planePoint, normal) - pc->radiusA - pc->radiusB;
+				point = clipPoint;
+			}
+			break;
+
+		case b2Manifold::e_faceB:
+			{
+				normal = b2Mul(xfB.q, pc->localNormal);
+				b2Vec2 planePoint = b2Mul(xfB, pc->localPoint);
+
+				b2Vec2 clipPoint = b2Mul(xfA, pc->localPoints[index]);
+				separation = b2Dot(clipPoint - planePoint, normal) - pc->radiusA - pc->radiusB;
+				point = clipPoint;
+
+				// Ensure normal points from A to B
+				normal = -normal;
+			}
+			break;
+		}
+	}
+
+	b2Vec2 normal;
+	b2Vec2 point;
+	float separation;
+};
+
+// Sequential solver.
+bool b2ContactSolver::SolvePositionConstraints()
+{
+	float minSeparation = 0.0f;
+
+	for (int32 i = 0; i < m_count; ++i)
+	{
+		b2ContactPositionConstraint* pc = m_positionConstraints + i;
+
+		int32 indexA = pc->indexA;
+		int32 indexB = pc->indexB;
+		b2Vec2 localCenterA = pc->localCenterA;
+		float mA = pc->invMassA;
+		float iA = pc->invIA;
+		b2Vec2 localCenterB = pc->localCenterB;
+		float mB = pc->invMassB;
+		float iB = pc->invIB;
+		int32 pointCount = pc->pointCount;
+
+		b2Vec2 cA = m_positions[indexA].c;
+		float aA = m_positions[indexA].a;
+
+		b2Vec2 cB = m_positions[indexB].c;
+		float aB = m_positions[indexB].a;
+
+		// Solve normal constraints
+		for (int32 j = 0; j < pointCount; ++j)
+		{
+			b2Transform xfA, xfB;
+			xfA.q.Set(aA);
+			xfB.q.Set(aB);
+			xfA.p = cA - b2Mul(xfA.q, localCenterA);
+			xfB.p = cB - b2Mul(xfB.q, localCenterB);
+
+			b2PositionSolverManifold psm;
+			psm.Initialize(pc, xfA, xfB, j);
+			b2Vec2 normal = psm.normal;
+
+			b2Vec2 point = psm.point;
+			float separation = psm.separation;
+
+			b2Vec2 rA = point - cA;
+			b2Vec2 rB = point - cB;
+
+			// Track max constraint error.
+			minSeparation = b2Min(minSeparation, separation);
+
+			// Prevent large corrections and allow slop.
+			float C = b2Clamp(b2_baumgarte * (separation + b2_linearSlop), -b2_maxLinearCorrection, 0.0f);
+
+			// Compute the effective mass.
+			float rnA = b2Cross(rA, normal);
+			float rnB = b2Cross(rB, normal);
+			float K = mA + mB + iA * rnA * rnA + iB * rnB * rnB;
+
+			// Compute normal impulse
+			float impulse = K > 0.0f ? - C / K : 0.0f;
+
+			b2Vec2 P = impulse * normal;
+
+			cA -= mA * P;
+			aA -= iA * b2Cross(rA, P);
+
+			cB += mB * P;
+			aB += iB * b2Cross(rB, P);
+		}
+
+		m_positions[indexA].c = cA;
+		m_positions[indexA].a = aA;
+
+		m_positions[indexB].c = cB;
+		m_positions[indexB].a = aB;
+	}
+
+	// We can't expect minSpeparation >= -b2_linearSlop because we don't
+	// push the separation above -b2_linearSlop.
+	return minSeparation >= -3.0f * b2_linearSlop;
+}
+
+// Sequential position solver for position constraints.
+bool b2ContactSolver::SolveTOIPositionConstraints(int32 toiIndexA, int32 toiIndexB)
+{
+	float minSeparation = 0.0f;
+
+	for (int32 i = 0; i < m_count; ++i)
+	{
+		b2ContactPositionConstraint* pc = m_positionConstraints + i;
+
+		int32 indexA = pc->indexA;
+		int32 indexB = pc->indexB;
+		b2Vec2 localCenterA = pc->localCenterA;
+		b2Vec2 localCenterB = pc->localCenterB;
+		int32 pointCount = pc->pointCount;
+
+		float mA = 0.0f;
+		float iA = 0.0f;
+		if (indexA == toiIndexA || indexA == toiIndexB)
+		{
+			mA = pc->invMassA;
+			iA = pc->invIA;
+		}
+
+		float mB = 0.0f;
+		float iB = 0.0f;
+		if (indexB == toiIndexA || indexB == toiIndexB)
+		{
+			mB = pc->invMassB;
+			iB = pc->invIB;
+		}
+
+		b2Vec2 cA = m_positions[indexA].c;
+		float aA = m_positions[indexA].a;
+
+		b2Vec2 cB = m_positions[indexB].c;
+		float aB = m_positions[indexB].a;
+
+		// Solve normal constraints
+		for (int32 j = 0; j < pointCount; ++j)
+		{
+			b2Transform xfA, xfB;
+			xfA.q.Set(aA);
+			xfB.q.Set(aB);
+			xfA.p = cA - b2Mul(xfA.q, localCenterA);
+			xfB.p = cB - b2Mul(xfB.q, localCenterB);
+
+			b2PositionSolverManifold psm;
+			psm.Initialize(pc, xfA, xfB, j);
+			b2Vec2 normal = psm.normal;
+
+			b2Vec2 point = psm.point;
+			float separation = psm.separation;
+
+			b2Vec2 rA = point - cA;
+			b2Vec2 rB = point - cB;
+
+			// Track max constraint error.
+			minSeparation = b2Min(minSeparation, separation);
+
+			// Prevent large corrections and allow slop.
+			float C = b2Clamp(b2_toiBaumgarte * (separation + b2_linearSlop), -b2_maxLinearCorrection, 0.0f);
+
+			// Compute the effective mass.
+			float rnA = b2Cross(rA, normal);
+			float rnB = b2Cross(rB, normal);
+			float K = mA + mB + iA * rnA * rnA + iB * rnB * rnB;
+
+			// Compute normal impulse
+			float impulse = K > 0.0f ? - C / K : 0.0f;
+
+			b2Vec2 P = impulse * normal;
+
+			cA -= mA * P;
+			aA -= iA * b2Cross(rA, P);
+
+			cB += mB * P;
+			aB += iB * b2Cross(rB, P);
+		}
+
+		m_positions[indexA].c = cA;
+		m_positions[indexA].a = aA;
+
+		m_positions[indexB].c = cB;
+		m_positions[indexB].a = aB;
+	}
+
+	// We can't expect minSpeparation >= -b2_linearSlop because we don't
+	// push the separation above -b2_linearSlop.
+	return minSeparation >= -1.5f * b2_linearSlop;
+}

3rd/box2d/src/dynamics/b2_contact_solver.h

@@ -0,0 +1,100 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#ifndef B2_CONTACT_SOLVER_H
+#define B2_CONTACT_SOLVER_H
+
+#include "box2d/b2_collision.h"
+#include "box2d/b2_math.h"
+#include "box2d/b2_time_step.h"
+
+class b2Contact;
+class b2Body;
+class b2StackAllocator;
+struct b2ContactPositionConstraint;
+
+struct b2VelocityConstraintPoint
+{
+	b2Vec2 rA;
+	b2Vec2 rB;
+	float normalImpulse;
+	float tangentImpulse;
+	float normalMass;
+	float tangentMass;
+	float velocityBias;
+};
+
+struct b2ContactVelocityConstraint
+{
+	b2VelocityConstraintPoint points[b2_maxManifoldPoints];
+	b2Vec2 normal;
+	b2Mat22 normalMass;
+	b2Mat22 K;
+	int32 indexA;
+	int32 indexB;
+	float invMassA, invMassB;
+	float invIA, invIB;
+	float friction;
+	float restitution;
+	float threshold;
+	float tangentSpeed;
+	int32 pointCount;
+	int32 contactIndex;
+};
+
+struct b2ContactSolverDef
+{
+	b2TimeStep step;
+	b2Contact** contacts;
+	int32 count;
+	b2Position* positions;
+	b2Velocity* velocities;
+	b2StackAllocator* allocator;
+};
+
+class b2ContactSolver
+{
+public:
+	b2ContactSolver(b2ContactSolverDef* def);
+	~b2ContactSolver();
+
+	void InitializeVelocityConstraints();
+
+	void WarmStart();
+	void SolveVelocityConstraints();
+	void StoreImpulses();
+
+	bool SolvePositionConstraints();
+	bool SolveTOIPositionConstraints(int32 toiIndexA, int32 toiIndexB);
+
+	b2TimeStep m_step;
+	b2Position* m_positions;
+	b2Velocity* m_velocities;
+	b2StackAllocator* m_allocator;
+	b2ContactPositionConstraint* m_positionConstraints;
+	b2ContactVelocityConstraint* m_velocityConstraints;
+	b2Contact** m_contacts;
+	int m_count;
+};
+
+#endif
+

3rd/box2d/src/dynamics/b2_distance_joint.cpp

@@ -0,0 +1,421 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#include "box2d/b2_body.h"
+#include "box2d/b2_draw.h"
+#include "box2d/b2_distance_joint.h"
+#include "box2d/b2_time_step.h"
+
+// 1-D constrained system
+// m (v2 - v1) = lambda
+// v2 + (beta/h) * x1 + gamma * lambda = 0, gamma has units of inverse mass.
+// x2 = x1 + h * v2
+
+// 1-D mass-damper-spring system
+// m (v2 - v1) + h * d * v2 + h * k * 
+
+// C = norm(p2 - p1) - L
+// u = (p2 - p1) / norm(p2 - p1)
+// Cdot = dot(u, v2 + cross(w2, r2) - v1 - cross(w1, r1))
+// J = [-u -cross(r1, u) u cross(r2, u)]
+// K = J * invM * JT
+//   = invMass1 + invI1 * cross(r1, u)^2 + invMass2 + invI2 * cross(r2, u)^2
+
+
+void b2DistanceJointDef::Initialize(b2Body* b1, b2Body* b2,
+									const b2Vec2& anchor1, const b2Vec2& anchor2)
+{
+	bodyA = b1;
+	bodyB = b2;
+	localAnchorA = bodyA->GetLocalPoint(anchor1);
+	localAnchorB = bodyB->GetLocalPoint(anchor2);
+	b2Vec2 d = anchor2 - anchor1;
+	length = b2Max(d.Length(), b2_linearSlop);
+	minLength = length;
+	maxLength = length;
+}
+
+b2DistanceJoint::b2DistanceJoint(const b2DistanceJointDef* def)
+: b2Joint(def)
+{
+	m_localAnchorA = def->localAnchorA;
+	m_localAnchorB = def->localAnchorB;
+	m_length = b2Max(def->length, b2_linearSlop);
+	m_minLength = b2Max(def->minLength, b2_linearSlop);
+	m_maxLength = b2Max(def->maxLength, m_minLength);
+	m_stiffness = def->stiffness;
+	m_damping = def->damping;
+
+	m_gamma = 0.0f;
+	m_bias = 0.0f;
+	m_impulse = 0.0f;
+	m_lowerImpulse = 0.0f;
+	m_upperImpulse = 0.0f;
+	m_currentLength = 0.0f;
+}
+
+void b2DistanceJoint::InitVelocityConstraints(const b2SolverData& data)
+{
+	m_indexA = m_bodyA->m_islandIndex;
+	m_indexB = m_bodyB->m_islandIndex;
+	m_localCenterA = m_bodyA->m_sweep.localCenter;
+	m_localCenterB = m_bodyB->m_sweep.localCenter;
+	m_invMassA = m_bodyA->m_invMass;
+	m_invMassB = m_bodyB->m_invMass;
+	m_invIA = m_bodyA->m_invI;
+	m_invIB = m_bodyB->m_invI;
+
+	b2Vec2 cA = data.positions[m_indexA].c;
+	float aA = data.positions[m_indexA].a;
+	b2Vec2 vA = data.velocities[m_indexA].v;
+	float wA = data.velocities[m_indexA].w;
+
+	b2Vec2 cB = data.positions[m_indexB].c;
+	float aB = data.positions[m_indexB].a;
+	b2Vec2 vB = data.velocities[m_indexB].v;
+	float wB = data.velocities[m_indexB].w;
+
+	b2Rot qA(aA), qB(aB);
+
+	m_rA = b2Mul(qA, m_localAnchorA - m_localCenterA);
+	m_rB = b2Mul(qB, m_localAnchorB - m_localCenterB);
+	m_u = cB + m_rB - cA - m_rA;
+
+	// Handle singularity.
+	m_currentLength = m_u.Length();
+	if (m_currentLength > b2_linearSlop)
+	{
+		m_u *= 1.0f / m_currentLength;
+	}
+	else
+	{
+		m_u.Set(0.0f, 0.0f);
+		m_mass = 0.0f;
+		m_impulse = 0.0f;
+		m_lowerImpulse = 0.0f;
+		m_upperImpulse = 0.0f;
+	}
+
+	float crAu = b2Cross(m_rA, m_u);
+	float crBu = b2Cross(m_rB, m_u);
+	float invMass = m_invMassA + m_invIA * crAu * crAu + m_invMassB + m_invIB * crBu * crBu;
+	m_mass = invMass != 0.0f ? 1.0f / invMass : 0.0f;
+
+	if (m_stiffness > 0.0f && m_minLength < m_maxLength)
+	{
+		// soft
+		float C = m_currentLength - m_length;
+
+		float d = m_damping;
+		float k = m_stiffness;
+
+		// magic formulas
+		float h = data.step.dt;
+
+		// gamma = 1 / (h * (d + h * k))
+		// the extra factor of h in the denominator is since the lambda is an impulse, not a force
+		m_gamma = h * (d + h * k);
+		m_gamma = m_gamma != 0.0f ? 1.0f / m_gamma : 0.0f;
+		m_bias = C * h * k * m_gamma;
+
+		invMass += m_gamma;
+		m_softMass = invMass != 0.0f ? 1.0f / invMass : 0.0f;
+	}
+	else
+	{
+		// rigid
+		m_gamma = 0.0f;
+		m_bias = 0.0f;
+		m_softMass = m_mass;
+	}
+
+	if (data.step.warmStarting)
+	{
+		// Scale the impulse to support a variable time step.
+		m_impulse *= data.step.dtRatio;
+		m_lowerImpulse *= data.step.dtRatio;
+		m_upperImpulse *= data.step.dtRatio;
+
+		b2Vec2 P = (m_impulse + m_lowerImpulse - m_upperImpulse) * m_u;
+		vA -= m_invMassA * P;
+		wA -= m_invIA * b2Cross(m_rA, P);
+		vB += m_invMassB * P;
+		wB += m_invIB * b2Cross(m_rB, P);
+	}
+	else
+	{
+		m_impulse = 0.0f;
+	}
+
+	data.velocities[m_indexA].v = vA;
+	data.velocities[m_indexA].w = wA;
+	data.velocities[m_indexB].v = vB;
+	data.velocities[m_indexB].w = wB;
+}
+
+void b2DistanceJoint::SolveVelocityConstraints(const b2SolverData& data)
+{
+	b2Vec2 vA = data.velocities[m_indexA].v;
+	float wA = data.velocities[m_indexA].w;
+	b2Vec2 vB = data.velocities[m_indexB].v;
+	float wB = data.velocities[m_indexB].w;
+
+	if (m_minLength < m_maxLength)
+	{
+		if (m_stiffness > 0.0f)
+		{
+			// Cdot = dot(u, v + cross(w, r))
+			b2Vec2 vpA = vA + b2Cross(wA, m_rA);
+			b2Vec2 vpB = vB + b2Cross(wB, m_rB);
+			float Cdot = b2Dot(m_u, vpB - vpA);
+
+			float impulse = -m_softMass * (Cdot + m_bias + m_gamma * m_impulse);
+			m_impulse += impulse;
+
+			b2Vec2 P = impulse * m_u;
+			vA -= m_invMassA * P;
+			wA -= m_invIA * b2Cross(m_rA, P);
+			vB += m_invMassB * P;
+			wB += m_invIB * b2Cross(m_rB, P);
+		}
+
+		// lower
+		{
+			float C = m_currentLength - m_minLength;
+			float bias = b2Max(0.0f, C) * data.step.inv_dt;
+
+			b2Vec2 vpA = vA + b2Cross(wA, m_rA);
+			b2Vec2 vpB = vB + b2Cross(wB, m_rB);
+			float Cdot = b2Dot(m_u, vpB - vpA);
+
+			float impulse = -m_mass * (Cdot + bias);
+			float oldImpulse = m_lowerImpulse;
+			m_lowerImpulse = b2Max(0.0f, m_lowerImpulse + impulse);
+			impulse = m_lowerImpulse - oldImpulse;
+			b2Vec2 P = impulse * m_u;
+
+			vA -= m_invMassA * P;
+			wA -= m_invIA * b2Cross(m_rA, P);
+			vB += m_invMassB * P;
+			wB += m_invIB * b2Cross(m_rB, P);
+		}
+
+		// upper
+		{
+			float C = m_maxLength - m_currentLength;
+			float bias = b2Max(0.0f, C) * data.step.inv_dt;
+
+			b2Vec2 vpA = vA + b2Cross(wA, m_rA);
+			b2Vec2 vpB = vB + b2Cross(wB, m_rB);
+			float Cdot = b2Dot(m_u, vpA - vpB);
+
+			float impulse = -m_mass * (Cdot + bias);
+			float oldImpulse = m_upperImpulse;
+			m_upperImpulse = b2Max(0.0f, m_upperImpulse + impulse);
+			impulse = m_upperImpulse - oldImpulse;
+			b2Vec2 P = -impulse * m_u;
+
+			vA -= m_invMassA * P;
+			wA -= m_invIA * b2Cross(m_rA, P);
+			vB += m_invMassB * P;
+			wB += m_invIB * b2Cross(m_rB, P);
+		}
+	}
+	else
+	{
+		// Equal limits
+
+		// Cdot = dot(u, v + cross(w, r))
+		b2Vec2 vpA = vA + b2Cross(wA, m_rA);
+		b2Vec2 vpB = vB + b2Cross(wB, m_rB);
+		float Cdot = b2Dot(m_u, vpB - vpA);
+
+		float impulse = -m_mass * Cdot;
+		m_impulse += impulse;
+
+		b2Vec2 P = impulse * m_u;
+		vA -= m_invMassA * P;
+		wA -= m_invIA * b2Cross(m_rA, P);
+		vB += m_invMassB * P;
+		wB += m_invIB * b2Cross(m_rB, P);
+	}
+
+	data.velocities[m_indexA].v = vA;
+	data.velocities[m_indexA].w = wA;
+	data.velocities[m_indexB].v = vB;
+	data.velocities[m_indexB].w = wB;
+}
+
+bool b2DistanceJoint::SolvePositionConstraints(const b2SolverData& data)
+{
+	b2Vec2 cA = data.positions[m_indexA].c;
+	float aA = data.positions[m_indexA].a;
+	b2Vec2 cB = data.positions[m_indexB].c;
+	float aB = data.positions[m_indexB].a;
+
+	b2Rot qA(aA), qB(aB);
+
+	b2Vec2 rA = b2Mul(qA, m_localAnchorA - m_localCenterA);
+	b2Vec2 rB = b2Mul(qB, m_localAnchorB - m_localCenterB);
+	b2Vec2 u = cB + rB - cA - rA;
+
+	float length = u.Normalize();
+	float C;
+	if (m_minLength == m_maxLength)
+	{
+		C = length - m_minLength;
+	}
+	else if (length < m_minLength)
+	{
+		C = length - m_minLength;
+	}
+	else if (m_maxLength < length)
+	{
+		C = length - m_maxLength;
+	}
+	else
+	{
+		return true;
+	}
+
+	float impulse = -m_mass * C;
+	b2Vec2 P = impulse * u;
+
+	cA -= m_invMassA * P;
+	aA -= m_invIA * b2Cross(rA, P);
+	cB += m_invMassB * P;
+	aB += m_invIB * b2Cross(rB, P);
+
+	data.positions[m_indexA].c = cA;
+	data.positions[m_indexA].a = aA;
+	data.positions[m_indexB].c = cB;
+	data.positions[m_indexB].a = aB;
+
+	return b2Abs(C) < b2_linearSlop;
+}
+
+b2Vec2 b2DistanceJoint::GetAnchorA() const
+{
+	return m_bodyA->GetWorldPoint(m_localAnchorA);
+}
+
+b2Vec2 b2DistanceJoint::GetAnchorB() const
+{
+	return m_bodyB->GetWorldPoint(m_localAnchorB);
+}
+
+b2Vec2 b2DistanceJoint::GetReactionForce(float inv_dt) const
+{
+	b2Vec2 F = inv_dt * (m_impulse + m_lowerImpulse - m_upperImpulse) * m_u;
+	return F;
+}
+
+float b2DistanceJoint::GetReactionTorque(float inv_dt) const
+{
+	B2_NOT_USED(inv_dt);
+	return 0.0f;
+}
+
+float b2DistanceJoint::SetLength(float length)
+{
+	m_impulse = 0.0f;
+	m_length = b2Max(b2_linearSlop, length);
+	return m_length;
+}
+
+float b2DistanceJoint::SetMinLength(float minLength)
+{
+	m_lowerImpulse = 0.0f;
+	m_minLength = b2Clamp(minLength, b2_linearSlop, m_maxLength);
+	return m_minLength;
+}
+
+float b2DistanceJoint::SetMaxLength(float maxLength)
+{
+	m_upperImpulse = 0.0f;
+	m_maxLength = b2Max(maxLength, m_minLength);
+	return m_maxLength;
+}
+
+float b2DistanceJoint::GetCurrentLength() const
+{
+	b2Vec2 pA = m_bodyA->GetWorldPoint(m_localAnchorA);
+	b2Vec2 pB = m_bodyB->GetWorldPoint(m_localAnchorB);
+	b2Vec2 d = pB - pA;
+	float length = d.Length();
+	return length;
+}
+
+void b2DistanceJoint::Dump()
+{
+	int32 indexA = m_bodyA->m_islandIndex;
+	int32 indexB = m_bodyB->m_islandIndex;
+
+	b2Dump("  b2DistanceJointDef jd;\n");
+	b2Dump("  jd.bodyA = bodies[%d];\n", indexA);
+	b2Dump("  jd.bodyB = bodies[%d];\n", indexB);
+	b2Dump("  jd.collideConnected = bool(%d);\n", m_collideConnected);
+	b2Dump("  jd.localAnchorA.Set(%.9g, %.9g);\n", m_localAnchorA.x, m_localAnchorA.y);
+	b2Dump("  jd.localAnchorB.Set(%.9g, %.9g);\n", m_localAnchorB.x, m_localAnchorB.y);
+	b2Dump("  jd.length = %.9g;\n", m_length);
+	b2Dump("  jd.minLength = %.9g;\n", m_minLength);
+	b2Dump("  jd.maxLength = %.9g;\n", m_maxLength);
+	b2Dump("  jd.stiffness = %.9g;\n", m_stiffness);
+	b2Dump("  jd.damping = %.9g;\n", m_damping);
+	b2Dump("  joints[%d] = m_world->CreateJoint(&jd);\n", m_index);
+}
+
+void b2DistanceJoint::Draw(b2Draw* draw) const
+{
+	const b2Transform& xfA = m_bodyA->GetTransform();
+	const b2Transform& xfB = m_bodyB->GetTransform();
+	b2Vec2 pA = b2Mul(xfA, m_localAnchorA);
+	b2Vec2 pB = b2Mul(xfB, m_localAnchorB);
+
+	b2Vec2 axis = pB - pA;
+	axis.Normalize();
+
+	b2Color c1(0.7f, 0.7f, 0.7f);
+	b2Color c2(0.3f, 0.9f, 0.3f);
+	b2Color c3(0.9f, 0.3f, 0.3f);
+	b2Color c4(0.4f, 0.4f, 0.4f);
+
+	draw->DrawSegment(pA, pB, c4);
+	
+	b2Vec2 pRest = pA + m_length * axis;
+	draw->DrawPoint(pRest, 8.0f, c1);
+
+	if (m_minLength != m_maxLength)
+	{
+		if (m_minLength > b2_linearSlop)
+		{
+			b2Vec2 pMin = pA + m_minLength * axis;
+			draw->DrawPoint(pMin, 4.0f, c2);
+		}
+
+		if (m_maxLength < FLT_MAX)
+		{
+			b2Vec2 pMax = pA + m_maxLength * axis;
+			draw->DrawPoint(pMax, 4.0f, c3);
+		}
+	}
+}

3rd/box2d/src/dynamics/b2_edge_circle_contact.cpp

@@ -0,0 +1,54 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#include "b2_edge_circle_contact.h"
+
+#include "box2d/b2_block_allocator.h"
+#include "box2d/b2_fixture.h"
+
+#include <new>
+
+b2Contact* b2EdgeAndCircleContact::Create(b2Fixture* fixtureA, int32, b2Fixture* fixtureB, int32, b2BlockAllocator* allocator)
+{
+	void* mem = allocator->Allocate(sizeof(b2EdgeAndCircleContact));
+	return new (mem) b2EdgeAndCircleContact(fixtureA, fixtureB);
+}
+
+void b2EdgeAndCircleContact::Destroy(b2Contact* contact, b2BlockAllocator* allocator)
+{
+	((b2EdgeAndCircleContact*)contact)->~b2EdgeAndCircleContact();
+	allocator->Free(contact, sizeof(b2EdgeAndCircleContact));
+}
+
+b2EdgeAndCircleContact::b2EdgeAndCircleContact(b2Fixture* fixtureA, b2Fixture* fixtureB)
+: b2Contact(fixtureA, 0, fixtureB, 0)
+{
+	b2Assert(m_fixtureA->GetType() == b2Shape::e_edge);
+	b2Assert(m_fixtureB->GetType() == b2Shape::e_circle);
+}
+
+void b2EdgeAndCircleContact::Evaluate(b2Manifold* manifold, const b2Transform& xfA, const b2Transform& xfB)
+{
+	b2CollideEdgeAndCircle(	manifold,
+								(b2EdgeShape*)m_fixtureA->GetShape(), xfA,
+								(b2CircleShape*)m_fixtureB->GetShape(), xfB);
+}

3rd/box2d/src/dynamics/b2_edge_circle_contact.h

@@ -0,0 +1,43 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#ifndef B2_EDGE_AND_CIRCLE_CONTACT_H
+#define B2_EDGE_AND_CIRCLE_CONTACT_H
+
+#include "box2d/b2_contact.h"
+
+class b2BlockAllocator;
+
+class b2EdgeAndCircleContact : public b2Contact
+{
+public:
+	static b2Contact* Create(	b2Fixture* fixtureA, int32 indexA,
+								b2Fixture* fixtureB, int32 indexB, b2BlockAllocator* allocator);
+	static void Destroy(b2Contact* contact, b2BlockAllocator* allocator);
+
+	b2EdgeAndCircleContact(b2Fixture* fixtureA, b2Fixture* fixtureB);
+	~b2EdgeAndCircleContact() {}
+
+	void Evaluate(b2Manifold* manifold, const b2Transform& xfA, const b2Transform& xfB) override;
+};
+
+#endif

3rd/box2d/src/dynamics/b2_edge_polygon_contact.cpp

@@ -0,0 +1,54 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#include "b2_edge_polygon_contact.h"
+
+#include "box2d/b2_block_allocator.h"
+#include "box2d/b2_fixture.h"
+
+#include <new>
+
+b2Contact* b2EdgeAndPolygonContact::Create(b2Fixture* fixtureA, int32, b2Fixture* fixtureB, int32, b2BlockAllocator* allocator)
+{
+	void* mem = allocator->Allocate(sizeof(b2EdgeAndPolygonContact));
+	return new (mem) b2EdgeAndPolygonContact(fixtureA, fixtureB);
+}
+
+void b2EdgeAndPolygonContact::Destroy(b2Contact* contact, b2BlockAllocator* allocator)
+{
+	((b2EdgeAndPolygonContact*)contact)->~b2EdgeAndPolygonContact();
+	allocator->Free(contact, sizeof(b2EdgeAndPolygonContact));
+}
+
+b2EdgeAndPolygonContact::b2EdgeAndPolygonContact(b2Fixture* fixtureA, b2Fixture* fixtureB)
+: b2Contact(fixtureA, 0, fixtureB, 0)
+{
+	b2Assert(m_fixtureA->GetType() == b2Shape::e_edge);
+	b2Assert(m_fixtureB->GetType() == b2Shape::e_polygon);
+}
+
+void b2EdgeAndPolygonContact::Evaluate(b2Manifold* manifold, const b2Transform& xfA, const b2Transform& xfB)
+{
+	b2CollideEdgeAndPolygon(	manifold,
+								(b2EdgeShape*)m_fixtureA->GetShape(), xfA,
+								(b2PolygonShape*)m_fixtureB->GetShape(), xfB);
+}

3rd/box2d/src/dynamics/b2_edge_polygon_contact.h

@@ -0,0 +1,43 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#ifndef B2_EDGE_AND_POLYGON_CONTACT_H
+#define B2_EDGE_AND_POLYGON_CONTACT_H
+
+#include "box2d/b2_contact.h"
+
+class b2BlockAllocator;
+
+class b2EdgeAndPolygonContact : public b2Contact
+{
+public:
+	static b2Contact* Create(	b2Fixture* fixtureA, int32 indexA,
+								b2Fixture* fixtureB, int32 indexB, b2BlockAllocator* allocator);
+	static void Destroy(b2Contact* contact, b2BlockAllocator* allocator);
+
+	b2EdgeAndPolygonContact(b2Fixture* fixtureA, b2Fixture* fixtureB);
+	~b2EdgeAndPolygonContact() {}
+
+	void Evaluate(b2Manifold* manifold, const b2Transform& xfA, const b2Transform& xfB) override;
+};
+
+#endif

3rd/box2d/src/dynamics/b2_fixture.cpp

@@ -0,0 +1,305 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#include "box2d/b2_fixture.h"
+#include "box2d/b2_block_allocator.h"
+#include "box2d/b2_broad_phase.h"
+#include "box2d/b2_chain_shape.h"
+#include "box2d/b2_circle_shape.h"
+#include "box2d/b2_collision.h"
+#include "box2d/b2_contact.h"
+#include "box2d/b2_edge_shape.h"
+#include "box2d/b2_polygon_shape.h"
+#include "box2d/b2_world.h"
+
+b2Fixture::b2Fixture()
+{
+	m_body = nullptr;
+	m_next = nullptr;
+	m_proxies = nullptr;
+	m_proxyCount = 0;
+	m_shape = nullptr;
+	m_density = 0.0f;
+}
+
+void b2Fixture::Create(b2BlockAllocator* allocator, b2Body* body, const b2FixtureDef* def)
+{
+	m_userData = def->userData;
+	m_friction = def->friction;
+	m_restitution = def->restitution;
+	m_restitutionThreshold = def->restitutionThreshold;
+
+	m_body = body;
+	m_next = nullptr;
+
+	m_filter = def->filter;
+
+	m_isSensor = def->isSensor;
+
+	m_shape = def->shape->Clone(allocator);
+
+	// Reserve proxy space
+	int32 childCount = m_shape->GetChildCount();
+	m_proxies = (b2FixtureProxy*)allocator->Allocate(childCount * sizeof(b2FixtureProxy));
+	for (int32 i = 0; i < childCount; ++i)
+	{
+		m_proxies[i].fixture = nullptr;
+		m_proxies[i].proxyId = b2BroadPhase::e_nullProxy;
+	}
+	m_proxyCount = 0;
+
+	m_density = def->density;
+}
+
+void b2Fixture::Destroy(b2BlockAllocator* allocator)
+{
+	// The proxies must be destroyed before calling this.
+	b2Assert(m_proxyCount == 0);
+
+	// Free the proxy array.
+	int32 childCount = m_shape->GetChildCount();
+	allocator->Free(m_proxies, childCount * sizeof(b2FixtureProxy));
+	m_proxies = nullptr;
+
+	// Free the child shape.
+	switch (m_shape->m_type)
+	{
+	case b2Shape::e_circle:
+		{
+			b2CircleShape* s = (b2CircleShape*)m_shape;
+			s->~b2CircleShape();
+			allocator->Free(s, sizeof(b2CircleShape));
+		}
+		break;
+
+	case b2Shape::e_edge:
+		{
+			b2EdgeShape* s = (b2EdgeShape*)m_shape;
+			s->~b2EdgeShape();
+			allocator->Free(s, sizeof(b2EdgeShape));
+		}
+		break;
+
+	case b2Shape::e_polygon:
+		{
+			b2PolygonShape* s = (b2PolygonShape*)m_shape;
+			s->~b2PolygonShape();
+			allocator->Free(s, sizeof(b2PolygonShape));
+		}
+		break;
+
+	case b2Shape::e_chain:
+		{
+			b2ChainShape* s = (b2ChainShape*)m_shape;
+			s->~b2ChainShape();
+			allocator->Free(s, sizeof(b2ChainShape));
+		}
+		break;
+
+	default:
+		b2Assert(false);
+		break;
+	}
+
+	m_shape = nullptr;
+}
+
+void b2Fixture::CreateProxies(b2BroadPhase* broadPhase, const b2Transform& xf)
+{
+	b2Assert(m_proxyCount == 0);
+
+	// Create proxies in the broad-phase.
+	m_proxyCount = m_shape->GetChildCount();
+
+	for (int32 i = 0; i < m_proxyCount; ++i)
+	{
+		b2FixtureProxy* proxy = m_proxies + i;
+		m_shape->ComputeAABB(&proxy->aabb, xf, i);
+		proxy->proxyId = broadPhase->CreateProxy(proxy->aabb, proxy);
+		proxy->fixture = this;
+		proxy->childIndex = i;
+	}
+}
+
+void b2Fixture::DestroyProxies(b2BroadPhase* broadPhase)
+{
+	// Destroy proxies in the broad-phase.
+	for (int32 i = 0; i < m_proxyCount; ++i)
+	{
+		b2FixtureProxy* proxy = m_proxies + i;
+		broadPhase->DestroyProxy(proxy->proxyId);
+		proxy->proxyId = b2BroadPhase::e_nullProxy;
+	}
+
+	m_proxyCount = 0;
+}
+
+void b2Fixture::Synchronize(b2BroadPhase* broadPhase, const b2Transform& transform1, const b2Transform& transform2)
+{
+	if (m_proxyCount == 0)
+	{	
+		return;
+	}
+
+	for (int32 i = 0; i < m_proxyCount; ++i)
+	{
+		b2FixtureProxy* proxy = m_proxies + i;
+
+		// Compute an AABB that covers the swept shape (may miss some rotation effect).
+		b2AABB aabb1, aabb2;
+		m_shape->ComputeAABB(&aabb1, transform1, proxy->childIndex);
+		m_shape->ComputeAABB(&aabb2, transform2, proxy->childIndex);
+	
+		proxy->aabb.Combine(aabb1, aabb2);
+
+		b2Vec2 displacement = aabb2.GetCenter() - aabb1.GetCenter();
+
+		broadPhase->MoveProxy(proxy->proxyId, proxy->aabb, displacement);
+	}
+}
+
+void b2Fixture::SetFilterData(const b2Filter& filter)
+{
+	m_filter = filter;
+
+	Refilter();
+}
+
+void b2Fixture::Refilter()
+{
+	if (m_body == nullptr)
+	{
+		return;
+	}
+
+	// Flag associated contacts for filtering.
+	b2ContactEdge* edge = m_body->GetContactList();
+	while (edge)
+	{
+		b2Contact* contact = edge->contact;
+		b2Fixture* fixtureA = contact->GetFixtureA();
+		b2Fixture* fixtureB = contact->GetFixtureB();
+		if (fixtureA == this || fixtureB == this)
+		{
+			contact->FlagForFiltering();
+		}
+
+		edge = edge->next;
+	}
+
+	b2World* world = m_body->GetWorld();
+
+	if (world == nullptr)
+	{
+		return;
+	}
+
+	// Touch each proxy so that new pairs may be created
+	b2BroadPhase* broadPhase = &world->m_contactManager.m_broadPhase;
+	for (int32 i = 0; i < m_proxyCount; ++i)
+	{
+		broadPhase->TouchProxy(m_proxies[i].proxyId);
+	}
+}
+
+void b2Fixture::SetSensor(bool sensor)
+{
+	if (sensor != m_isSensor)
+	{
+		m_body->SetAwake(true);
+		m_isSensor = sensor;
+	}
+}
+
+void b2Fixture::Dump(int32 bodyIndex)
+{
+	b2Dump("    b2FixtureDef fd;\n");
+	b2Dump("    fd.friction = %.9g;\n", m_friction);
+	b2Dump("    fd.restitution = %.9g;\n", m_restitution);
+	b2Dump("    fd.restitutionThreshold = %.9g;\n", m_restitutionThreshold);
+	b2Dump("    fd.density = %.9g;\n", m_density);
+	b2Dump("    fd.isSensor = bool(%d);\n", m_isSensor);
+	b2Dump("    fd.filter.categoryBits = uint16(%d);\n", m_filter.categoryBits);
+	b2Dump("    fd.filter.maskBits = uint16(%d);\n", m_filter.maskBits);
+	b2Dump("    fd.filter.groupIndex = int16(%d);\n", m_filter.groupIndex);
+
+	switch (m_shape->m_type)
+	{
+	case b2Shape::e_circle:
+		{
+			b2CircleShape* s = (b2CircleShape*)m_shape;
+			b2Dump("    b2CircleShape shape;\n");
+			b2Dump("    shape.m_radius = %.9g;\n", s->m_radius);
+			b2Dump("    shape.m_p.Set(%.9g, %.9g);\n", s->m_p.x, s->m_p.y);
+		}
+		break;
+
+	case b2Shape::e_edge:
+		{
+			b2EdgeShape* s = (b2EdgeShape*)m_shape;
+			b2Dump("    b2EdgeShape shape;\n");
+			b2Dump("    shape.m_radius = %.9g;\n", s->m_radius);
+			b2Dump("    shape.m_vertex0.Set(%.9g, %.9g);\n", s->m_vertex0.x, s->m_vertex0.y);
+			b2Dump("    shape.m_vertex1.Set(%.9g, %.9g);\n", s->m_vertex1.x, s->m_vertex1.y);
+			b2Dump("    shape.m_vertex2.Set(%.9g, %.9g);\n", s->m_vertex2.x, s->m_vertex2.y);
+			b2Dump("    shape.m_vertex3.Set(%.9g, %.9g);\n", s->m_vertex3.x, s->m_vertex3.y);
+			b2Dump("    shape.m_oneSided = bool(%d);\n", s->m_oneSided);
+		}
+		break;
+
+	case b2Shape::e_polygon:
+		{
+			b2PolygonShape* s = (b2PolygonShape*)m_shape;
+			b2Dump("    b2PolygonShape shape;\n");
+			b2Dump("    b2Vec2 vs[%d];\n", b2_maxPolygonVertices);
+			for (int32 i = 0; i < s->m_count; ++i)
+			{
+				b2Dump("    vs[%d].Set(%.9g, %.9g);\n", i, s->m_vertices[i].x, s->m_vertices[i].y);
+			}
+			b2Dump("    shape.Set(vs, %d);\n", s->m_count);
+		}
+		break;
+
+	case b2Shape::e_chain:
+		{
+			b2ChainShape* s = (b2ChainShape*)m_shape;
+			b2Dump("    b2ChainShape shape;\n");
+			b2Dump("    b2Vec2 vs[%d];\n", s->m_count);
+			for (int32 i = 0; i < s->m_count; ++i)
+			{
+				b2Dump("    vs[%d].Set(%.9g, %.9g);\n", i, s->m_vertices[i].x, s->m_vertices[i].y);
+			}
+			b2Dump("    shape.CreateChain(vs, %d);\n", s->m_count);
+			b2Dump("    shape.m_prevVertex.Set(%.9g, %.9g);\n", s->m_prevVertex.x, s->m_prevVertex.y);
+			b2Dump("    shape.m_nextVertex.Set(%.9g, %.9g);\n", s->m_nextVertex.x, s->m_nextVertex.y);
+		}
+		break;
+
+	default:
+		return;
+	}
+
+	b2Dump("\n");
+	b2Dump("    fd.shape = &shape;\n");
+	b2Dump("\n");
+	b2Dump("    bodies[%d]->CreateFixture(&fd);\n", bodyIndex);
+}

3rd/box2d/src/dynamics/b2_friction_joint.cpp

@@ -0,0 +1,255 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#include "box2d/b2_friction_joint.h"
+#include "box2d/b2_body.h"
+#include "box2d/b2_time_step.h"
+
+// Point-to-point constraint
+// Cdot = v2 - v1
+//      = v2 + cross(w2, r2) - v1 - cross(w1, r1)
+// J = [-I -r1_skew I r2_skew ]
+// Identity used:
+// w k % (rx i + ry j) = w * (-ry i + rx j)
+
+// Angle constraint
+// Cdot = w2 - w1
+// J = [0 0 -1 0 0 1]
+// K = invI1 + invI2
+
+void b2FrictionJointDef::Initialize(b2Body* bA, b2Body* bB, const b2Vec2& anchor)
+{
+	bodyA = bA;
+	bodyB = bB;
+	localAnchorA = bodyA->GetLocalPoint(anchor);
+	localAnchorB = bodyB->GetLocalPoint(anchor);
+}
+
+b2FrictionJoint::b2FrictionJoint(const b2FrictionJointDef* def)
+: b2Joint(def)
+{
+	m_localAnchorA = def->localAnchorA;
+	m_localAnchorB = def->localAnchorB;
+
+	m_linearImpulse.SetZero();
+	m_angularImpulse = 0.0f;
+
+	m_maxForce = def->maxForce;
+	m_maxTorque = def->maxTorque;
+}
+
+void b2FrictionJoint::InitVelocityConstraints(const b2SolverData& data)
+{
+	m_indexA = m_bodyA->m_islandIndex;
+	m_indexB = m_bodyB->m_islandIndex;
+	m_localCenterA = m_bodyA->m_sweep.localCenter;
+	m_localCenterB = m_bodyB->m_sweep.localCenter;
+	m_invMassA = m_bodyA->m_invMass;
+	m_invMassB = m_bodyB->m_invMass;
+	m_invIA = m_bodyA->m_invI;
+	m_invIB = m_bodyB->m_invI;
+
+	float aA = data.positions[m_indexA].a;
+	b2Vec2 vA = data.velocities[m_indexA].v;
+	float wA = data.velocities[m_indexA].w;
+
+	float aB = data.positions[m_indexB].a;
+	b2Vec2 vB = data.velocities[m_indexB].v;
+	float wB = data.velocities[m_indexB].w;
+
+	b2Rot qA(aA), qB(aB);
+
+	// Compute the effective mass matrix.
+	m_rA = b2Mul(qA, m_localAnchorA - m_localCenterA);
+	m_rB = b2Mul(qB, m_localAnchorB - m_localCenterB);
+
+	// J = [-I -r1_skew I r2_skew]
+	//     [ 0       -1 0       1]
+	// r_skew = [-ry; rx]
+
+	// Matlab
+	// K = [ mA+r1y^2*iA+mB+r2y^2*iB,  -r1y*iA*r1x-r2y*iB*r2x,          -r1y*iA-r2y*iB]
+	//     [  -r1y*iA*r1x-r2y*iB*r2x, mA+r1x^2*iA+mB+r2x^2*iB,           r1x*iA+r2x*iB]
+	//     [          -r1y*iA-r2y*iB,           r1x*iA+r2x*iB,                   iA+iB]
+
+	float mA = m_invMassA, mB = m_invMassB;
+	float iA = m_invIA, iB = m_invIB;
+
+	b2Mat22 K;
+	K.ex.x = mA + mB + iA * m_rA.y * m_rA.y + iB * m_rB.y * m_rB.y;
+	K.ex.y = -iA * m_rA.x * m_rA.y - iB * m_rB.x * m_rB.y;
+	K.ey.x = K.ex.y;
+	K.ey.y = mA + mB + iA * m_rA.x * m_rA.x + iB * m_rB.x * m_rB.x;
+
+	m_linearMass = K.GetInverse();
+
+	m_angularMass = iA + iB;
+	if (m_angularMass > 0.0f)
+	{
+		m_angularMass = 1.0f / m_angularMass;
+	}
+
+	if (data.step.warmStarting)
+	{
+		// Scale impulses to support a variable time step.
+		m_linearImpulse *= data.step.dtRatio;
+		m_angularImpulse *= data.step.dtRatio;
+
+		b2Vec2 P(m_linearImpulse.x, m_linearImpulse.y);
+		vA -= mA * P;
+		wA -= iA * (b2Cross(m_rA, P) + m_angularImpulse);
+		vB += mB * P;
+		wB += iB * (b2Cross(m_rB, P) + m_angularImpulse);
+	}
+	else
+	{
+		m_linearImpulse.SetZero();
+		m_angularImpulse = 0.0f;
+	}
+
+	data.velocities[m_indexA].v = vA;
+	data.velocities[m_indexA].w = wA;
+	data.velocities[m_indexB].v = vB;
+	data.velocities[m_indexB].w = wB;
+}
+
+void b2FrictionJoint::SolveVelocityConstraints(const b2SolverData& data)
+{
+	b2Vec2 vA = data.velocities[m_indexA].v;
+	float wA = data.velocities[m_indexA].w;
+	b2Vec2 vB = data.velocities[m_indexB].v;
+	float wB = data.velocities[m_indexB].w;
+
+	float mA = m_invMassA, mB = m_invMassB;
+	float iA = m_invIA, iB = m_invIB;
+
+	float h = data.step.dt;
+
+	// Solve angular friction
+	{
+		float Cdot = wB - wA;
+		float impulse = -m_angularMass * Cdot;
+
+		float oldImpulse = m_angularImpulse;
+		float maxImpulse = h * m_maxTorque;
+		m_angularImpulse = b2Clamp(m_angularImpulse + impulse, -maxImpulse, maxImpulse);
+		impulse = m_angularImpulse - oldImpulse;
+
+		wA -= iA * impulse;
+		wB += iB * impulse;
+	}
+
+	// Solve linear friction
+	{
+		b2Vec2 Cdot = vB + b2Cross(wB, m_rB) - vA - b2Cross(wA, m_rA);
+
+		b2Vec2 impulse = -b2Mul(m_linearMass, Cdot);
+		b2Vec2 oldImpulse = m_linearImpulse;
+		m_linearImpulse += impulse;
+
+		float maxImpulse = h * m_maxForce;
+
+		if (m_linearImpulse.LengthSquared() > maxImpulse * maxImpulse)
+		{
+			m_linearImpulse.Normalize();
+			m_linearImpulse *= maxImpulse;
+		}
+
+		impulse = m_linearImpulse - oldImpulse;
+
+		vA -= mA * impulse;
+		wA -= iA * b2Cross(m_rA, impulse);
+
+		vB += mB * impulse;
+		wB += iB * b2Cross(m_rB, impulse);
+	}
+
+	data.velocities[m_indexA].v = vA;
+	data.velocities[m_indexA].w = wA;
+	data.velocities[m_indexB].v = vB;
+	data.velocities[m_indexB].w = wB;
+}
+
+bool b2FrictionJoint::SolvePositionConstraints(const b2SolverData& data)
+{
+	B2_NOT_USED(data);
+
+	return true;
+}
+
+b2Vec2 b2FrictionJoint::GetAnchorA() const
+{
+	return m_bodyA->GetWorldPoint(m_localAnchorA);
+}
+
+b2Vec2 b2FrictionJoint::GetAnchorB() const
+{
+	return m_bodyB->GetWorldPoint(m_localAnchorB);
+}
+
+b2Vec2 b2FrictionJoint::GetReactionForce(float inv_dt) const
+{
+	return inv_dt * m_linearImpulse;
+}
+
+float b2FrictionJoint::GetReactionTorque(float inv_dt) const
+{
+	return inv_dt * m_angularImpulse;
+}
+
+void b2FrictionJoint::SetMaxForce(float force)
+{
+	b2Assert(b2IsValid(force) && force >= 0.0f);
+	m_maxForce = force;
+}
+
+float b2FrictionJoint::GetMaxForce() const
+{
+	return m_maxForce;
+}
+
+void b2FrictionJoint::SetMaxTorque(float torque)
+{
+	b2Assert(b2IsValid(torque) && torque >= 0.0f);
+	m_maxTorque = torque;
+}
+
+float b2FrictionJoint::GetMaxTorque() const
+{
+	return m_maxTorque;
+}
+
+void b2FrictionJoint::Dump()
+{
+	int32 indexA = m_bodyA->m_islandIndex;
+	int32 indexB = m_bodyB->m_islandIndex;
+
+	b2Dump("  b2FrictionJointDef jd;\n");
+	b2Dump("  jd.bodyA = bodies[%d];\n", indexA);
+	b2Dump("  jd.bodyB = bodies[%d];\n", indexB);
+	b2Dump("  jd.collideConnected = bool(%d);\n", m_collideConnected);
+	b2Dump("  jd.localAnchorA.Set(%.9g, %.9g);\n", m_localAnchorA.x, m_localAnchorA.y);
+	b2Dump("  jd.localAnchorB.Set(%.9g, %.9g);\n", m_localAnchorB.x, m_localAnchorB.y);
+	b2Dump("  jd.maxForce = %.9g;\n", m_maxForce);
+	b2Dump("  jd.maxTorque = %.9g;\n", m_maxTorque);
+	b2Dump("  joints[%d] = m_world->CreateJoint(&jd);\n", m_index);
+}

3rd/box2d/src/dynamics/b2_gear_joint.cpp

@@ -0,0 +1,437 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#include "box2d/b2_gear_joint.h"
+#include "box2d/b2_revolute_joint.h"
+#include "box2d/b2_prismatic_joint.h"
+#include "box2d/b2_body.h"
+#include "box2d/b2_time_step.h"
+
+// Gear Joint:
+// C0 = (coordinate1 + ratio * coordinate2)_initial
+// C = (coordinate1 + ratio * coordinate2) - C0 = 0
+// J = [J1 ratio * J2]
+// K = J * invM * JT
+//   = J1 * invM1 * J1T + ratio * ratio * J2 * invM2 * J2T
+//
+// Revolute:
+// coordinate = rotation
+// Cdot = angularVelocity
+// J = [0 0 1]
+// K = J * invM * JT = invI
+//
+// Prismatic:
+// coordinate = dot(p - pg, ug)
+// Cdot = dot(v + cross(w, r), ug)
+// J = [ug cross(r, ug)]
+// K = J * invM * JT = invMass + invI * cross(r, ug)^2
+
+b2GearJoint::b2GearJoint(const b2GearJointDef* def)
+: b2Joint(def)
+{
+	m_joint1 = def->joint1;
+	m_joint2 = def->joint2;
+
+	m_typeA = m_joint1->GetType();
+	m_typeB = m_joint2->GetType();
+
+	b2Assert(m_typeA == e_revoluteJoint || m_typeA == e_prismaticJoint);
+	b2Assert(m_typeB == e_revoluteJoint || m_typeB == e_prismaticJoint);
+
+	float coordinateA, coordinateB;
+
+	// TODO_ERIN there might be some problem with the joint edges in b2Joint.
+
+	m_bodyC = m_joint1->GetBodyA();
+	m_bodyA = m_joint1->GetBodyB();
+
+	// Body B on joint1 must be dynamic
+	b2Assert(m_bodyA->m_type == b2_dynamicBody);
+
+	// Get geometry of joint1
+	b2Transform xfA = m_bodyA->m_xf;
+	float aA = m_bodyA->m_sweep.a;
+	b2Transform xfC = m_bodyC->m_xf;
+	float aC = m_bodyC->m_sweep.a;
+
+	if (m_typeA == e_revoluteJoint)
+	{
+		b2RevoluteJoint* revolute = (b2RevoluteJoint*)def->joint1;
+		m_localAnchorC = revolute->m_localAnchorA;
+		m_localAnchorA = revolute->m_localAnchorB;
+		m_referenceAngleA = revolute->m_referenceAngle;
+		m_localAxisC.SetZero();
+
+		coordinateA = aA - aC - m_referenceAngleA;
+
+		// position error is measured in radians
+		m_tolerance = b2_angularSlop;
+	}
+	else
+	{
+		b2PrismaticJoint* prismatic = (b2PrismaticJoint*)def->joint1;
+		m_localAnchorC = prismatic->m_localAnchorA;
+		m_localAnchorA = prismatic->m_localAnchorB;
+		m_referenceAngleA = prismatic->m_referenceAngle;
+		m_localAxisC = prismatic->m_localXAxisA;
+
+		b2Vec2 pC = m_localAnchorC;
+		b2Vec2 pA = b2MulT(xfC.q, b2Mul(xfA.q, m_localAnchorA) + (xfA.p - xfC.p));
+		coordinateA = b2Dot(pA - pC, m_localAxisC);
+
+		// position error is measured in meters
+		m_tolerance = b2_linearSlop;
+	}
+
+	m_bodyD = m_joint2->GetBodyA();
+	m_bodyB = m_joint2->GetBodyB();
+
+	// Body B on joint2 must be dynamic
+	b2Assert(m_bodyB->m_type == b2_dynamicBody);
+
+	// Get geometry of joint2
+	b2Transform xfB = m_bodyB->m_xf;
+	float aB = m_bodyB->m_sweep.a;
+	b2Transform xfD = m_bodyD->m_xf;
+	float aD = m_bodyD->m_sweep.a;
+
+	if (m_typeB == e_revoluteJoint)
+	{
+		b2RevoluteJoint* revolute = (b2RevoluteJoint*)def->joint2;
+		m_localAnchorD = revolute->m_localAnchorA;
+		m_localAnchorB = revolute->m_localAnchorB;
+		m_referenceAngleB = revolute->m_referenceAngle;
+		m_localAxisD.SetZero();
+
+		coordinateB = aB - aD - m_referenceAngleB;
+	}
+	else
+	{
+		b2PrismaticJoint* prismatic = (b2PrismaticJoint*)def->joint2;
+		m_localAnchorD = prismatic->m_localAnchorA;
+		m_localAnchorB = prismatic->m_localAnchorB;
+		m_referenceAngleB = prismatic->m_referenceAngle;
+		m_localAxisD = prismatic->m_localXAxisA;
+
+		b2Vec2 pD = m_localAnchorD;
+		b2Vec2 pB = b2MulT(xfD.q, b2Mul(xfB.q, m_localAnchorB) + (xfB.p - xfD.p));
+		coordinateB = b2Dot(pB - pD, m_localAxisD);
+	}
+
+	m_ratio = def->ratio;
+
+	m_constant = coordinateA + m_ratio * coordinateB;
+
+	m_impulse = 0.0f;
+}
+
+void b2GearJoint::InitVelocityConstraints(const b2SolverData& data)
+{
+	m_indexA = m_bodyA->m_islandIndex;
+	m_indexB = m_bodyB->m_islandIndex;
+	m_indexC = m_bodyC->m_islandIndex;
+	m_indexD = m_bodyD->m_islandIndex;
+	m_lcA = m_bodyA->m_sweep.localCenter;
+	m_lcB = m_bodyB->m_sweep.localCenter;
+	m_lcC = m_bodyC->m_sweep.localCenter;
+	m_lcD = m_bodyD->m_sweep.localCenter;
+	m_mA = m_bodyA->m_invMass;
+	m_mB = m_bodyB->m_invMass;
+	m_mC = m_bodyC->m_invMass;
+	m_mD = m_bodyD->m_invMass;
+	m_iA = m_bodyA->m_invI;
+	m_iB = m_bodyB->m_invI;
+	m_iC = m_bodyC->m_invI;
+	m_iD = m_bodyD->m_invI;
+
+	float aA = data.positions[m_indexA].a;
+	b2Vec2 vA = data.velocities[m_indexA].v;
+	float wA = data.velocities[m_indexA].w;
+
+	float aB = data.positions[m_indexB].a;
+	b2Vec2 vB = data.velocities[m_indexB].v;
+	float wB = data.velocities[m_indexB].w;
+
+	float aC = data.positions[m_indexC].a;
+	b2Vec2 vC = data.velocities[m_indexC].v;
+	float wC = data.velocities[m_indexC].w;
+
+	float aD = data.positions[m_indexD].a;
+	b2Vec2 vD = data.velocities[m_indexD].v;
+	float wD = data.velocities[m_indexD].w;
+
+	b2Rot qA(aA), qB(aB), qC(aC), qD(aD);
+
+	m_mass = 0.0f;
+
+	if (m_typeA == e_revoluteJoint)
+	{
+		m_JvAC.SetZero();
+		m_JwA = 1.0f;
+		m_JwC = 1.0f;
+		m_mass += m_iA + m_iC;
+	}
+	else
+	{
+		b2Vec2 u = b2Mul(qC, m_localAxisC);
+		b2Vec2 rC = b2Mul(qC, m_localAnchorC - m_lcC);
+		b2Vec2 rA = b2Mul(qA, m_localAnchorA - m_lcA);
+		m_JvAC = u;
+		m_JwC = b2Cross(rC, u);
+		m_JwA = b2Cross(rA, u);
+		m_mass += m_mC + m_mA + m_iC * m_JwC * m_JwC + m_iA * m_JwA * m_JwA;
+	}
+
+	if (m_typeB == e_revoluteJoint)
+	{
+		m_JvBD.SetZero();
+		m_JwB = m_ratio;
+		m_JwD = m_ratio;
+		m_mass += m_ratio * m_ratio * (m_iB + m_iD);
+	}
+	else
+	{
+		b2Vec2 u = b2Mul(qD, m_localAxisD);
+		b2Vec2 rD = b2Mul(qD, m_localAnchorD - m_lcD);
+		b2Vec2 rB = b2Mul(qB, m_localAnchorB - m_lcB);
+		m_JvBD = m_ratio * u;
+		m_JwD = m_ratio * b2Cross(rD, u);
+		m_JwB = m_ratio * b2Cross(rB, u);
+		m_mass += m_ratio * m_ratio * (m_mD + m_mB) + m_iD * m_JwD * m_JwD + m_iB * m_JwB * m_JwB;
+	}
+
+	// Compute effective mass.
+	m_mass = m_mass > 0.0f ? 1.0f / m_mass : 0.0f;
+
+	if (data.step.warmStarting)
+	{
+		vA += (m_mA * m_impulse) * m_JvAC;
+		wA += m_iA * m_impulse * m_JwA;
+		vB += (m_mB * m_impulse) * m_JvBD;
+		wB += m_iB * m_impulse * m_JwB;
+		vC -= (m_mC * m_impulse) * m_JvAC;
+		wC -= m_iC * m_impulse * m_JwC;
+		vD -= (m_mD * m_impulse) * m_JvBD;
+		wD -= m_iD * m_impulse * m_JwD;
+	}
+	else
+	{
+		m_impulse = 0.0f;
+	}
+
+	data.velocities[m_indexA].v = vA;
+	data.velocities[m_indexA].w = wA;
+	data.velocities[m_indexB].v = vB;
+	data.velocities[m_indexB].w = wB;
+	data.velocities[m_indexC].v = vC;
+	data.velocities[m_indexC].w = wC;
+	data.velocities[m_indexD].v = vD;
+	data.velocities[m_indexD].w = wD;
+}
+
+void b2GearJoint::SolveVelocityConstraints(const b2SolverData& data)
+{
+	b2Vec2 vA = data.velocities[m_indexA].v;
+	float wA = data.velocities[m_indexA].w;
+	b2Vec2 vB = data.velocities[m_indexB].v;
+	float wB = data.velocities[m_indexB].w;
+	b2Vec2 vC = data.velocities[m_indexC].v;
+	float wC = data.velocities[m_indexC].w;
+	b2Vec2 vD = data.velocities[m_indexD].v;
+	float wD = data.velocities[m_indexD].w;
+
+	float Cdot = b2Dot(m_JvAC, vA - vC) + b2Dot(m_JvBD, vB - vD);
+	Cdot += (m_JwA * wA - m_JwC * wC) + (m_JwB * wB - m_JwD * wD);
+
+	float impulse = -m_mass * Cdot;
+	m_impulse += impulse;
+
+	vA += (m_mA * impulse) * m_JvAC;
+	wA += m_iA * impulse * m_JwA;
+	vB += (m_mB * impulse) * m_JvBD;
+	wB += m_iB * impulse * m_JwB;
+	vC -= (m_mC * impulse) * m_JvAC;
+	wC -= m_iC * impulse * m_JwC;
+	vD -= (m_mD * impulse) * m_JvBD;
+	wD -= m_iD * impulse * m_JwD;
+
+	data.velocities[m_indexA].v = vA;
+	data.velocities[m_indexA].w = wA;
+	data.velocities[m_indexB].v = vB;
+	data.velocities[m_indexB].w = wB;
+	data.velocities[m_indexC].v = vC;
+	data.velocities[m_indexC].w = wC;
+	data.velocities[m_indexD].v = vD;
+	data.velocities[m_indexD].w = wD;
+}
+
+bool b2GearJoint::SolvePositionConstraints(const b2SolverData& data)
+{
+	b2Vec2 cA = data.positions[m_indexA].c;
+	float aA = data.positions[m_indexA].a;
+	b2Vec2 cB = data.positions[m_indexB].c;
+	float aB = data.positions[m_indexB].a;
+	b2Vec2 cC = data.positions[m_indexC].c;
+	float aC = data.positions[m_indexC].a;
+	b2Vec2 cD = data.positions[m_indexD].c;
+	float aD = data.positions[m_indexD].a;
+
+	b2Rot qA(aA), qB(aB), qC(aC), qD(aD);
+
+	float coordinateA, coordinateB;
+
+	b2Vec2 JvAC, JvBD;
+	float JwA, JwB, JwC, JwD;
+	float mass = 0.0f;
+
+	if (m_typeA == e_revoluteJoint)
+	{
+		JvAC.SetZero();
+		JwA = 1.0f;
+		JwC = 1.0f;
+		mass += m_iA + m_iC;
+
+		coordinateA = aA - aC - m_referenceAngleA;
+	}
+	else
+	{
+		b2Vec2 u = b2Mul(qC, m_localAxisC);
+		b2Vec2 rC = b2Mul(qC, m_localAnchorC - m_lcC);
+		b2Vec2 rA = b2Mul(qA, m_localAnchorA - m_lcA);
+		JvAC = u;
+		JwC = b2Cross(rC, u);
+		JwA = b2Cross(rA, u);
+		mass += m_mC + m_mA + m_iC * JwC * JwC + m_iA * JwA * JwA;
+
+		b2Vec2 pC = m_localAnchorC - m_lcC;
+		b2Vec2 pA = b2MulT(qC, rA + (cA - cC));
+		coordinateA = b2Dot(pA - pC, m_localAxisC);
+	}
+
+	if (m_typeB == e_revoluteJoint)
+	{
+		JvBD.SetZero();
+		JwB = m_ratio;
+		JwD = m_ratio;
+		mass += m_ratio * m_ratio * (m_iB + m_iD);
+
+		coordinateB = aB - aD - m_referenceAngleB;
+	}
+	else
+	{
+		b2Vec2 u = b2Mul(qD, m_localAxisD);
+		b2Vec2 rD = b2Mul(qD, m_localAnchorD - m_lcD);
+		b2Vec2 rB = b2Mul(qB, m_localAnchorB - m_lcB);
+		JvBD = m_ratio * u;
+		JwD = m_ratio * b2Cross(rD, u);
+		JwB = m_ratio * b2Cross(rB, u);
+		mass += m_ratio * m_ratio * (m_mD + m_mB) + m_iD * JwD * JwD + m_iB * JwB * JwB;
+
+		b2Vec2 pD = m_localAnchorD - m_lcD;
+		b2Vec2 pB = b2MulT(qD, rB + (cB - cD));
+		coordinateB = b2Dot(pB - pD, m_localAxisD);
+	}
+
+	float C = (coordinateA + m_ratio * coordinateB) - m_constant;
+
+	float impulse = 0.0f;
+	if (mass > 0.0f)
+	{
+		impulse = -C / mass;
+	}
+
+	cA += m_mA * impulse * JvAC;
+	aA += m_iA * impulse * JwA;
+	cB += m_mB * impulse * JvBD;
+	aB += m_iB * impulse * JwB;
+	cC -= m_mC * impulse * JvAC;
+	aC -= m_iC * impulse * JwC;
+	cD -= m_mD * impulse * JvBD;
+	aD -= m_iD * impulse * JwD;
+
+	data.positions[m_indexA].c = cA;
+	data.positions[m_indexA].a = aA;
+	data.positions[m_indexB].c = cB;
+	data.positions[m_indexB].a = aB;
+	data.positions[m_indexC].c = cC;
+	data.positions[m_indexC].a = aC;
+	data.positions[m_indexD].c = cD;
+	data.positions[m_indexD].a = aD;
+
+	if (b2Abs(C) < m_tolerance)
+	{
+		return true;
+	}
+
+	return false;
+}
+
+b2Vec2 b2GearJoint::GetAnchorA() const
+{
+	return m_bodyA->GetWorldPoint(m_localAnchorA);
+}
+
+b2Vec2 b2GearJoint::GetAnchorB() const
+{
+	return m_bodyB->GetWorldPoint(m_localAnchorB);
+}
+
+b2Vec2 b2GearJoint::GetReactionForce(float inv_dt) const
+{
+	b2Vec2 P = m_impulse * m_JvAC;
+	return inv_dt * P;
+}
+
+float b2GearJoint::GetReactionTorque(float inv_dt) const
+{
+	float L = m_impulse * m_JwA;
+	return inv_dt * L;
+}
+
+void b2GearJoint::SetRatio(float ratio)
+{
+	b2Assert(b2IsValid(ratio));
+	m_ratio = ratio;
+}
+
+float b2GearJoint::GetRatio() const
+{
+	return m_ratio;
+}
+
+void b2GearJoint::Dump()
+{
+	int32 indexA = m_bodyA->m_islandIndex;
+	int32 indexB = m_bodyB->m_islandIndex;
+
+	int32 index1 = m_joint1->m_index;
+	int32 index2 = m_joint2->m_index;
+
+	b2Dump("  b2GearJointDef jd;\n");
+	b2Dump("  jd.bodyA = bodies[%d];\n", indexA);
+	b2Dump("  jd.bodyB = bodies[%d];\n", indexB);
+	b2Dump("  jd.collideConnected = bool(%d);\n", m_collideConnected);
+	b2Dump("  jd.joint1 = joints[%d];\n", index1);
+	b2Dump("  jd.joint2 = joints[%d];\n", index2);
+	b2Dump("  jd.ratio = %.9g;\n", m_ratio);
+	b2Dump("  joints[%d] = m_world->CreateJoint(&jd);\n", m_index);
+}

3rd/box2d/src/dynamics/b2_island.cpp

@@ -0,0 +1,544 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#include "box2d/b2_body.h"
+#include "box2d/b2_contact.h"
+#include "box2d/b2_distance.h"
+#include "box2d/b2_fixture.h"
+#include "box2d/b2_joint.h"
+#include "box2d/b2_stack_allocator.h"
+#include "box2d/b2_timer.h"
+#include "box2d/b2_world.h"
+
+#include "b2_contact_solver.h"
+#include "b2_island.h"
+
+/*
+Position Correction Notes
+=========================
+I tried the several algorithms for position correction of the 2D revolute joint.
+I looked at these systems:
+- simple pendulum (1m diameter sphere on massless 5m stick) with initial angular velocity of 100 rad/s.
+- suspension bridge with 30 1m long planks of length 1m.
+- multi-link chain with 30 1m long links.
+
+Here are the algorithms:
+
+Baumgarte - A fraction of the position error is added to the velocity error. There is no
+separate position solver.
+
+Pseudo Velocities - After the velocity solver and position integration,
+the position error, Jacobian, and effective mass are recomputed. Then
+the velocity constraints are solved with pseudo velocities and a fraction
+of the position error is added to the pseudo velocity error. The pseudo
+velocities are initialized to zero and there is no warm-starting. After
+the position solver, the pseudo velocities are added to the positions.
+This is also called the First Order World method or the Position LCP method.
+
+Modified Nonlinear Gauss-Seidel (NGS) - Like Pseudo Velocities except the
+position error is re-computed for each constraint and the positions are updated
+after the constraint is solved. The radius vectors (aka Jacobians) are
+re-computed too (otherwise the algorithm has horrible instability). The pseudo
+velocity states are not needed because they are effectively zero at the beginning
+of each iteration. Since we have the current position error, we allow the
+iterations to terminate early if the error becomes smaller than b2_linearSlop.
+
+Full NGS or just NGS - Like Modified NGS except the effective mass are re-computed
+each time a constraint is solved.
+
+Here are the results:
+Baumgarte - this is the cheapest algorithm but it has some stability problems,
+especially with the bridge. The chain links separate easily close to the root
+and they jitter as they struggle to pull together. This is one of the most common
+methods in the field. The big drawback is that the position correction artificially
+affects the momentum, thus leading to instabilities and false bounce. I used a
+bias factor of 0.2. A larger bias factor makes the bridge less stable, a smaller
+factor makes joints and contacts more spongy.
+
+Pseudo Velocities - the is more stable than the Baumgarte method. The bridge is
+stable. However, joints still separate with large angular velocities. Drag the
+simple pendulum in a circle quickly and the joint will separate. The chain separates
+easily and does not recover. I used a bias factor of 0.2. A larger value lead to
+the bridge collapsing when a heavy cube drops on it.
+
+Modified NGS - this algorithm is better in some ways than Baumgarte and Pseudo
+Velocities, but in other ways it is worse. The bridge and chain are much more
+stable, but the simple pendulum goes unstable at high angular velocities.
+
+Full NGS - stable in all tests. The joints display good stiffness. The bridge
+still sags, but this is better than infinite forces.
+
+Recommendations
+Pseudo Velocities are not really worthwhile because the bridge and chain cannot
+recover from joint separation. In other cases the benefit over Baumgarte is small.
+
+Modified NGS is not a robust method for the revolute joint due to the violent
+instability seen in the simple pendulum. Perhaps it is viable with other constraint
+types, especially scalar constraints where the effective mass is a scalar.
+
+This leaves Baumgarte and Full NGS. Baumgarte has small, but manageable instabilities
+and is very fast. I don't think we can escape Baumgarte, especially in highly
+demanding cases where high constraint fidelity is not needed.
+
+Full NGS is robust and easy on the eyes. I recommend this as an option for
+higher fidelity simulation and certainly for suspension bridges and long chains.
+Full NGS might be a good choice for ragdolls, especially motorized ragdolls where
+joint separation can be problematic. The number of NGS iterations can be reduced
+for better performance without harming robustness much.
+
+Each joint in a can be handled differently in the position solver. So I recommend
+a system where the user can select the algorithm on a per joint basis. I would
+probably default to the slower Full NGS and let the user select the faster
+Baumgarte method in performance critical scenarios.
+*/
+
+/*
+Cache Performance
+
+The Box2D solvers are dominated by cache misses. Data structures are designed
+to increase the number of cache hits. Much of misses are due to random access
+to body data. The constraint structures are iterated over linearly, which leads
+to few cache misses.
+
+The bodies are not accessed during iteration. Instead read only data, such as
+the mass values are stored with the constraints. The mutable data are the constraint
+impulses and the bodies velocities/positions. The impulses are held inside the
+constraint structures. The body velocities/positions are held in compact, temporary
+arrays to increase the number of cache hits. Linear and angular velocity are
+stored in a single array since multiple arrays lead to multiple misses.
+*/
+
+/*
+2D Rotation
+
+R = [cos(theta) -sin(theta)]
+    [sin(theta) cos(theta) ]
+
+thetaDot = omega
+
+Let q1 = cos(theta), q2 = sin(theta).
+R = [q1 -q2]
+    [q2  q1]
+
+q1Dot = -thetaDot * q2
+q2Dot = thetaDot * q1
+
+q1_new = q1_old - dt * w * q2
+q2_new = q2_old + dt * w * q1
+then normalize.
+
+This might be faster than computing sin+cos.
+However, we can compute sin+cos of the same angle fast.
+*/
+
+b2Island::b2Island(
+	int32 bodyCapacity,
+	int32 contactCapacity,
+	int32 jointCapacity,
+	b2StackAllocator* allocator,
+	b2ContactListener* listener)
+{
+	m_bodyCapacity = bodyCapacity;
+	m_contactCapacity = contactCapacity;
+	m_jointCapacity	 = jointCapacity;
+	m_bodyCount = 0;
+	m_contactCount = 0;
+	m_jointCount = 0;
+
+	m_allocator = allocator;
+	m_listener = listener;
+
+	m_bodies = (b2Body**)m_allocator->Allocate(bodyCapacity * sizeof(b2Body*));
+	m_contacts = (b2Contact**)m_allocator->Allocate(contactCapacity	 * sizeof(b2Contact*));
+	m_joints = (b2Joint**)m_allocator->Allocate(jointCapacity * sizeof(b2Joint*));
+
+	m_velocities = (b2Velocity*)m_allocator->Allocate(m_bodyCapacity * sizeof(b2Velocity));
+	m_positions = (b2Position*)m_allocator->Allocate(m_bodyCapacity * sizeof(b2Position));
+}
+
+b2Island::~b2Island()
+{
+	// Warning: the order should reverse the constructor order.
+	m_allocator->Free(m_positions);
+	m_allocator->Free(m_velocities);
+	m_allocator->Free(m_joints);
+	m_allocator->Free(m_contacts);
+	m_allocator->Free(m_bodies);
+}
+
+void b2Island::Solve(b2Profile* profile, const b2TimeStep& step, const b2Vec2& gravity, bool allowSleep)
+{
+	b2Timer timer;
+
+	float h = step.dt;
+
+	// Integrate velocities and apply damping. Initialize the body state.
+	for (int32 i = 0; i < m_bodyCount; ++i)
+	{
+		b2Body* b = m_bodies[i];
+
+		b2Vec2 c = b->m_sweep.c;
+		float a = b->m_sweep.a;
+		b2Vec2 v = b->m_linearVelocity;
+		float w = b->m_angularVelocity;
+
+		// Store positions for continuous collision.
+		b->m_sweep.c0 = b->m_sweep.c;
+		b->m_sweep.a0 = b->m_sweep.a;
+
+		if (b->m_type == b2_dynamicBody)
+		{
+			// Integrate velocities.
+			v += h * b->m_invMass * (b->m_gravityScale * b->m_mass * gravity + b->m_force);
+			w += h * b->m_invI * b->m_torque;
+
+			// Apply damping.
+			// ODE: dv/dt + c * v = 0
+			// Solution: v(t) = v0 * exp(-c * t)
+			// Time step: v(t + dt) = v0 * exp(-c * (t + dt)) = v0 * exp(-c * t) * exp(-c * dt) = v * exp(-c * dt)
+			// v2 = exp(-c * dt) * v1
+			// Pade approximation:
+			// v2 = v1 * 1 / (1 + c * dt)
+			v *= 1.0f / (1.0f + h * b->m_linearDamping);
+			w *= 1.0f / (1.0f + h * b->m_angularDamping);
+		}
+
+		m_positions[i].c = c;
+		m_positions[i].a = a;
+		m_velocities[i].v = v;
+		m_velocities[i].w = w;
+	}
+
+	timer.Reset();
+
+	// Solver data
+	b2SolverData solverData;
+	solverData.step = step;
+	solverData.positions = m_positions;
+	solverData.velocities = m_velocities;
+
+	// Initialize velocity constraints.
+	b2ContactSolverDef contactSolverDef;
+	contactSolverDef.step = step;
+	contactSolverDef.contacts = m_contacts;
+	contactSolverDef.count = m_contactCount;
+	contactSolverDef.positions = m_positions;
+	contactSolverDef.velocities = m_velocities;
+	contactSolverDef.allocator = m_allocator;
+
+	b2ContactSolver contactSolver(&contactSolverDef);
+	contactSolver.InitializeVelocityConstraints();
+
+	if (step.warmStarting)
+	{
+		contactSolver.WarmStart();
+	}
+	
+	for (int32 i = 0; i < m_jointCount; ++i)
+	{
+		m_joints[i]->InitVelocityConstraints(solverData);
+	}
+
+	profile->solveInit = timer.GetMilliseconds();
+
+	// Solve velocity constraints
+	timer.Reset();
+	for (int32 i = 0; i < step.velocityIterations; ++i)
+	{
+		for (int32 j = 0; j < m_jointCount; ++j)
+		{
+			m_joints[j]->SolveVelocityConstraints(solverData);
+		}
+
+		contactSolver.SolveVelocityConstraints();
+	}
+
+	// Store impulses for warm starting
+	contactSolver.StoreImpulses();
+	profile->solveVelocity = timer.GetMilliseconds();
+
+	// Integrate positions
+	for (int32 i = 0; i < m_bodyCount; ++i)
+	{
+		b2Vec2 c = m_positions[i].c;
+		float a = m_positions[i].a;
+		b2Vec2 v = m_velocities[i].v;
+		float w = m_velocities[i].w;
+
+		// Check for large velocities
+		b2Vec2 translation = h * v;
+		if (b2Dot(translation, translation) > b2_maxTranslationSquared)
+		{
+			float ratio = b2_maxTranslation / translation.Length();
+			v *= ratio;
+		}
+
+		float rotation = h * w;
+		if (rotation * rotation > b2_maxRotationSquared)
+		{
+			float ratio = b2_maxRotation / b2Abs(rotation);
+			w *= ratio;
+		}
+
+		// Integrate
+		c += h * v;
+		a += h * w;
+
+		m_positions[i].c = c;
+		m_positions[i].a = a;
+		m_velocities[i].v = v;
+		m_velocities[i].w = w;
+	}
+
+	// Solve position constraints
+	timer.Reset();
+	bool positionSolved = false;
+	for (int32 i = 0; i < step.positionIterations; ++i)
+	{
+		bool contactsOkay = contactSolver.SolvePositionConstraints();
+
+		bool jointsOkay = true;
+		for (int32 j = 0; j < m_jointCount; ++j)
+		{
+			bool jointOkay = m_joints[j]->SolvePositionConstraints(solverData);
+			jointsOkay = jointsOkay && jointOkay;
+		}
+
+		if (contactsOkay && jointsOkay)
+		{
+			// Exit early if the position errors are small.
+			positionSolved = true;
+			break;
+		}
+	}
+
+	// Copy state buffers back to the bodies
+	for (int32 i = 0; i < m_bodyCount; ++i)
+	{
+		b2Body* body = m_bodies[i];
+		body->m_sweep.c = m_positions[i].c;
+		body->m_sweep.a = m_positions[i].a;
+		body->m_linearVelocity = m_velocities[i].v;
+		body->m_angularVelocity = m_velocities[i].w;
+		body->SynchronizeTransform();
+	}
+
+	profile->solvePosition = timer.GetMilliseconds();
+
+	Report(contactSolver.m_velocityConstraints);
+
+	if (allowSleep)
+	{
+		float minSleepTime = b2_maxFloat;
+
+		const float linTolSqr = b2_linearSleepTolerance * b2_linearSleepTolerance;
+		const float angTolSqr = b2_angularSleepTolerance * b2_angularSleepTolerance;
+
+		for (int32 i = 0; i < m_bodyCount; ++i)
+		{
+			b2Body* b = m_bodies[i];
+			if (b->GetType() == b2_staticBody)
+			{
+				continue;
+			}
+
+			if ((b->m_flags & b2Body::e_autoSleepFlag) == 0 ||
+				b->m_angularVelocity * b->m_angularVelocity > angTolSqr ||
+				b2Dot(b->m_linearVelocity, b->m_linearVelocity) > linTolSqr)
+			{
+				b->m_sleepTime = 0.0f;
+				minSleepTime = 0.0f;
+			}
+			else
+			{
+				b->m_sleepTime += h;
+				minSleepTime = b2Min(minSleepTime, b->m_sleepTime);
+			}
+		}
+
+		if (minSleepTime >= b2_timeToSleep && positionSolved)
+		{
+			for (int32 i = 0; i < m_bodyCount; ++i)
+			{
+				b2Body* b = m_bodies[i];
+				b->SetAwake(false);
+			}
+		}
+	}
+}
+
+void b2Island::SolveTOI(const b2TimeStep& subStep, int32 toiIndexA, int32 toiIndexB)
+{
+	b2Assert(toiIndexA < m_bodyCount);
+	b2Assert(toiIndexB < m_bodyCount);
+
+	// Initialize the body state.
+	for (int32 i = 0; i < m_bodyCount; ++i)
+	{
+		b2Body* b = m_bodies[i];
+		m_positions[i].c = b->m_sweep.c;
+		m_positions[i].a = b->m_sweep.a;
+		m_velocities[i].v = b->m_linearVelocity;
+		m_velocities[i].w = b->m_angularVelocity;
+	}
+
+	b2ContactSolverDef contactSolverDef;
+	contactSolverDef.contacts = m_contacts;
+	contactSolverDef.count = m_contactCount;
+	contactSolverDef.allocator = m_allocator;
+	contactSolverDef.step = subStep;
+	contactSolverDef.positions = m_positions;
+	contactSolverDef.velocities = m_velocities;
+	b2ContactSolver contactSolver(&contactSolverDef);
+
+	// Solve position constraints.
+	for (int32 i = 0; i < subStep.positionIterations; ++i)
+	{
+		bool contactsOkay = contactSolver.SolveTOIPositionConstraints(toiIndexA, toiIndexB);
+		if (contactsOkay)
+		{
+			break;
+		}
+	}
+
+#if 0
+	// Is the new position really safe?
+	for (int32 i = 0; i < m_contactCount; ++i)
+	{
+		b2Contact* c = m_contacts[i];
+		b2Fixture* fA = c->GetFixtureA();
+		b2Fixture* fB = c->GetFixtureB();
+
+		b2Body* bA = fA->GetBody();
+		b2Body* bB = fB->GetBody();
+
+		int32 indexA = c->GetChildIndexA();
+		int32 indexB = c->GetChildIndexB();
+
+		b2DistanceInput input;
+		input.proxyA.Set(fA->GetShape(), indexA);
+		input.proxyB.Set(fB->GetShape(), indexB);
+		input.transformA = bA->GetTransform();
+		input.transformB = bB->GetTransform();
+		input.useRadii = false;
+
+		b2DistanceOutput output;
+		b2SimplexCache cache;
+		cache.count = 0;
+		b2Distance(&output, &cache, &input);
+
+		if (output.distance == 0 || cache.count == 3)
+		{
+			cache.count += 0;
+		}
+	}
+#endif
+
+	// Leap of faith to new safe state.
+	m_bodies[toiIndexA]->m_sweep.c0 = m_positions[toiIndexA].c;
+	m_bodies[toiIndexA]->m_sweep.a0 = m_positions[toiIndexA].a;
+	m_bodies[toiIndexB]->m_sweep.c0 = m_positions[toiIndexB].c;
+	m_bodies[toiIndexB]->m_sweep.a0 = m_positions[toiIndexB].a;
+
+	// No warm starting is needed for TOI events because warm
+	// starting impulses were applied in the discrete solver.
+	contactSolver.InitializeVelocityConstraints();
+
+	// Solve velocity constraints.
+	for (int32 i = 0; i < subStep.velocityIterations; ++i)
+	{
+		contactSolver.SolveVelocityConstraints();
+	}
+
+	// Don't store the TOI contact forces for warm starting
+	// because they can be quite large.
+
+	float h = subStep.dt;
+
+	// Integrate positions
+	for (int32 i = 0; i < m_bodyCount; ++i)
+	{
+		b2Vec2 c = m_positions[i].c;
+		float a = m_positions[i].a;
+		b2Vec2 v = m_velocities[i].v;
+		float w = m_velocities[i].w;
+
+		// Check for large velocities
+		b2Vec2 translation = h * v;
+		if (b2Dot(translation, translation) > b2_maxTranslationSquared)
+		{
+			float ratio = b2_maxTranslation / translation.Length();
+			v *= ratio;
+		}
+
+		float rotation = h * w;
+		if (rotation * rotation > b2_maxRotationSquared)
+		{
+			float ratio = b2_maxRotation / b2Abs(rotation);
+			w *= ratio;
+		}
+
+		// Integrate
+		c += h * v;
+		a += h * w;
+
+		m_positions[i].c = c;
+		m_positions[i].a = a;
+		m_velocities[i].v = v;
+		m_velocities[i].w = w;
+
+		// Sync bodies
+		b2Body* body = m_bodies[i];
+		body->m_sweep.c = c;
+		body->m_sweep.a = a;
+		body->m_linearVelocity = v;
+		body->m_angularVelocity = w;
+		body->SynchronizeTransform();
+	}
+
+	Report(contactSolver.m_velocityConstraints);
+}
+
+void b2Island::Report(const b2ContactVelocityConstraint* constraints)
+{
+	if (m_listener == nullptr)
+	{
+		return;
+	}
+
+	for (int32 i = 0; i < m_contactCount; ++i)
+	{
+		b2Contact* c = m_contacts[i];
+
+		const b2ContactVelocityConstraint* vc = constraints + i;
+		
+		b2ContactImpulse impulse;
+		impulse.count = vc->pointCount;
+		for (int32 j = 0; j < vc->pointCount; ++j)
+		{
+			impulse.normalImpulses[j] = vc->points[j].normalImpulse;
+			impulse.tangentImpulses[j] = vc->points[j].tangentImpulse;
+		}
+
+		m_listener->PostSolve(c, &impulse);
+	}
+}

3rd/box2d/src/dynamics/b2_island.h

@@ -0,0 +1,97 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#ifndef B2_ISLAND_H
+#define B2_ISLAND_H
+
+#include "box2d/b2_body.h"
+#include "box2d/b2_math.h"
+#include "box2d/b2_time_step.h"
+
+class b2Contact;
+class b2Joint;
+class b2StackAllocator;
+class b2ContactListener;
+struct b2ContactVelocityConstraint;
+struct b2Profile;
+
+/// This is an internal class.
+class b2Island
+{
+public:
+	b2Island(int32 bodyCapacity, int32 contactCapacity, int32 jointCapacity,
+			b2StackAllocator* allocator, b2ContactListener* listener);
+	~b2Island();
+
+	void Clear()
+	{
+		m_bodyCount = 0;
+		m_contactCount = 0;
+		m_jointCount = 0;
+	}
+
+	void Solve(b2Profile* profile, const b2TimeStep& step, const b2Vec2& gravity, bool allowSleep);
+
+	void SolveTOI(const b2TimeStep& subStep, int32 toiIndexA, int32 toiIndexB);
+
+	void Add(b2Body* body)
+	{
+		b2Assert(m_bodyCount < m_bodyCapacity);
+		body->m_islandIndex = m_bodyCount;
+		m_bodies[m_bodyCount] = body;
+		++m_bodyCount;
+	}
+
+	void Add(b2Contact* contact)
+	{
+		b2Assert(m_contactCount < m_contactCapacity);
+		m_contacts[m_contactCount++] = contact;
+	}
+
+	void Add(b2Joint* joint)
+	{
+		b2Assert(m_jointCount < m_jointCapacity);
+		m_joints[m_jointCount++] = joint;
+	}
+
+	void Report(const b2ContactVelocityConstraint* constraints);
+
+	b2StackAllocator* m_allocator;
+	b2ContactListener* m_listener;
+
+	b2Body** m_bodies;
+	b2Contact** m_contacts;
+	b2Joint** m_joints;
+
+	b2Position* m_positions;
+	b2Velocity* m_velocities;
+
+	int32 m_bodyCount;
+	int32 m_jointCount;
+	int32 m_contactCount;
+
+	int32 m_bodyCapacity;
+	int32 m_contactCapacity;
+	int32 m_jointCapacity;
+};
+
+#endif

3rd/box2d/src/dynamics/b2_joint.cpp

@@ -0,0 +1,301 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#include "box2d/b2_block_allocator.h"
+#include "box2d/b2_body.h"
+#include "box2d/b2_distance_joint.h"
+#include "box2d/b2_draw.h"
+#include "box2d/b2_friction_joint.h"
+#include "box2d/b2_gear_joint.h"
+#include "box2d/b2_motor_joint.h"
+#include "box2d/b2_mouse_joint.h"
+#include "box2d/b2_prismatic_joint.h"
+#include "box2d/b2_pulley_joint.h"
+#include "box2d/b2_revolute_joint.h"
+#include "box2d/b2_weld_joint.h"
+#include "box2d/b2_wheel_joint.h"
+#include "box2d/b2_world.h"
+
+#include <new>
+
+void b2LinearStiffness(float& stiffness, float& damping,
+	float frequencyHertz, float dampingRatio,
+	const b2Body* bodyA, const b2Body* bodyB)
+{
+	float massA = bodyA->GetMass();
+	float massB = bodyB->GetMass();
+	float mass;
+	if (massA > 0.0f && massB > 0.0f)
+	{
+		mass = massA * massB / (massA + massB);
+	}
+	else if (massA > 0.0f)
+	{
+		mass = massA;
+	}
+	else
+	{
+		mass = massB;
+	}
+
+	float omega = 2.0f * b2_pi * frequencyHertz;
+	stiffness = mass * omega * omega;
+	damping = 2.0f * mass * dampingRatio * omega;
+}
+
+void b2AngularStiffness(float& stiffness, float& damping,
+	float frequencyHertz, float dampingRatio,
+	const b2Body* bodyA, const b2Body* bodyB)
+{
+	float IA = bodyA->GetInertia();
+	float IB = bodyB->GetInertia();
+	float I;
+	if (IA > 0.0f && IB > 0.0f)
+	{
+		I = IA * IB / (IA + IB);
+	}
+	else if (IA > 0.0f)
+	{
+		I = IA;
+	}
+	else
+	{
+		I = IB;
+	}
+
+	float omega = 2.0f * b2_pi * frequencyHertz;
+	stiffness = I * omega * omega;
+	damping = 2.0f * I * dampingRatio * omega;
+}
+
+b2Joint* b2Joint::Create(const b2JointDef* def, b2BlockAllocator* allocator)
+{
+	b2Joint* joint = nullptr;
+
+	switch (def->type)
+	{
+	case e_distanceJoint:
+		{
+			void* mem = allocator->Allocate(sizeof(b2DistanceJoint));
+			joint = new (mem) b2DistanceJoint(static_cast<const b2DistanceJointDef*>(def));
+		}
+		break;
+
+	case e_mouseJoint:
+		{
+			void* mem = allocator->Allocate(sizeof(b2MouseJoint));
+			joint = new (mem) b2MouseJoint(static_cast<const b2MouseJointDef*>(def));
+		}
+		break;
+
+	case e_prismaticJoint:
+		{
+			void* mem = allocator->Allocate(sizeof(b2PrismaticJoint));
+			joint = new (mem) b2PrismaticJoint(static_cast<const b2PrismaticJointDef*>(def));
+		}
+		break;
+
+	case e_revoluteJoint:
+		{
+			void* mem = allocator->Allocate(sizeof(b2RevoluteJoint));
+			joint = new (mem) b2RevoluteJoint(static_cast<const b2RevoluteJointDef*>(def));
+		}
+		break;
+
+	case e_pulleyJoint:
+		{
+			void* mem = allocator->Allocate(sizeof(b2PulleyJoint));
+			joint = new (mem) b2PulleyJoint(static_cast<const b2PulleyJointDef*>(def));
+		}
+		break;
+
+	case e_gearJoint:
+		{
+			void* mem = allocator->Allocate(sizeof(b2GearJoint));
+			joint = new (mem) b2GearJoint(static_cast<const b2GearJointDef*>(def));
+		}
+		break;
+
+	case e_wheelJoint:
+		{
+			void* mem = allocator->Allocate(sizeof(b2WheelJoint));
+			joint = new (mem) b2WheelJoint(static_cast<const b2WheelJointDef*>(def));
+		}
+		break;
+
+	case e_weldJoint:
+		{
+			void* mem = allocator->Allocate(sizeof(b2WeldJoint));
+			joint = new (mem) b2WeldJoint(static_cast<const b2WeldJointDef*>(def));
+		}
+		break;
+        
+	case e_frictionJoint:
+		{
+			void* mem = allocator->Allocate(sizeof(b2FrictionJoint));
+			joint = new (mem) b2FrictionJoint(static_cast<const b2FrictionJointDef*>(def));
+		}
+		break;
+
+	case e_motorJoint:
+		{
+			void* mem = allocator->Allocate(sizeof(b2MotorJoint));
+			joint = new (mem) b2MotorJoint(static_cast<const b2MotorJointDef*>(def));
+		}
+		break;
+
+	default:
+		b2Assert(false);
+		break;
+	}
+
+	return joint;
+}
+
+void b2Joint::Destroy(b2Joint* joint, b2BlockAllocator* allocator)
+{
+	joint->~b2Joint();
+	switch (joint->m_type)
+	{
+	case e_distanceJoint:
+		allocator->Free(joint, sizeof(b2DistanceJoint));
+		break;
+
+	case e_mouseJoint:
+		allocator->Free(joint, sizeof(b2MouseJoint));
+		break;
+
+	case e_prismaticJoint:
+		allocator->Free(joint, sizeof(b2PrismaticJoint));
+		break;
+
+	case e_revoluteJoint:
+		allocator->Free(joint, sizeof(b2RevoluteJoint));
+		break;
+
+	case e_pulleyJoint:
+		allocator->Free(joint, sizeof(b2PulleyJoint));
+		break;
+
+	case e_gearJoint:
+		allocator->Free(joint, sizeof(b2GearJoint));
+		break;
+
+	case e_wheelJoint:
+		allocator->Free(joint, sizeof(b2WheelJoint));
+		break;
+    
+	case e_weldJoint:
+		allocator->Free(joint, sizeof(b2WeldJoint));
+		break;
+
+	case e_frictionJoint:
+		allocator->Free(joint, sizeof(b2FrictionJoint));
+		break;
+
+	case e_motorJoint:
+		allocator->Free(joint, sizeof(b2MotorJoint));
+		break;
+
+	default:
+		b2Assert(false);
+		break;
+	}
+}
+
+b2Joint::b2Joint(const b2JointDef* def)
+{
+	b2Assert(def->bodyA != def->bodyB);
+
+	m_type = def->type;
+	m_prev = nullptr;
+	m_next = nullptr;
+	m_bodyA = def->bodyA;
+	m_bodyB = def->bodyB;
+	m_index = 0;
+	m_collideConnected = def->collideConnected;
+	m_islandFlag = false;
+	m_userData = def->userData;
+
+	m_edgeA.joint = nullptr;
+	m_edgeA.other = nullptr;
+	m_edgeA.prev = nullptr;
+	m_edgeA.next = nullptr;
+
+	m_edgeB.joint = nullptr;
+	m_edgeB.other = nullptr;
+	m_edgeB.prev = nullptr;
+	m_edgeB.next = nullptr;
+}
+
+bool b2Joint::IsEnabled() const
+{
+	return m_bodyA->IsEnabled() && m_bodyB->IsEnabled();
+}
+
+void b2Joint::Draw(b2Draw* draw) const
+{
+	const b2Transform& xf1 = m_bodyA->GetTransform();
+	const b2Transform& xf2 = m_bodyB->GetTransform();
+	b2Vec2 x1 = xf1.p;
+	b2Vec2 x2 = xf2.p;
+	b2Vec2 p1 = GetAnchorA();
+	b2Vec2 p2 = GetAnchorB();
+
+	b2Color color(0.5f, 0.8f, 0.8f);
+
+	switch (m_type)
+	{
+	case e_distanceJoint:
+		draw->DrawSegment(p1, p2, color);
+		break;
+
+	case e_pulleyJoint:
+	{
+		b2PulleyJoint* pulley = (b2PulleyJoint*)this;
+		b2Vec2 s1 = pulley->GetGroundAnchorA();
+		b2Vec2 s2 = pulley->GetGroundAnchorB();
+		draw->DrawSegment(s1, p1, color);
+		draw->DrawSegment(s2, p2, color);
+		draw->DrawSegment(s1, s2, color);
+	}
+	break;
+
+	case e_mouseJoint:
+	{
+		b2Color c;
+		c.Set(0.0f, 1.0f, 0.0f);
+		draw->DrawPoint(p1, 4.0f, c);
+		draw->DrawPoint(p2, 4.0f, c);
+
+		c.Set(0.8f, 0.8f, 0.8f);
+		draw->DrawSegment(p1, p2, c);
+
+	}
+	break;
+
+	default:
+		draw->DrawSegment(x1, p1, color);
+		draw->DrawSegment(p1, p2, color);
+		draw->DrawSegment(x2, p2, color);
+	}
+}

3rd/box2d/src/dynamics/b2_motor_joint.cpp

@@ -0,0 +1,311 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#include "box2d/b2_body.h"
+#include "box2d/b2_motor_joint.h"
+#include "box2d/b2_time_step.h"
+
+// Point-to-point constraint
+// Cdot = v2 - v1
+//      = v2 + cross(w2, r2) - v1 - cross(w1, r1)
+// J = [-I -r1_skew I r2_skew ]
+// Identity used:
+// w k % (rx i + ry j) = w * (-ry i + rx j)
+//
+// r1 = offset - c1
+// r2 = -c2
+
+// Angle constraint
+// Cdot = w2 - w1
+// J = [0 0 -1 0 0 1]
+// K = invI1 + invI2
+
+void b2MotorJointDef::Initialize(b2Body* bA, b2Body* bB)
+{
+	bodyA = bA;
+	bodyB = bB;
+	b2Vec2 xB = bodyB->GetPosition();
+	linearOffset = bodyA->GetLocalPoint(xB);
+
+	float angleA = bodyA->GetAngle();
+	float angleB = bodyB->GetAngle();
+	angularOffset = angleB - angleA;
+}
+
+b2MotorJoint::b2MotorJoint(const b2MotorJointDef* def)
+: b2Joint(def)
+{
+	m_linearOffset = def->linearOffset;
+	m_angularOffset = def->angularOffset;
+
+	m_linearImpulse.SetZero();
+	m_angularImpulse = 0.0f;
+
+	m_maxForce = def->maxForce;
+	m_maxTorque = def->maxTorque;
+	m_correctionFactor = def->correctionFactor;
+}
+
+void b2MotorJoint::InitVelocityConstraints(const b2SolverData& data)
+{
+	m_indexA = m_bodyA->m_islandIndex;
+	m_indexB = m_bodyB->m_islandIndex;
+	m_localCenterA = m_bodyA->m_sweep.localCenter;
+	m_localCenterB = m_bodyB->m_sweep.localCenter;
+	m_invMassA = m_bodyA->m_invMass;
+	m_invMassB = m_bodyB->m_invMass;
+	m_invIA = m_bodyA->m_invI;
+	m_invIB = m_bodyB->m_invI;
+
+	b2Vec2 cA = data.positions[m_indexA].c;
+	float aA = data.positions[m_indexA].a;
+	b2Vec2 vA = data.velocities[m_indexA].v;
+	float wA = data.velocities[m_indexA].w;
+
+	b2Vec2 cB = data.positions[m_indexB].c;
+	float aB = data.positions[m_indexB].a;
+	b2Vec2 vB = data.velocities[m_indexB].v;
+	float wB = data.velocities[m_indexB].w;
+
+	b2Rot qA(aA), qB(aB);
+
+	// Compute the effective mass matrix.
+	m_rA = b2Mul(qA, m_linearOffset - m_localCenterA);
+	m_rB = b2Mul(qB, -m_localCenterB);
+
+	// J = [-I -r1_skew I r2_skew]
+	// r_skew = [-ry; rx]
+
+	// Matlab
+	// K = [ mA+r1y^2*iA+mB+r2y^2*iB,  -r1y*iA*r1x-r2y*iB*r2x,          -r1y*iA-r2y*iB]
+	//     [  -r1y*iA*r1x-r2y*iB*r2x, mA+r1x^2*iA+mB+r2x^2*iB,           r1x*iA+r2x*iB]
+	//     [          -r1y*iA-r2y*iB,           r1x*iA+r2x*iB,                   iA+iB]
+
+	float mA = m_invMassA, mB = m_invMassB;
+	float iA = m_invIA, iB = m_invIB;
+
+	// Upper 2 by 2 of K for point to point
+	b2Mat22 K;
+	K.ex.x = mA + mB + iA * m_rA.y * m_rA.y + iB * m_rB.y * m_rB.y;
+	K.ex.y = -iA * m_rA.x * m_rA.y - iB * m_rB.x * m_rB.y;
+	K.ey.x = K.ex.y;
+	K.ey.y = mA + mB + iA * m_rA.x * m_rA.x + iB * m_rB.x * m_rB.x;
+
+	m_linearMass = K.GetInverse();
+
+	m_angularMass = iA + iB;
+	if (m_angularMass > 0.0f)
+	{
+		m_angularMass = 1.0f / m_angularMass;
+	}
+
+	m_linearError = cB + m_rB - cA - m_rA;
+	m_angularError = aB - aA - m_angularOffset;
+
+	if (data.step.warmStarting)
+	{
+		// Scale impulses to support a variable time step.
+		m_linearImpulse *= data.step.dtRatio;
+		m_angularImpulse *= data.step.dtRatio;
+
+		b2Vec2 P(m_linearImpulse.x, m_linearImpulse.y);
+		vA -= mA * P;
+		wA -= iA * (b2Cross(m_rA, P) + m_angularImpulse);
+		vB += mB * P;
+		wB += iB * (b2Cross(m_rB, P) + m_angularImpulse);
+	}
+	else
+	{
+		m_linearImpulse.SetZero();
+		m_angularImpulse = 0.0f;
+	}
+
+	data.velocities[m_indexA].v = vA;
+	data.velocities[m_indexA].w = wA;
+	data.velocities[m_indexB].v = vB;
+	data.velocities[m_indexB].w = wB;
+}
+
+void b2MotorJoint::SolveVelocityConstraints(const b2SolverData& data)
+{
+	b2Vec2 vA = data.velocities[m_indexA].v;
+	float wA = data.velocities[m_indexA].w;
+	b2Vec2 vB = data.velocities[m_indexB].v;
+	float wB = data.velocities[m_indexB].w;
+
+	float mA = m_invMassA, mB = m_invMassB;
+	float iA = m_invIA, iB = m_invIB;
+
+	float h = data.step.dt;
+	float inv_h = data.step.inv_dt;
+
+	// Solve angular friction
+	{
+		float Cdot = wB - wA + inv_h * m_correctionFactor * m_angularError;
+		float impulse = -m_angularMass * Cdot;
+
+		float oldImpulse = m_angularImpulse;
+		float maxImpulse = h * m_maxTorque;
+		m_angularImpulse = b2Clamp(m_angularImpulse + impulse, -maxImpulse, maxImpulse);
+		impulse = m_angularImpulse - oldImpulse;
+
+		wA -= iA * impulse;
+		wB += iB * impulse;
+	}
+
+	// Solve linear friction
+	{
+		b2Vec2 Cdot = vB + b2Cross(wB, m_rB) - vA - b2Cross(wA, m_rA) + inv_h * m_correctionFactor * m_linearError;
+
+		b2Vec2 impulse = -b2Mul(m_linearMass, Cdot);
+		b2Vec2 oldImpulse = m_linearImpulse;
+		m_linearImpulse += impulse;
+
+		float maxImpulse = h * m_maxForce;
+
+		if (m_linearImpulse.LengthSquared() > maxImpulse * maxImpulse)
+		{
+			m_linearImpulse.Normalize();
+			m_linearImpulse *= maxImpulse;
+		}
+
+		impulse = m_linearImpulse - oldImpulse;
+
+		vA -= mA * impulse;
+		wA -= iA * b2Cross(m_rA, impulse);
+
+		vB += mB * impulse;
+		wB += iB * b2Cross(m_rB, impulse);
+	}
+
+	data.velocities[m_indexA].v = vA;
+	data.velocities[m_indexA].w = wA;
+	data.velocities[m_indexB].v = vB;
+	data.velocities[m_indexB].w = wB;
+}
+
+bool b2MotorJoint::SolvePositionConstraints(const b2SolverData& data)
+{
+	B2_NOT_USED(data);
+
+	return true;
+}
+
+b2Vec2 b2MotorJoint::GetAnchorA() const
+{
+	return m_bodyA->GetPosition();
+}
+
+b2Vec2 b2MotorJoint::GetAnchorB() const
+{
+	return m_bodyB->GetPosition();
+}
+
+b2Vec2 b2MotorJoint::GetReactionForce(float inv_dt) const
+{
+	return inv_dt * m_linearImpulse;
+}
+
+float b2MotorJoint::GetReactionTorque(float inv_dt) const
+{
+	return inv_dt * m_angularImpulse;
+}
+
+void b2MotorJoint::SetMaxForce(float force)
+{
+	b2Assert(b2IsValid(force) && force >= 0.0f);
+	m_maxForce = force;
+}
+
+float b2MotorJoint::GetMaxForce() const
+{
+	return m_maxForce;
+}
+
+void b2MotorJoint::SetMaxTorque(float torque)
+{
+	b2Assert(b2IsValid(torque) && torque >= 0.0f);
+	m_maxTorque = torque;
+}
+
+float b2MotorJoint::GetMaxTorque() const
+{
+	return m_maxTorque;
+}
+
+void b2MotorJoint::SetCorrectionFactor(float factor)
+{
+	b2Assert(b2IsValid(factor) && 0.0f <= factor && factor <= 1.0f);
+	m_correctionFactor = factor;
+}
+
+float b2MotorJoint::GetCorrectionFactor() const
+{
+	return m_correctionFactor;
+}
+
+void b2MotorJoint::SetLinearOffset(const b2Vec2& linearOffset)
+{
+	if (linearOffset.x != m_linearOffset.x || linearOffset.y != m_linearOffset.y)
+	{
+		m_bodyA->SetAwake(true);
+		m_bodyB->SetAwake(true);
+		m_linearOffset = linearOffset;
+	}
+}
+
+const b2Vec2& b2MotorJoint::GetLinearOffset() const
+{
+	return m_linearOffset;
+}
+
+void b2MotorJoint::SetAngularOffset(float angularOffset)
+{
+	if (angularOffset != m_angularOffset)
+	{
+		m_bodyA->SetAwake(true);
+		m_bodyB->SetAwake(true);
+		m_angularOffset = angularOffset;
+	}
+}
+
+float b2MotorJoint::GetAngularOffset() const
+{
+	return m_angularOffset;
+}
+
+void b2MotorJoint::Dump()
+{
+	int32 indexA = m_bodyA->m_islandIndex;
+	int32 indexB = m_bodyB->m_islandIndex;
+
+	b2Dump("  b2MotorJointDef jd;\n");
+	b2Dump("  jd.bodyA = bodies[%d];\n", indexA);
+	b2Dump("  jd.bodyB = bodies[%d];\n", indexB);
+	b2Dump("  jd.collideConnected = bool(%d);\n", m_collideConnected);
+	b2Dump("  jd.linearOffset.Set(%.9g, %.9g);\n", m_linearOffset.x, m_linearOffset.y);
+	b2Dump("  jd.angularOffset = %.9g;\n", m_angularOffset);
+	b2Dump("  jd.maxForce = %.9g;\n", m_maxForce);
+	b2Dump("  jd.maxTorque = %.9g;\n", m_maxTorque);
+	b2Dump("  jd.correctionFactor = %.9g;\n", m_correctionFactor);
+	b2Dump("  joints[%d] = m_world->CreateJoint(&jd);\n", m_index);
+}

3rd/box2d/src/dynamics/b2_mouse_joint.cpp

@@ -0,0 +1,190 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#include "box2d/b2_body.h"
+#include "box2d/b2_mouse_joint.h"
+#include "box2d/b2_time_step.h"
+
+// p = attached point, m = mouse point
+// C = p - m
+// Cdot = v
+//      = v + cross(w, r)
+// J = [I r_skew]
+// Identity used:
+// w k % (rx i + ry j) = w * (-ry i + rx j)
+
+b2MouseJoint::b2MouseJoint(const b2MouseJointDef* def)
+: b2Joint(def)
+{
+	m_targetA = def->target;
+	m_localAnchorB = b2MulT(m_bodyB->GetTransform(), m_targetA);
+	m_maxForce = def->maxForce;
+	m_stiffness = def->stiffness;
+	m_damping = def->damping;
+
+	m_impulse.SetZero();
+	m_beta = 0.0f;
+	m_gamma = 0.0f;
+}
+
+void b2MouseJoint::SetTarget(const b2Vec2& target)
+{
+	if (target != m_targetA)
+	{
+		m_bodyB->SetAwake(true);
+		m_targetA = target;
+	}
+}
+
+const b2Vec2& b2MouseJoint::GetTarget() const
+{
+	return m_targetA;
+}
+
+void b2MouseJoint::SetMaxForce(float force)
+{
+	m_maxForce = force;
+}
+
+float b2MouseJoint::GetMaxForce() const
+{
+	return m_maxForce;
+}
+
+void b2MouseJoint::InitVelocityConstraints(const b2SolverData& data)
+{
+	m_indexB = m_bodyB->m_islandIndex;
+	m_localCenterB = m_bodyB->m_sweep.localCenter;
+	m_invMassB = m_bodyB->m_invMass;
+	m_invIB = m_bodyB->m_invI;
+
+	b2Vec2 cB = data.positions[m_indexB].c;
+	float aB = data.positions[m_indexB].a;
+	b2Vec2 vB = data.velocities[m_indexB].v;
+	float wB = data.velocities[m_indexB].w;
+
+	b2Rot qB(aB);
+
+	float d = m_damping;
+	float k = m_stiffness;
+
+	// magic formulas
+	// gamma has units of inverse mass.
+	// beta has units of inverse time.
+	float h = data.step.dt;
+	m_gamma = h * (d + h * k);
+	if (m_gamma != 0.0f)
+	{
+		m_gamma = 1.0f / m_gamma;
+	}
+	m_beta = h * k * m_gamma;
+
+	// Compute the effective mass matrix.
+	m_rB = b2Mul(qB, m_localAnchorB - m_localCenterB);
+
+	// K    = [(1/m1 + 1/m2) * eye(2) - skew(r1) * invI1 * skew(r1) - skew(r2) * invI2 * skew(r2)]
+	//      = [1/m1+1/m2     0    ] + invI1 * [r1.y*r1.y -r1.x*r1.y] + invI2 * [r1.y*r1.y -r1.x*r1.y]
+	//        [    0     1/m1+1/m2]           [-r1.x*r1.y r1.x*r1.x]           [-r1.x*r1.y r1.x*r1.x]
+	b2Mat22 K;
+	K.ex.x = m_invMassB + m_invIB * m_rB.y * m_rB.y + m_gamma;
+	K.ex.y = -m_invIB * m_rB.x * m_rB.y;
+	K.ey.x = K.ex.y;
+	K.ey.y = m_invMassB + m_invIB * m_rB.x * m_rB.x + m_gamma;
+
+	m_mass = K.GetInverse();
+
+	m_C = cB + m_rB - m_targetA;
+	m_C *= m_beta;
+
+	// Cheat with some damping
+	wB *= b2Max(0.0f, 1.0f - 0.02f * (60.0f * data.step.dt));
+
+	if (data.step.warmStarting)
+	{
+		m_impulse *= data.step.dtRatio;
+		vB += m_invMassB * m_impulse;
+		wB += m_invIB * b2Cross(m_rB, m_impulse);
+	}
+	else
+	{
+		m_impulse.SetZero();
+	}
+
+	data.velocities[m_indexB].v = vB;
+	data.velocities[m_indexB].w = wB;
+}
+
+void b2MouseJoint::SolveVelocityConstraints(const b2SolverData& data)
+{
+	b2Vec2 vB = data.velocities[m_indexB].v;
+	float wB = data.velocities[m_indexB].w;
+
+	// Cdot = v + cross(w, r)
+	b2Vec2 Cdot = vB + b2Cross(wB, m_rB);
+	b2Vec2 impulse = b2Mul(m_mass, -(Cdot + m_C + m_gamma * m_impulse));
+
+	b2Vec2 oldImpulse = m_impulse;
+	m_impulse += impulse;
+	float maxImpulse = data.step.dt * m_maxForce;
+	if (m_impulse.LengthSquared() > maxImpulse * maxImpulse)
+	{
+		m_impulse *= maxImpulse / m_impulse.Length();
+	}
+	impulse = m_impulse - oldImpulse;
+
+	vB += m_invMassB * impulse;
+	wB += m_invIB * b2Cross(m_rB, impulse);
+
+	data.velocities[m_indexB].v = vB;
+	data.velocities[m_indexB].w = wB;
+}
+
+bool b2MouseJoint::SolvePositionConstraints(const b2SolverData& data)
+{
+	B2_NOT_USED(data);
+	return true;
+}
+
+b2Vec2 b2MouseJoint::GetAnchorA() const
+{
+	return m_targetA;
+}
+
+b2Vec2 b2MouseJoint::GetAnchorB() const
+{
+	return m_bodyB->GetWorldPoint(m_localAnchorB);
+}
+
+b2Vec2 b2MouseJoint::GetReactionForce(float inv_dt) const
+{
+	return inv_dt * m_impulse;
+}
+
+float b2MouseJoint::GetReactionTorque(float inv_dt) const
+{
+	return inv_dt * 0.0f;
+}
+
+void b2MouseJoint::ShiftOrigin(const b2Vec2& newOrigin)
+{
+	m_targetA -= newOrigin;
+}

3rd/box2d/src/dynamics/b2_polygon_circle_contact.cpp

@@ -0,0 +1,54 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#include "b2_polygon_circle_contact.h"
+
+#include "box2d/b2_block_allocator.h"
+#include "box2d/b2_fixture.h"
+
+#include <new>
+
+b2Contact* b2PolygonAndCircleContact::Create(b2Fixture* fixtureA, int32, b2Fixture* fixtureB, int32, b2BlockAllocator* allocator)
+{
+	void* mem = allocator->Allocate(sizeof(b2PolygonAndCircleContact));
+	return new (mem) b2PolygonAndCircleContact(fixtureA, fixtureB);
+}
+
+void b2PolygonAndCircleContact::Destroy(b2Contact* contact, b2BlockAllocator* allocator)
+{
+	((b2PolygonAndCircleContact*)contact)->~b2PolygonAndCircleContact();
+	allocator->Free(contact, sizeof(b2PolygonAndCircleContact));
+}
+
+b2PolygonAndCircleContact::b2PolygonAndCircleContact(b2Fixture* fixtureA, b2Fixture* fixtureB)
+: b2Contact(fixtureA, 0, fixtureB, 0)
+{
+	b2Assert(m_fixtureA->GetType() == b2Shape::e_polygon);
+	b2Assert(m_fixtureB->GetType() == b2Shape::e_circle);
+}
+
+void b2PolygonAndCircleContact::Evaluate(b2Manifold* manifold, const b2Transform& xfA, const b2Transform& xfB)
+{
+	b2CollidePolygonAndCircle(	manifold,
+								(b2PolygonShape*)m_fixtureA->GetShape(), xfA,
+								(b2CircleShape*)m_fixtureB->GetShape(), xfB);
+}

3rd/box2d/src/dynamics/b2_polygon_circle_contact.h

@@ -0,0 +1,42 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#ifndef B2_POLYGON_AND_CIRCLE_CONTACT_H
+#define B2_POLYGON_AND_CIRCLE_CONTACT_H
+
+#include "box2d/b2_contact.h"
+
+class b2BlockAllocator;
+
+class b2PolygonAndCircleContact : public b2Contact
+{
+public:
+	static b2Contact* Create(b2Fixture* fixtureA, int32 indexA, b2Fixture* fixtureB, int32 indexB, b2BlockAllocator* allocator);
+	static void Destroy(b2Contact* contact, b2BlockAllocator* allocator);
+
+	b2PolygonAndCircleContact(b2Fixture* fixtureA, b2Fixture* fixtureB);
+	~b2PolygonAndCircleContact() {}
+
+	void Evaluate(b2Manifold* manifold, const b2Transform& xfA, const b2Transform& xfB) override;
+};
+
+#endif

3rd/box2d/src/dynamics/b2_polygon_contact.cpp

@@ -0,0 +1,57 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#include "b2_polygon_contact.h"
+
+#include "box2d/b2_block_allocator.h"
+#include "box2d/b2_body.h"
+#include "box2d/b2_fixture.h"
+#include "box2d/b2_time_of_impact.h"
+#include "box2d/b2_world_callbacks.h"
+
+#include <new>
+
+b2Contact* b2PolygonContact::Create(b2Fixture* fixtureA, int32, b2Fixture* fixtureB, int32, b2BlockAllocator* allocator)
+{
+	void* mem = allocator->Allocate(sizeof(b2PolygonContact));
+	return new (mem) b2PolygonContact(fixtureA, fixtureB);
+}
+
+void b2PolygonContact::Destroy(b2Contact* contact, b2BlockAllocator* allocator)
+{
+	((b2PolygonContact*)contact)->~b2PolygonContact();
+	allocator->Free(contact, sizeof(b2PolygonContact));
+}
+
+b2PolygonContact::b2PolygonContact(b2Fixture* fixtureA, b2Fixture* fixtureB)
+	: b2Contact(fixtureA, 0, fixtureB, 0)
+{
+	b2Assert(m_fixtureA->GetType() == b2Shape::e_polygon);
+	b2Assert(m_fixtureB->GetType() == b2Shape::e_polygon);
+}
+
+void b2PolygonContact::Evaluate(b2Manifold* manifold, const b2Transform& xfA, const b2Transform& xfB)
+{
+	b2CollidePolygons(	manifold,
+						(b2PolygonShape*)m_fixtureA->GetShape(), xfA,
+						(b2PolygonShape*)m_fixtureB->GetShape(), xfB);
+}

3rd/box2d/src/dynamics/b2_polygon_contact.h

@@ -0,0 +1,43 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#ifndef B2_POLYGON_CONTACT_H
+#define B2_POLYGON_CONTACT_H
+
+#include "box2d/b2_contact.h"
+
+class b2BlockAllocator;
+
+class b2PolygonContact : public b2Contact
+{
+public:
+	static b2Contact* Create(	b2Fixture* fixtureA, int32 indexA,
+								b2Fixture* fixtureB, int32 indexB, b2BlockAllocator* allocator);
+	static void Destroy(b2Contact* contact, b2BlockAllocator* allocator);
+
+	b2PolygonContact(b2Fixture* fixtureA, b2Fixture* fixtureB);
+	~b2PolygonContact() {}
+
+	void Evaluate(b2Manifold* manifold, const b2Transform& xfA, const b2Transform& xfB) override;
+};
+
+#endif

3rd/box2d/src/dynamics/b2_prismatic_joint.cpp

@@ -0,0 +1,643 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#include "box2d/b2_body.h"
+#include "box2d/b2_draw.h"
+#include "box2d/b2_prismatic_joint.h"
+#include "box2d/b2_time_step.h"
+
+// Linear constraint (point-to-line)
+// d = p2 - p1 = x2 + r2 - x1 - r1
+// C = dot(perp, d)
+// Cdot = dot(d, cross(w1, perp)) + dot(perp, v2 + cross(w2, r2) - v1 - cross(w1, r1))
+//      = -dot(perp, v1) - dot(cross(d + r1, perp), w1) + dot(perp, v2) + dot(cross(r2, perp), v2)
+// J = [-perp, -cross(d + r1, perp), perp, cross(r2,perp)]
+//
+// Angular constraint
+// C = a2 - a1 + a_initial
+// Cdot = w2 - w1
+// J = [0 0 -1 0 0 1]
+//
+// K = J * invM * JT
+//
+// J = [-a -s1 a s2]
+//     [0  -1  0  1]
+// a = perp
+// s1 = cross(d + r1, a) = cross(p2 - x1, a)
+// s2 = cross(r2, a) = cross(p2 - x2, a)
+
+// Motor/Limit linear constraint
+// C = dot(ax1, d)
+// Cdot = -dot(ax1, v1) - dot(cross(d + r1, ax1), w1) + dot(ax1, v2) + dot(cross(r2, ax1), v2)
+// J = [-ax1 -cross(d+r1,ax1) ax1 cross(r2,ax1)]
+
+// Predictive limit is applied even when the limit is not active.
+// Prevents a constraint speed that can lead to a constraint error in one time step.
+// Want C2 = C1 + h * Cdot >= 0
+// Or:
+// Cdot + C1/h >= 0
+// I do not apply a negative constraint error because that is handled in position correction.
+// So:
+// Cdot + max(C1, 0)/h >= 0
+
+// Block Solver
+// We develop a block solver that includes the angular and linear constraints. This makes the limit stiffer.
+//
+// The Jacobian has 2 rows:
+// J = [-uT -s1 uT s2] // linear
+//     [0   -1   0  1] // angular
+//
+// u = perp
+// s1 = cross(d + r1, u), s2 = cross(r2, u)
+// a1 = cross(d + r1, v), a2 = cross(r2, v)
+
+void b2PrismaticJointDef::Initialize(b2Body* bA, b2Body* bB, const b2Vec2& anchor, const b2Vec2& axis)
+{
+	bodyA = bA;
+	bodyB = bB;
+	localAnchorA = bodyA->GetLocalPoint(anchor);
+	localAnchorB = bodyB->GetLocalPoint(anchor);
+	localAxisA = bodyA->GetLocalVector(axis);
+	referenceAngle = bodyB->GetAngle() - bodyA->GetAngle();
+}
+
+b2PrismaticJoint::b2PrismaticJoint(const b2PrismaticJointDef* def)
+: b2Joint(def)
+{
+	m_localAnchorA = def->localAnchorA;
+	m_localAnchorB = def->localAnchorB;
+	m_localXAxisA = def->localAxisA;
+	m_localXAxisA.Normalize();
+	m_localYAxisA = b2Cross(1.0f, m_localXAxisA);
+	m_referenceAngle = def->referenceAngle;
+
+	m_impulse.SetZero();
+	m_axialMass = 0.0f;
+	m_motorImpulse = 0.0f;
+	m_lowerImpulse = 0.0f;
+	m_upperImpulse = 0.0f;
+
+	m_lowerTranslation = def->lowerTranslation;
+	m_upperTranslation = def->upperTranslation;
+
+	b2Assert(m_lowerTranslation <= m_upperTranslation);
+
+	m_maxMotorForce = def->maxMotorForce;
+	m_motorSpeed = def->motorSpeed;
+	m_enableLimit = def->enableLimit;
+	m_enableMotor = def->enableMotor;
+
+	m_translation = 0.0f;
+	m_axis.SetZero();
+	m_perp.SetZero();
+}
+
+void b2PrismaticJoint::InitVelocityConstraints(const b2SolverData& data)
+{
+	m_indexA = m_bodyA->m_islandIndex;
+	m_indexB = m_bodyB->m_islandIndex;
+	m_localCenterA = m_bodyA->m_sweep.localCenter;
+	m_localCenterB = m_bodyB->m_sweep.localCenter;
+	m_invMassA = m_bodyA->m_invMass;
+	m_invMassB = m_bodyB->m_invMass;
+	m_invIA = m_bodyA->m_invI;
+	m_invIB = m_bodyB->m_invI;
+
+	b2Vec2 cA = data.positions[m_indexA].c;
+	float aA = data.positions[m_indexA].a;
+	b2Vec2 vA = data.velocities[m_indexA].v;
+	float wA = data.velocities[m_indexA].w;
+
+	b2Vec2 cB = data.positions[m_indexB].c;
+	float aB = data.positions[m_indexB].a;
+	b2Vec2 vB = data.velocities[m_indexB].v;
+	float wB = data.velocities[m_indexB].w;
+
+	b2Rot qA(aA), qB(aB);
+
+	// Compute the effective masses.
+	b2Vec2 rA = b2Mul(qA, m_localAnchorA - m_localCenterA);
+	b2Vec2 rB = b2Mul(qB, m_localAnchorB - m_localCenterB);
+	b2Vec2 d = (cB - cA) + rB - rA;
+
+	float mA = m_invMassA, mB = m_invMassB;
+	float iA = m_invIA, iB = m_invIB;
+
+	// Compute motor Jacobian and effective mass.
+	{
+		m_axis = b2Mul(qA, m_localXAxisA);
+		m_a1 = b2Cross(d + rA, m_axis);
+		m_a2 = b2Cross(rB, m_axis);
+
+		m_axialMass = mA + mB + iA * m_a1 * m_a1 + iB * m_a2 * m_a2;
+		if (m_axialMass > 0.0f)
+		{
+			m_axialMass = 1.0f / m_axialMass;
+		}
+	}
+
+	// Prismatic constraint.
+	{
+		m_perp = b2Mul(qA, m_localYAxisA);
+
+		m_s1 = b2Cross(d + rA, m_perp);
+		m_s2 = b2Cross(rB, m_perp);
+
+		float k11 = mA + mB + iA * m_s1 * m_s1 + iB * m_s2 * m_s2;
+		float k12 = iA * m_s1 + iB * m_s2;
+		float k22 = iA + iB;
+		if (k22 == 0.0f)
+		{
+			// For bodies with fixed rotation.
+			k22 = 1.0f;
+		}
+
+		m_K.ex.Set(k11, k12);
+		m_K.ey.Set(k12, k22);
+	}
+
+	if (m_enableLimit)
+	{
+		m_translation = b2Dot(m_axis, d);
+	}
+	else
+	{
+		m_lowerImpulse = 0.0f;
+		m_upperImpulse = 0.0f;
+	}
+
+	if (m_enableMotor == false)
+	{
+		m_motorImpulse = 0.0f;
+	}
+
+	if (data.step.warmStarting)
+	{
+		// Account for variable time step.
+		m_impulse *= data.step.dtRatio;
+		m_motorImpulse *= data.step.dtRatio;
+		m_lowerImpulse *= data.step.dtRatio;
+		m_upperImpulse *= data.step.dtRatio;
+
+		float axialImpulse = m_motorImpulse + m_lowerImpulse - m_upperImpulse;
+		b2Vec2 P = m_impulse.x * m_perp + axialImpulse * m_axis;
+		float LA = m_impulse.x * m_s1 + m_impulse.y + axialImpulse * m_a1;
+		float LB = m_impulse.x * m_s2 + m_impulse.y + axialImpulse * m_a2;
+
+		vA -= mA * P;
+		wA -= iA * LA;
+
+		vB += mB * P;
+		wB += iB * LB;
+	}
+	else
+	{
+		m_impulse.SetZero();
+		m_motorImpulse = 0.0f;
+		m_lowerImpulse = 0.0f;
+		m_upperImpulse = 0.0f;
+	}
+
+	data.velocities[m_indexA].v = vA;
+	data.velocities[m_indexA].w = wA;
+	data.velocities[m_indexB].v = vB;
+	data.velocities[m_indexB].w = wB;
+}
+
+void b2PrismaticJoint::SolveVelocityConstraints(const b2SolverData& data)
+{
+	b2Vec2 vA = data.velocities[m_indexA].v;
+	float wA = data.velocities[m_indexA].w;
+	b2Vec2 vB = data.velocities[m_indexB].v;
+	float wB = data.velocities[m_indexB].w;
+
+	float mA = m_invMassA, mB = m_invMassB;
+	float iA = m_invIA, iB = m_invIB;
+
+	// Solve linear motor constraint
+	if (m_enableMotor)
+	{
+		float Cdot = b2Dot(m_axis, vB - vA) + m_a2 * wB - m_a1 * wA;
+		float impulse = m_axialMass * (m_motorSpeed - Cdot);
+		float oldImpulse = m_motorImpulse;
+		float maxImpulse = data.step.dt * m_maxMotorForce;
+		m_motorImpulse = b2Clamp(m_motorImpulse + impulse, -maxImpulse, maxImpulse);
+		impulse = m_motorImpulse - oldImpulse;
+
+		b2Vec2 P = impulse * m_axis;
+		float LA = impulse * m_a1;
+		float LB = impulse * m_a2;
+
+		vA -= mA * P;
+		wA -= iA * LA;
+		vB += mB * P;
+		wB += iB * LB;
+	}
+
+	if (m_enableLimit)
+	{
+		// Lower limit
+		{
+			float C = m_translation - m_lowerTranslation;
+			float Cdot = b2Dot(m_axis, vB - vA) + m_a2 * wB - m_a1 * wA;
+			float impulse = -m_axialMass * (Cdot + b2Max(C, 0.0f) * data.step.inv_dt);
+			float oldImpulse = m_lowerImpulse;
+			m_lowerImpulse = b2Max(m_lowerImpulse + impulse, 0.0f);
+			impulse = m_lowerImpulse - oldImpulse;
+
+			b2Vec2 P = impulse * m_axis;
+			float LA = impulse * m_a1;
+			float LB = impulse * m_a2;
+
+			vA -= mA * P;
+			wA -= iA * LA;
+			vB += mB * P;
+			wB += iB * LB;
+		}
+
+		// Upper limit
+		// Note: signs are flipped to keep C positive when the constraint is satisfied.
+		// This also keeps the impulse positive when the limit is active.
+		{
+			float C = m_upperTranslation - m_translation;
+			float Cdot = b2Dot(m_axis, vA - vB) + m_a1 * wA - m_a2 * wB;
+			float impulse = -m_axialMass * (Cdot + b2Max(C, 0.0f) * data.step.inv_dt);
+			float oldImpulse = m_upperImpulse;
+			m_upperImpulse = b2Max(m_upperImpulse + impulse, 0.0f);
+			impulse = m_upperImpulse - oldImpulse;
+
+			b2Vec2 P = impulse * m_axis;
+			float LA = impulse * m_a1;
+			float LB = impulse * m_a2;
+
+			vA += mA * P;
+			wA += iA * LA;
+			vB -= mB * P;
+			wB -= iB * LB;
+		}
+	}
+
+	// Solve the prismatic constraint in block form.
+	{
+		b2Vec2 Cdot;
+		Cdot.x = b2Dot(m_perp, vB - vA) + m_s2 * wB - m_s1 * wA;
+		Cdot.y = wB - wA;
+
+		b2Vec2 df = m_K.Solve(-Cdot);
+		m_impulse += df;
+
+		b2Vec2 P = df.x * m_perp;
+		float LA = df.x * m_s1 + df.y;
+		float LB = df.x * m_s2 + df.y;
+
+		vA -= mA * P;
+		wA -= iA * LA;
+
+		vB += mB * P;
+		wB += iB * LB;
+	}
+
+	data.velocities[m_indexA].v = vA;
+	data.velocities[m_indexA].w = wA;
+	data.velocities[m_indexB].v = vB;
+	data.velocities[m_indexB].w = wB;
+}
+
+// A velocity based solver computes reaction forces(impulses) using the velocity constraint solver.Under this context,
+// the position solver is not there to resolve forces.It is only there to cope with integration error.
+//
+// Therefore, the pseudo impulses in the position solver do not have any physical meaning.Thus it is okay if they suck.
+//
+// We could take the active state from the velocity solver.However, the joint might push past the limit when the velocity
+// solver indicates the limit is inactive.
+bool b2PrismaticJoint::SolvePositionConstraints(const b2SolverData& data)
+{
+	b2Vec2 cA = data.positions[m_indexA].c;
+	float aA = data.positions[m_indexA].a;
+	b2Vec2 cB = data.positions[m_indexB].c;
+	float aB = data.positions[m_indexB].a;
+
+	b2Rot qA(aA), qB(aB);
+
+	float mA = m_invMassA, mB = m_invMassB;
+	float iA = m_invIA, iB = m_invIB;
+
+	// Compute fresh Jacobians
+	b2Vec2 rA = b2Mul(qA, m_localAnchorA - m_localCenterA);
+	b2Vec2 rB = b2Mul(qB, m_localAnchorB - m_localCenterB);
+	b2Vec2 d = cB + rB - cA - rA;
+
+	b2Vec2 axis = b2Mul(qA, m_localXAxisA);
+	float a1 = b2Cross(d + rA, axis);
+	float a2 = b2Cross(rB, axis);
+	b2Vec2 perp = b2Mul(qA, m_localYAxisA);
+
+	float s1 = b2Cross(d + rA, perp);
+	float s2 = b2Cross(rB, perp);
+
+	b2Vec3 impulse;
+	b2Vec2 C1;
+	C1.x = b2Dot(perp, d);
+	C1.y = aB - aA - m_referenceAngle;
+
+	float linearError = b2Abs(C1.x);
+	float angularError = b2Abs(C1.y);
+
+	bool active = false;
+	float C2 = 0.0f;
+	if (m_enableLimit)
+	{
+		float translation = b2Dot(axis, d);
+		if (b2Abs(m_upperTranslation - m_lowerTranslation) < 2.0f * b2_linearSlop)
+		{
+			C2 = translation;
+			linearError = b2Max(linearError, b2Abs(translation));
+			active = true;
+		}
+		else if (translation <= m_lowerTranslation)
+		{
+			C2 = b2Min(translation - m_lowerTranslation, 0.0f);
+			linearError = b2Max(linearError, m_lowerTranslation - translation);
+			active = true;
+		}
+		else if (translation >= m_upperTranslation)
+		{
+			C2 = b2Max(translation - m_upperTranslation, 0.0f);
+			linearError = b2Max(linearError, translation - m_upperTranslation);
+			active = true;
+		}
+	}
+
+	if (active)
+	{
+		float k11 = mA + mB + iA * s1 * s1 + iB * s2 * s2;
+		float k12 = iA * s1 + iB * s2;
+		float k13 = iA * s1 * a1 + iB * s2 * a2;
+		float k22 = iA + iB;
+		if (k22 == 0.0f)
+		{
+			// For fixed rotation
+			k22 = 1.0f;
+		}
+		float k23 = iA * a1 + iB * a2;
+		float k33 = mA + mB + iA * a1 * a1 + iB * a2 * a2;
+
+		b2Mat33 K;
+		K.ex.Set(k11, k12, k13);
+		K.ey.Set(k12, k22, k23);
+		K.ez.Set(k13, k23, k33);
+
+		b2Vec3 C;
+		C.x = C1.x;
+		C.y = C1.y;
+		C.z = C2;
+
+		impulse = K.Solve33(-C);
+	}
+	else
+	{
+		float k11 = mA + mB + iA * s1 * s1 + iB * s2 * s2;
+		float k12 = iA * s1 + iB * s2;
+		float k22 = iA + iB;
+		if (k22 == 0.0f)
+		{
+			k22 = 1.0f;
+		}
+
+		b2Mat22 K;
+		K.ex.Set(k11, k12);
+		K.ey.Set(k12, k22);
+
+		b2Vec2 impulse1 = K.Solve(-C1);
+		impulse.x = impulse1.x;
+		impulse.y = impulse1.y;
+		impulse.z = 0.0f;
+	}
+
+	b2Vec2 P = impulse.x * perp + impulse.z * axis;
+	float LA = impulse.x * s1 + impulse.y + impulse.z * a1;
+	float LB = impulse.x * s2 + impulse.y + impulse.z * a2;
+
+	cA -= mA * P;
+	aA -= iA * LA;
+	cB += mB * P;
+	aB += iB * LB;
+
+	data.positions[m_indexA].c = cA;
+	data.positions[m_indexA].a = aA;
+	data.positions[m_indexB].c = cB;
+	data.positions[m_indexB].a = aB;
+
+	return linearError <= b2_linearSlop && angularError <= b2_angularSlop;
+}
+
+b2Vec2 b2PrismaticJoint::GetAnchorA() const
+{
+	return m_bodyA->GetWorldPoint(m_localAnchorA);
+}
+
+b2Vec2 b2PrismaticJoint::GetAnchorB() const
+{
+	return m_bodyB->GetWorldPoint(m_localAnchorB);
+}
+
+b2Vec2 b2PrismaticJoint::GetReactionForce(float inv_dt) const
+{
+	return inv_dt * (m_impulse.x * m_perp + (m_motorImpulse + m_lowerImpulse - m_upperImpulse) * m_axis);
+}
+
+float b2PrismaticJoint::GetReactionTorque(float inv_dt) const
+{
+	return inv_dt * m_impulse.y;
+}
+
+float b2PrismaticJoint::GetJointTranslation() const
+{
+	b2Vec2 pA = m_bodyA->GetWorldPoint(m_localAnchorA);
+	b2Vec2 pB = m_bodyB->GetWorldPoint(m_localAnchorB);
+	b2Vec2 d = pB - pA;
+	b2Vec2 axis = m_bodyA->GetWorldVector(m_localXAxisA);
+
+	float translation = b2Dot(d, axis);
+	return translation;
+}
+
+float b2PrismaticJoint::GetJointSpeed() const
+{
+	b2Body* bA = m_bodyA;
+	b2Body* bB = m_bodyB;
+
+	b2Vec2 rA = b2Mul(bA->m_xf.q, m_localAnchorA - bA->m_sweep.localCenter);
+	b2Vec2 rB = b2Mul(bB->m_xf.q, m_localAnchorB - bB->m_sweep.localCenter);
+	b2Vec2 p1 = bA->m_sweep.c + rA;
+	b2Vec2 p2 = bB->m_sweep.c + rB;
+	b2Vec2 d = p2 - p1;
+	b2Vec2 axis = b2Mul(bA->m_xf.q, m_localXAxisA);
+
+	b2Vec2 vA = bA->m_linearVelocity;
+	b2Vec2 vB = bB->m_linearVelocity;
+	float wA = bA->m_angularVelocity;
+	float wB = bB->m_angularVelocity;
+
+	float speed = b2Dot(d, b2Cross(wA, axis)) + b2Dot(axis, vB + b2Cross(wB, rB) - vA - b2Cross(wA, rA));
+	return speed;
+}
+
+bool b2PrismaticJoint::IsLimitEnabled() const
+{
+	return m_enableLimit;
+}
+
+void b2PrismaticJoint::EnableLimit(bool flag)
+{
+	if (flag != m_enableLimit)
+	{
+		m_bodyA->SetAwake(true);
+		m_bodyB->SetAwake(true);
+		m_enableLimit = flag;
+		m_lowerImpulse = 0.0f;
+		m_upperImpulse = 0.0f;
+	}
+}
+
+float b2PrismaticJoint::GetLowerLimit() const
+{
+	return m_lowerTranslation;
+}
+
+float b2PrismaticJoint::GetUpperLimit() const
+{
+	return m_upperTranslation;
+}
+
+void b2PrismaticJoint::SetLimits(float lower, float upper)
+{
+	b2Assert(lower <= upper);
+	if (lower != m_lowerTranslation || upper != m_upperTranslation)
+	{
+		m_bodyA->SetAwake(true);
+		m_bodyB->SetAwake(true);
+		m_lowerTranslation = lower;
+		m_upperTranslation = upper;
+		m_lowerImpulse = 0.0f;
+		m_upperImpulse = 0.0f;
+	}
+}
+
+bool b2PrismaticJoint::IsMotorEnabled() const
+{
+	return m_enableMotor;
+}
+
+void b2PrismaticJoint::EnableMotor(bool flag)
+{
+	if (flag != m_enableMotor)
+	{
+		m_bodyA->SetAwake(true);
+		m_bodyB->SetAwake(true);
+		m_enableMotor = flag;
+	}
+}
+
+void b2PrismaticJoint::SetMotorSpeed(float speed)
+{
+	if (speed != m_motorSpeed)
+	{
+		m_bodyA->SetAwake(true);
+		m_bodyB->SetAwake(true);
+		m_motorSpeed = speed;
+	}
+}
+
+void b2PrismaticJoint::SetMaxMotorForce(float force)
+{
+	if (force != m_maxMotorForce)
+	{
+		m_bodyA->SetAwake(true);
+		m_bodyB->SetAwake(true);
+		m_maxMotorForce = force;
+	}
+}
+
+float b2PrismaticJoint::GetMotorForce(float inv_dt) const
+{
+	return inv_dt * m_motorImpulse;
+}
+
+void b2PrismaticJoint::Dump()
+{
+	// FLT_DECIMAL_DIG == 9
+
+	int32 indexA = m_bodyA->m_islandIndex;
+	int32 indexB = m_bodyB->m_islandIndex;
+
+	b2Dump("  b2PrismaticJointDef jd;\n");
+	b2Dump("  jd.bodyA = bodies[%d];\n", indexA);
+	b2Dump("  jd.bodyB = bodies[%d];\n", indexB);
+	b2Dump("  jd.collideConnected = bool(%d);\n", m_collideConnected);
+	b2Dump("  jd.localAnchorA.Set(%.9g, %.9g);\n", m_localAnchorA.x, m_localAnchorA.y);
+	b2Dump("  jd.localAnchorB.Set(%.9g, %.9g);\n", m_localAnchorB.x, m_localAnchorB.y);
+	b2Dump("  jd.localAxisA.Set(%.9g, %.9g);\n", m_localXAxisA.x, m_localXAxisA.y);
+	b2Dump("  jd.referenceAngle = %.9g;\n", m_referenceAngle);
+	b2Dump("  jd.enableLimit = bool(%d);\n", m_enableLimit);
+	b2Dump("  jd.lowerTranslation = %.9g;\n", m_lowerTranslation);
+	b2Dump("  jd.upperTranslation = %.9g;\n", m_upperTranslation);
+	b2Dump("  jd.enableMotor = bool(%d);\n", m_enableMotor);
+	b2Dump("  jd.motorSpeed = %.9g;\n", m_motorSpeed);
+	b2Dump("  jd.maxMotorForce = %.9g;\n", m_maxMotorForce);
+	b2Dump("  joints[%d] = m_world->CreateJoint(&jd);\n", m_index);
+}
+
+void b2PrismaticJoint::Draw(b2Draw* draw) const
+{
+	const b2Transform& xfA = m_bodyA->GetTransform();
+	const b2Transform& xfB = m_bodyB->GetTransform();
+	b2Vec2 pA = b2Mul(xfA, m_localAnchorA);
+	b2Vec2 pB = b2Mul(xfB, m_localAnchorB);
+
+	b2Vec2 axis = b2Mul(xfA.q, m_localXAxisA);
+
+	b2Color c1(0.7f, 0.7f, 0.7f);
+	b2Color c2(0.3f, 0.9f, 0.3f);
+	b2Color c3(0.9f, 0.3f, 0.3f);
+	b2Color c4(0.3f, 0.3f, 0.9f);
+	b2Color c5(0.4f, 0.4f, 0.4f);
+
+	draw->DrawSegment(pA, pB, c5);
+
+	if (m_enableLimit)
+	{
+		b2Vec2 lower = pA + m_lowerTranslation * axis;
+		b2Vec2 upper = pA + m_upperTranslation * axis;
+		b2Vec2 perp = b2Mul(xfA.q, m_localYAxisA);
+		draw->DrawSegment(lower, upper, c1);
+		draw->DrawSegment(lower - 0.5f * perp, lower + 0.5f * perp, c2);
+		draw->DrawSegment(upper - 0.5f * perp, upper + 0.5f * perp, c3);
+	}
+	else
+	{
+		draw->DrawSegment(pA - 1.0f * axis, pA + 1.0f * axis, c1);
+	}
+
+	draw->DrawPoint(pA, 5.0f, c1);
+	draw->DrawPoint(pB, 5.0f, c4);
+}

3rd/box2d/src/dynamics/b2_pulley_joint.cpp

@@ -0,0 +1,352 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#include "box2d/b2_body.h"
+#include "box2d/b2_pulley_joint.h"
+#include "box2d/b2_time_step.h"
+
+// Pulley:
+// length1 = norm(p1 - s1)
+// length2 = norm(p2 - s2)
+// C0 = (length1 + ratio * length2)_initial
+// C = C0 - (length1 + ratio * length2)
+// u1 = (p1 - s1) / norm(p1 - s1)
+// u2 = (p2 - s2) / norm(p2 - s2)
+// Cdot = -dot(u1, v1 + cross(w1, r1)) - ratio * dot(u2, v2 + cross(w2, r2))
+// J = -[u1 cross(r1, u1) ratio * u2  ratio * cross(r2, u2)]
+// K = J * invM * JT
+//   = invMass1 + invI1 * cross(r1, u1)^2 + ratio^2 * (invMass2 + invI2 * cross(r2, u2)^2)
+
+void b2PulleyJointDef::Initialize(b2Body* bA, b2Body* bB,
+				const b2Vec2& groundA, const b2Vec2& groundB,
+				const b2Vec2& anchorA, const b2Vec2& anchorB,
+				float r)
+{
+	bodyA = bA;
+	bodyB = bB;
+	groundAnchorA = groundA;
+	groundAnchorB = groundB;
+	localAnchorA = bodyA->GetLocalPoint(anchorA);
+	localAnchorB = bodyB->GetLocalPoint(anchorB);
+	b2Vec2 dA = anchorA - groundA;
+	lengthA = dA.Length();
+	b2Vec2 dB = anchorB - groundB;
+	lengthB = dB.Length();
+	ratio = r;
+	b2Assert(ratio > b2_epsilon);
+}
+
+b2PulleyJoint::b2PulleyJoint(const b2PulleyJointDef* def)
+: b2Joint(def)
+{
+	m_groundAnchorA = def->groundAnchorA;
+	m_groundAnchorB = def->groundAnchorB;
+	m_localAnchorA = def->localAnchorA;
+	m_localAnchorB = def->localAnchorB;
+
+	m_lengthA = def->lengthA;
+	m_lengthB = def->lengthB;
+
+	b2Assert(def->ratio != 0.0f);
+	m_ratio = def->ratio;
+
+	m_constant = def->lengthA + m_ratio * def->lengthB;
+
+	m_impulse = 0.0f;
+}
+
+void b2PulleyJoint::InitVelocityConstraints(const b2SolverData& data)
+{
+	m_indexA = m_bodyA->m_islandIndex;
+	m_indexB = m_bodyB->m_islandIndex;
+	m_localCenterA = m_bodyA->m_sweep.localCenter;
+	m_localCenterB = m_bodyB->m_sweep.localCenter;
+	m_invMassA = m_bodyA->m_invMass;
+	m_invMassB = m_bodyB->m_invMass;
+	m_invIA = m_bodyA->m_invI;
+	m_invIB = m_bodyB->m_invI;
+
+	b2Vec2 cA = data.positions[m_indexA].c;
+	float aA = data.positions[m_indexA].a;
+	b2Vec2 vA = data.velocities[m_indexA].v;
+	float wA = data.velocities[m_indexA].w;
+
+	b2Vec2 cB = data.positions[m_indexB].c;
+	float aB = data.positions[m_indexB].a;
+	b2Vec2 vB = data.velocities[m_indexB].v;
+	float wB = data.velocities[m_indexB].w;
+
+	b2Rot qA(aA), qB(aB);
+
+	m_rA = b2Mul(qA, m_localAnchorA - m_localCenterA);
+	m_rB = b2Mul(qB, m_localAnchorB - m_localCenterB);
+
+	// Get the pulley axes.
+	m_uA = cA + m_rA - m_groundAnchorA;
+	m_uB = cB + m_rB - m_groundAnchorB;
+
+	float lengthA = m_uA.Length();
+	float lengthB = m_uB.Length();
+
+	if (lengthA > 10.0f * b2_linearSlop)
+	{
+		m_uA *= 1.0f / lengthA;
+	}
+	else
+	{
+		m_uA.SetZero();
+	}
+
+	if (lengthB > 10.0f * b2_linearSlop)
+	{
+		m_uB *= 1.0f / lengthB;
+	}
+	else
+	{
+		m_uB.SetZero();
+	}
+
+	// Compute effective mass.
+	float ruA = b2Cross(m_rA, m_uA);
+	float ruB = b2Cross(m_rB, m_uB);
+
+	float mA = m_invMassA + m_invIA * ruA * ruA;
+	float mB = m_invMassB + m_invIB * ruB * ruB;
+
+	m_mass = mA + m_ratio * m_ratio * mB;
+
+	if (m_mass > 0.0f)
+	{
+		m_mass = 1.0f / m_mass;
+	}
+
+	if (data.step.warmStarting)
+	{
+		// Scale impulses to support variable time steps.
+		m_impulse *= data.step.dtRatio;
+
+		// Warm starting.
+		b2Vec2 PA = -(m_impulse) * m_uA;
+		b2Vec2 PB = (-m_ratio * m_impulse) * m_uB;
+
+		vA += m_invMassA * PA;
+		wA += m_invIA * b2Cross(m_rA, PA);
+		vB += m_invMassB * PB;
+		wB += m_invIB * b2Cross(m_rB, PB);
+	}
+	else
+	{
+		m_impulse = 0.0f;
+	}
+
+	data.velocities[m_indexA].v = vA;
+	data.velocities[m_indexA].w = wA;
+	data.velocities[m_indexB].v = vB;
+	data.velocities[m_indexB].w = wB;
+}
+
+void b2PulleyJoint::SolveVelocityConstraints(const b2SolverData& data)
+{
+	b2Vec2 vA = data.velocities[m_indexA].v;
+	float wA = data.velocities[m_indexA].w;
+	b2Vec2 vB = data.velocities[m_indexB].v;
+	float wB = data.velocities[m_indexB].w;
+
+	b2Vec2 vpA = vA + b2Cross(wA, m_rA);
+	b2Vec2 vpB = vB + b2Cross(wB, m_rB);
+
+	float Cdot = -b2Dot(m_uA, vpA) - m_ratio * b2Dot(m_uB, vpB);
+	float impulse = -m_mass * Cdot;
+	m_impulse += impulse;
+
+	b2Vec2 PA = -impulse * m_uA;
+	b2Vec2 PB = -m_ratio * impulse * m_uB;
+	vA += m_invMassA * PA;
+	wA += m_invIA * b2Cross(m_rA, PA);
+	vB += m_invMassB * PB;
+	wB += m_invIB * b2Cross(m_rB, PB);
+
+	data.velocities[m_indexA].v = vA;
+	data.velocities[m_indexA].w = wA;
+	data.velocities[m_indexB].v = vB;
+	data.velocities[m_indexB].w = wB;
+}
+
+bool b2PulleyJoint::SolvePositionConstraints(const b2SolverData& data)
+{
+	b2Vec2 cA = data.positions[m_indexA].c;
+	float aA = data.positions[m_indexA].a;
+	b2Vec2 cB = data.positions[m_indexB].c;
+	float aB = data.positions[m_indexB].a;
+
+	b2Rot qA(aA), qB(aB);
+
+	b2Vec2 rA = b2Mul(qA, m_localAnchorA - m_localCenterA);
+	b2Vec2 rB = b2Mul(qB, m_localAnchorB - m_localCenterB);
+
+	// Get the pulley axes.
+	b2Vec2 uA = cA + rA - m_groundAnchorA;
+	b2Vec2 uB = cB + rB - m_groundAnchorB;
+
+	float lengthA = uA.Length();
+	float lengthB = uB.Length();
+
+	if (lengthA > 10.0f * b2_linearSlop)
+	{
+		uA *= 1.0f / lengthA;
+	}
+	else
+	{
+		uA.SetZero();
+	}
+
+	if (lengthB > 10.0f * b2_linearSlop)
+	{
+		uB *= 1.0f / lengthB;
+	}
+	else
+	{
+		uB.SetZero();
+	}
+
+	// Compute effective mass.
+	float ruA = b2Cross(rA, uA);
+	float ruB = b2Cross(rB, uB);
+
+	float mA = m_invMassA + m_invIA * ruA * ruA;
+	float mB = m_invMassB + m_invIB * ruB * ruB;
+
+	float mass = mA + m_ratio * m_ratio * mB;
+
+	if (mass > 0.0f)
+	{
+		mass = 1.0f / mass;
+	}
+
+	float C = m_constant - lengthA - m_ratio * lengthB;
+	float linearError = b2Abs(C);
+
+	float impulse = -mass * C;
+
+	b2Vec2 PA = -impulse * uA;
+	b2Vec2 PB = -m_ratio * impulse * uB;
+
+	cA += m_invMassA * PA;
+	aA += m_invIA * b2Cross(rA, PA);
+	cB += m_invMassB * PB;
+	aB += m_invIB * b2Cross(rB, PB);
+
+	data.positions[m_indexA].c = cA;
+	data.positions[m_indexA].a = aA;
+	data.positions[m_indexB].c = cB;
+	data.positions[m_indexB].a = aB;
+
+	return linearError < b2_linearSlop;
+}
+
+b2Vec2 b2PulleyJoint::GetAnchorA() const
+{
+	return m_bodyA->GetWorldPoint(m_localAnchorA);
+}
+
+b2Vec2 b2PulleyJoint::GetAnchorB() const
+{
+	return m_bodyB->GetWorldPoint(m_localAnchorB);
+}
+
+b2Vec2 b2PulleyJoint::GetReactionForce(float inv_dt) const
+{
+	b2Vec2 P = m_impulse * m_uB;
+	return inv_dt * P;
+}
+
+float b2PulleyJoint::GetReactionTorque(float inv_dt) const
+{
+	B2_NOT_USED(inv_dt);
+	return 0.0f;
+}
+
+b2Vec2 b2PulleyJoint::GetGroundAnchorA() const
+{
+	return m_groundAnchorA;
+}
+
+b2Vec2 b2PulleyJoint::GetGroundAnchorB() const
+{
+	return m_groundAnchorB;
+}
+
+float b2PulleyJoint::GetLengthA() const
+{
+	return m_lengthA;
+}
+
+float b2PulleyJoint::GetLengthB() const
+{
+	return m_lengthB;
+}
+
+float b2PulleyJoint::GetRatio() const
+{
+	return m_ratio;
+}
+
+float b2PulleyJoint::GetCurrentLengthA() const
+{
+	b2Vec2 p = m_bodyA->GetWorldPoint(m_localAnchorA);
+	b2Vec2 s = m_groundAnchorA;
+	b2Vec2 d = p - s;
+	return d.Length();
+}
+
+float b2PulleyJoint::GetCurrentLengthB() const
+{
+	b2Vec2 p = m_bodyB->GetWorldPoint(m_localAnchorB);
+	b2Vec2 s = m_groundAnchorB;
+	b2Vec2 d = p - s;
+	return d.Length();
+}
+
+void b2PulleyJoint::Dump()
+{
+	int32 indexA = m_bodyA->m_islandIndex;
+	int32 indexB = m_bodyB->m_islandIndex;
+
+	b2Dump("  b2PulleyJointDef jd;\n");
+	b2Dump("  jd.bodyA = bodies[%d];\n", indexA);
+	b2Dump("  jd.bodyB = bodies[%d];\n", indexB);
+	b2Dump("  jd.collideConnected = bool(%d);\n", m_collideConnected);
+	b2Dump("  jd.groundAnchorA.Set(%.9g, %.9g);\n", m_groundAnchorA.x, m_groundAnchorA.y);
+	b2Dump("  jd.groundAnchorB.Set(%.9g, %.9g);\n", m_groundAnchorB.x, m_groundAnchorB.y);
+	b2Dump("  jd.localAnchorA.Set(%.9g, %.9g);\n", m_localAnchorA.x, m_localAnchorA.y);
+	b2Dump("  jd.localAnchorB.Set(%.9g, %.9g);\n", m_localAnchorB.x, m_localAnchorB.y);
+	b2Dump("  jd.lengthA = %.9g;\n", m_lengthA);
+	b2Dump("  jd.lengthB = %.9g;\n", m_lengthB);
+	b2Dump("  jd.ratio = %.9g;\n", m_ratio);
+	b2Dump("  joints[%d] = m_world->CreateJoint(&jd);\n", m_index);
+}
+
+void b2PulleyJoint::ShiftOrigin(const b2Vec2& newOrigin)
+{
+	m_groundAnchorA -= newOrigin;
+	m_groundAnchorB -= newOrigin;
+}

3rd/box2d/src/dynamics/b2_revolute_joint.cpp

@@ -0,0 +1,501 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#include "box2d/b2_body.h"
+#include "box2d/b2_draw.h"
+#include "box2d/b2_revolute_joint.h"
+#include "box2d/b2_time_step.h"
+
+// Point-to-point constraint
+// C = p2 - p1
+// Cdot = v2 - v1
+//      = v2 + cross(w2, r2) - v1 - cross(w1, r1)
+// J = [-I -r1_skew I r2_skew ]
+// Identity used:
+// w k % (rx i + ry j) = w * (-ry i + rx j)
+
+// Motor constraint
+// Cdot = w2 - w1
+// J = [0 0 -1 0 0 1]
+// K = invI1 + invI2
+
+void b2RevoluteJointDef::Initialize(b2Body* bA, b2Body* bB, const b2Vec2& anchor)
+{
+	bodyA = bA;
+	bodyB = bB;
+	localAnchorA = bodyA->GetLocalPoint(anchor);
+	localAnchorB = bodyB->GetLocalPoint(anchor);
+	referenceAngle = bodyB->GetAngle() - bodyA->GetAngle();
+}
+
+b2RevoluteJoint::b2RevoluteJoint(const b2RevoluteJointDef* def)
+: b2Joint(def)
+{
+	m_localAnchorA = def->localAnchorA;
+	m_localAnchorB = def->localAnchorB;
+	m_referenceAngle = def->referenceAngle;
+
+	m_impulse.SetZero();
+	m_axialMass = 0.0f;
+	m_motorImpulse = 0.0f;
+	m_lowerImpulse = 0.0f;
+	m_upperImpulse = 0.0f;
+
+	m_lowerAngle = def->lowerAngle;
+	m_upperAngle = def->upperAngle;
+	m_maxMotorTorque = def->maxMotorTorque;
+	m_motorSpeed = def->motorSpeed;
+	m_enableLimit = def->enableLimit;
+	m_enableMotor = def->enableMotor;
+
+	m_angle = 0.0f;
+}
+
+void b2RevoluteJoint::InitVelocityConstraints(const b2SolverData& data)
+{
+	m_indexA = m_bodyA->m_islandIndex;
+	m_indexB = m_bodyB->m_islandIndex;
+	m_localCenterA = m_bodyA->m_sweep.localCenter;
+	m_localCenterB = m_bodyB->m_sweep.localCenter;
+	m_invMassA = m_bodyA->m_invMass;
+	m_invMassB = m_bodyB->m_invMass;
+	m_invIA = m_bodyA->m_invI;
+	m_invIB = m_bodyB->m_invI;
+
+	float aA = data.positions[m_indexA].a;
+	b2Vec2 vA = data.velocities[m_indexA].v;
+	float wA = data.velocities[m_indexA].w;
+
+	float aB = data.positions[m_indexB].a;
+	b2Vec2 vB = data.velocities[m_indexB].v;
+	float wB = data.velocities[m_indexB].w;
+
+	b2Rot qA(aA), qB(aB);
+
+	m_rA = b2Mul(qA, m_localAnchorA - m_localCenterA);
+	m_rB = b2Mul(qB, m_localAnchorB - m_localCenterB);
+
+	// J = [-I -r1_skew I r2_skew]
+	// r_skew = [-ry; rx]
+
+	// Matlab
+	// K = [ mA+r1y^2*iA+mB+r2y^2*iB,  -r1y*iA*r1x-r2y*iB*r2x]
+	//     [  -r1y*iA*r1x-r2y*iB*r2x, mA+r1x^2*iA+mB+r2x^2*iB]
+
+	float mA = m_invMassA, mB = m_invMassB;
+	float iA = m_invIA, iB = m_invIB;
+
+	m_K.ex.x = mA + mB + m_rA.y * m_rA.y * iA + m_rB.y * m_rB.y * iB;
+	m_K.ey.x = -m_rA.y * m_rA.x * iA - m_rB.y * m_rB.x * iB;
+	m_K.ex.y = m_K.ey.x;
+	m_K.ey.y = mA + mB + m_rA.x * m_rA.x * iA + m_rB.x * m_rB.x * iB;
+
+	m_axialMass = iA + iB;
+	bool fixedRotation;
+	if (m_axialMass > 0.0f)
+	{
+		m_axialMass = 1.0f / m_axialMass;
+		fixedRotation = false;
+	}
+	else
+	{
+		fixedRotation = true;
+	}
+
+	m_angle = aB - aA - m_referenceAngle;
+	if (m_enableLimit == false || fixedRotation)
+	{
+		m_lowerImpulse = 0.0f;
+		m_upperImpulse = 0.0f;
+	}
+
+	if (m_enableMotor == false || fixedRotation)
+	{
+		m_motorImpulse = 0.0f;
+	}
+
+	if (data.step.warmStarting)
+	{
+		// Scale impulses to support a variable time step.
+		m_impulse *= data.step.dtRatio;
+		m_motorImpulse *= data.step.dtRatio;
+		m_lowerImpulse *= data.step.dtRatio;
+		m_upperImpulse *= data.step.dtRatio;
+
+		float axialImpulse = m_motorImpulse + m_lowerImpulse - m_upperImpulse;
+		b2Vec2 P(m_impulse.x, m_impulse.y);
+
+		vA -= mA * P;
+		wA -= iA * (b2Cross(m_rA, P) + axialImpulse);
+
+		vB += mB * P;
+		wB += iB * (b2Cross(m_rB, P) + axialImpulse);
+	}
+	else
+	{
+		m_impulse.SetZero();
+		m_motorImpulse = 0.0f;
+		m_lowerImpulse = 0.0f;
+		m_upperImpulse = 0.0f;
+	}
+
+	data.velocities[m_indexA].v = vA;
+	data.velocities[m_indexA].w = wA;
+	data.velocities[m_indexB].v = vB;
+	data.velocities[m_indexB].w = wB;
+}
+
+void b2RevoluteJoint::SolveVelocityConstraints(const b2SolverData& data)
+{
+	b2Vec2 vA = data.velocities[m_indexA].v;
+	float wA = data.velocities[m_indexA].w;
+	b2Vec2 vB = data.velocities[m_indexB].v;
+	float wB = data.velocities[m_indexB].w;
+
+	float mA = m_invMassA, mB = m_invMassB;
+	float iA = m_invIA, iB = m_invIB;
+
+	bool fixedRotation = (iA + iB == 0.0f);
+
+	// Solve motor constraint.
+	if (m_enableMotor && fixedRotation == false)
+	{
+		float Cdot = wB - wA - m_motorSpeed;
+		float impulse = -m_axialMass * Cdot;
+		float oldImpulse = m_motorImpulse;
+		float maxImpulse = data.step.dt * m_maxMotorTorque;
+		m_motorImpulse = b2Clamp(m_motorImpulse + impulse, -maxImpulse, maxImpulse);
+		impulse = m_motorImpulse - oldImpulse;
+
+		wA -= iA * impulse;
+		wB += iB * impulse;
+	}
+
+	if (m_enableLimit && fixedRotation == false)
+	{
+		// Lower limit
+		{
+			float C = m_angle - m_lowerAngle;
+			float Cdot = wB - wA;
+			float impulse = -m_axialMass * (Cdot + b2Max(C, 0.0f) * data.step.inv_dt);
+			float oldImpulse = m_lowerImpulse;
+			m_lowerImpulse = b2Max(m_lowerImpulse + impulse, 0.0f);
+			impulse = m_lowerImpulse - oldImpulse;
+
+			wA -= iA * impulse;
+			wB += iB * impulse;
+		}
+
+		// Upper limit
+		// Note: signs are flipped to keep C positive when the constraint is satisfied.
+		// This also keeps the impulse positive when the limit is active.
+		{
+			float C = m_upperAngle - m_angle;
+			float Cdot = wA - wB;
+			float impulse = -m_axialMass * (Cdot + b2Max(C, 0.0f) * data.step.inv_dt);
+			float oldImpulse = m_upperImpulse;
+			m_upperImpulse = b2Max(m_upperImpulse + impulse, 0.0f);
+			impulse = m_upperImpulse - oldImpulse;
+
+			wA += iA * impulse;
+			wB -= iB * impulse;
+		}
+	}
+
+	// Solve point-to-point constraint
+	{
+		b2Vec2 Cdot = vB + b2Cross(wB, m_rB) - vA - b2Cross(wA, m_rA);
+		b2Vec2 impulse = m_K.Solve(-Cdot);
+
+		m_impulse.x += impulse.x;
+		m_impulse.y += impulse.y;
+
+		vA -= mA * impulse;
+		wA -= iA * b2Cross(m_rA, impulse);
+
+		vB += mB * impulse;
+		wB += iB * b2Cross(m_rB, impulse);
+	}
+
+	data.velocities[m_indexA].v = vA;
+	data.velocities[m_indexA].w = wA;
+	data.velocities[m_indexB].v = vB;
+	data.velocities[m_indexB].w = wB;
+}
+
+bool b2RevoluteJoint::SolvePositionConstraints(const b2SolverData& data)
+{
+	b2Vec2 cA = data.positions[m_indexA].c;
+	float aA = data.positions[m_indexA].a;
+	b2Vec2 cB = data.positions[m_indexB].c;
+	float aB = data.positions[m_indexB].a;
+
+	b2Rot qA(aA), qB(aB);
+
+	float angularError = 0.0f;
+	float positionError = 0.0f;
+
+	bool fixedRotation = (m_invIA + m_invIB == 0.0f);
+
+	// Solve angular limit constraint
+	if (m_enableLimit && fixedRotation == false)
+	{
+		float angle = aB - aA - m_referenceAngle;
+		float C = 0.0f;
+
+		if (b2Abs(m_upperAngle - m_lowerAngle) < 2.0f * b2_angularSlop)
+		{
+			// Prevent large angular corrections
+			C = b2Clamp(angle - m_lowerAngle, -b2_maxAngularCorrection, b2_maxAngularCorrection);
+		}
+		else if (angle <= m_lowerAngle)
+		{
+			// Prevent large angular corrections and allow some slop.
+			C = b2Clamp(angle - m_lowerAngle + b2_angularSlop, -b2_maxAngularCorrection, 0.0f);
+		}
+		else if (angle >= m_upperAngle)
+		{
+			// Prevent large angular corrections and allow some slop.
+			C = b2Clamp(angle - m_upperAngle - b2_angularSlop, 0.0f, b2_maxAngularCorrection);
+		}
+
+		float limitImpulse = -m_axialMass * C;
+		aA -= m_invIA * limitImpulse;
+		aB += m_invIB * limitImpulse;
+		angularError = b2Abs(C);
+	}
+
+	// Solve point-to-point constraint.
+	{
+		qA.Set(aA);
+		qB.Set(aB);
+		b2Vec2 rA = b2Mul(qA, m_localAnchorA - m_localCenterA);
+		b2Vec2 rB = b2Mul(qB, m_localAnchorB - m_localCenterB);
+
+		b2Vec2 C = cB + rB - cA - rA;
+		positionError = C.Length();
+
+		float mA = m_invMassA, mB = m_invMassB;
+		float iA = m_invIA, iB = m_invIB;
+
+		b2Mat22 K;
+		K.ex.x = mA + mB + iA * rA.y * rA.y + iB * rB.y * rB.y;
+		K.ex.y = -iA * rA.x * rA.y - iB * rB.x * rB.y;
+		K.ey.x = K.ex.y;
+		K.ey.y = mA + mB + iA * rA.x * rA.x + iB * rB.x * rB.x;
+
+		b2Vec2 impulse = -K.Solve(C);
+
+		cA -= mA * impulse;
+		aA -= iA * b2Cross(rA, impulse);
+
+		cB += mB * impulse;
+		aB += iB * b2Cross(rB, impulse);
+	}
+
+	data.positions[m_indexA].c = cA;
+	data.positions[m_indexA].a = aA;
+	data.positions[m_indexB].c = cB;
+	data.positions[m_indexB].a = aB;
+
+	return positionError <= b2_linearSlop && angularError <= b2_angularSlop;
+}
+
+b2Vec2 b2RevoluteJoint::GetAnchorA() const
+{
+	return m_bodyA->GetWorldPoint(m_localAnchorA);
+}
+
+b2Vec2 b2RevoluteJoint::GetAnchorB() const
+{
+	return m_bodyB->GetWorldPoint(m_localAnchorB);
+}
+
+b2Vec2 b2RevoluteJoint::GetReactionForce(float inv_dt) const
+{
+	b2Vec2 P(m_impulse.x, m_impulse.y);
+	return inv_dt * P;
+}
+
+float b2RevoluteJoint::GetReactionTorque(float inv_dt) const
+{
+	return inv_dt * (m_motorImpulse + m_lowerImpulse - m_upperImpulse);
+}
+
+float b2RevoluteJoint::GetJointAngle() const
+{
+	b2Body* bA = m_bodyA;
+	b2Body* bB = m_bodyB;
+	return bB->m_sweep.a - bA->m_sweep.a - m_referenceAngle;
+}
+
+float b2RevoluteJoint::GetJointSpeed() const
+{
+	b2Body* bA = m_bodyA;
+	b2Body* bB = m_bodyB;
+	return bB->m_angularVelocity - bA->m_angularVelocity;
+}
+
+bool b2RevoluteJoint::IsMotorEnabled() const
+{
+	return m_enableMotor;
+}
+
+void b2RevoluteJoint::EnableMotor(bool flag)
+{
+	if (flag != m_enableMotor)
+	{
+		m_bodyA->SetAwake(true);
+		m_bodyB->SetAwake(true);
+		m_enableMotor = flag;
+	}
+}
+
+float b2RevoluteJoint::GetMotorTorque(float inv_dt) const
+{
+	return inv_dt * m_motorImpulse;
+}
+
+void b2RevoluteJoint::SetMotorSpeed(float speed)
+{
+	if (speed != m_motorSpeed)
+	{
+		m_bodyA->SetAwake(true);
+		m_bodyB->SetAwake(true);
+		m_motorSpeed = speed;
+	}
+}
+
+void b2RevoluteJoint::SetMaxMotorTorque(float torque)
+{
+	if (torque != m_maxMotorTorque)
+	{
+		m_bodyA->SetAwake(true);
+		m_bodyB->SetAwake(true);
+		m_maxMotorTorque = torque;
+	}
+}
+
+bool b2RevoluteJoint::IsLimitEnabled() const
+{
+	return m_enableLimit;
+}
+
+void b2RevoluteJoint::EnableLimit(bool flag)
+{
+	if (flag != m_enableLimit)
+	{
+		m_bodyA->SetAwake(true);
+		m_bodyB->SetAwake(true);
+		m_enableLimit = flag;
+		m_lowerImpulse = 0.0f;
+		m_upperImpulse = 0.0f;
+	}
+}
+
+float b2RevoluteJoint::GetLowerLimit() const
+{
+	return m_lowerAngle;
+}
+
+float b2RevoluteJoint::GetUpperLimit() const
+{
+	return m_upperAngle;
+}
+
+void b2RevoluteJoint::SetLimits(float lower, float upper)
+{
+	b2Assert(lower <= upper);
+	
+	if (lower != m_lowerAngle || upper != m_upperAngle)
+	{
+		m_bodyA->SetAwake(true);
+		m_bodyB->SetAwake(true);
+		m_lowerImpulse = 0.0f;
+		m_upperImpulse = 0.0f;
+		m_lowerAngle = lower;
+		m_upperAngle = upper;
+	}
+}
+
+void b2RevoluteJoint::Dump()
+{
+	int32 indexA = m_bodyA->m_islandIndex;
+	int32 indexB = m_bodyB->m_islandIndex;
+
+	b2Dump("  b2RevoluteJointDef jd;\n");
+	b2Dump("  jd.bodyA = bodies[%d];\n", indexA);
+	b2Dump("  jd.bodyB = bodies[%d];\n", indexB);
+	b2Dump("  jd.collideConnected = bool(%d);\n", m_collideConnected);
+	b2Dump("  jd.localAnchorA.Set(%.9g, %.9g);\n", m_localAnchorA.x, m_localAnchorA.y);
+	b2Dump("  jd.localAnchorB.Set(%.9g, %.9g);\n", m_localAnchorB.x, m_localAnchorB.y);
+	b2Dump("  jd.referenceAngle = %.9g;\n", m_referenceAngle);
+	b2Dump("  jd.enableLimit = bool(%d);\n", m_enableLimit);
+	b2Dump("  jd.lowerAngle = %.9g;\n", m_lowerAngle);
+	b2Dump("  jd.upperAngle = %.9g;\n", m_upperAngle);
+	b2Dump("  jd.enableMotor = bool(%d);\n", m_enableMotor);
+	b2Dump("  jd.motorSpeed = %.9g;\n", m_motorSpeed);
+	b2Dump("  jd.maxMotorTorque = %.9g;\n", m_maxMotorTorque);
+	b2Dump("  joints[%d] = m_world->CreateJoint(&jd);\n", m_index);
+}
+
+///
+void b2RevoluteJoint::Draw(b2Draw* draw) const
+{
+	const b2Transform& xfA = m_bodyA->GetTransform();
+	const b2Transform& xfB = m_bodyB->GetTransform();
+	b2Vec2 pA = b2Mul(xfA, m_localAnchorA);
+	b2Vec2 pB = b2Mul(xfB, m_localAnchorB);
+
+	b2Color c1(0.7f, 0.7f, 0.7f);
+	b2Color c2(0.3f, 0.9f, 0.3f);
+	b2Color c3(0.9f, 0.3f, 0.3f);
+	b2Color c4(0.3f, 0.3f, 0.9f);
+	b2Color c5(0.4f, 0.4f, 0.4f);
+
+	draw->DrawPoint(pA, 5.0f, c4);
+	draw->DrawPoint(pB, 5.0f, c5);
+
+	float aA = m_bodyA->GetAngle();
+	float aB = m_bodyB->GetAngle();
+	float angle = aB - aA - m_referenceAngle;
+
+	const float L = 0.5f;
+
+	b2Vec2 r = L * b2Vec2(cosf(angle), sinf(angle));
+	draw->DrawSegment(pB, pB + r, c1);
+	draw->DrawCircle(pB, L, c1);
+
+	if (m_enableLimit)
+	{
+		b2Vec2 rlo = L * b2Vec2(cosf(m_lowerAngle), sinf(m_lowerAngle));
+		b2Vec2 rhi = L * b2Vec2(cosf(m_upperAngle), sinf(m_upperAngle));
+
+		draw->DrawSegment(pB, pB + rlo, c2);
+		draw->DrawSegment(pB, pB + rhi, c3);
+	}
+
+	b2Color color(0.5f, 0.8f, 0.8f);
+	draw->DrawSegment(xfA.p, pA, color);
+	draw->DrawSegment(pA, pB, color);
+	draw->DrawSegment(xfB.p, pB, color);
+}

3rd/box2d/src/dynamics/b2_weld_joint.cpp

@@ -0,0 +1,344 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#include "box2d/b2_body.h"
+#include "box2d/b2_time_step.h"
+#include "box2d/b2_weld_joint.h"
+
+// Point-to-point constraint
+// C = p2 - p1
+// Cdot = v2 - v1
+//      = v2 + cross(w2, r2) - v1 - cross(w1, r1)
+// J = [-I -r1_skew I r2_skew ]
+// Identity used:
+// w k % (rx i + ry j) = w * (-ry i + rx j)
+
+// Angle constraint
+// C = angle2 - angle1 - referenceAngle
+// Cdot = w2 - w1
+// J = [0 0 -1 0 0 1]
+// K = invI1 + invI2
+
+void b2WeldJointDef::Initialize(b2Body* bA, b2Body* bB, const b2Vec2& anchor)
+{
+	bodyA = bA;
+	bodyB = bB;
+	localAnchorA = bodyA->GetLocalPoint(anchor);
+	localAnchorB = bodyB->GetLocalPoint(anchor);
+	referenceAngle = bodyB->GetAngle() - bodyA->GetAngle();
+}
+
+b2WeldJoint::b2WeldJoint(const b2WeldJointDef* def)
+: b2Joint(def)
+{
+	m_localAnchorA = def->localAnchorA;
+	m_localAnchorB = def->localAnchorB;
+	m_referenceAngle = def->referenceAngle;
+	m_stiffness = def->stiffness;
+	m_damping = def->damping;
+
+	m_impulse.SetZero();
+}
+
+void b2WeldJoint::InitVelocityConstraints(const b2SolverData& data)
+{
+	m_indexA = m_bodyA->m_islandIndex;
+	m_indexB = m_bodyB->m_islandIndex;
+	m_localCenterA = m_bodyA->m_sweep.localCenter;
+	m_localCenterB = m_bodyB->m_sweep.localCenter;
+	m_invMassA = m_bodyA->m_invMass;
+	m_invMassB = m_bodyB->m_invMass;
+	m_invIA = m_bodyA->m_invI;
+	m_invIB = m_bodyB->m_invI;
+
+	float aA = data.positions[m_indexA].a;
+	b2Vec2 vA = data.velocities[m_indexA].v;
+	float wA = data.velocities[m_indexA].w;
+
+	float aB = data.positions[m_indexB].a;
+	b2Vec2 vB = data.velocities[m_indexB].v;
+	float wB = data.velocities[m_indexB].w;
+
+	b2Rot qA(aA), qB(aB);
+
+	m_rA = b2Mul(qA, m_localAnchorA - m_localCenterA);
+	m_rB = b2Mul(qB, m_localAnchorB - m_localCenterB);
+
+	// J = [-I -r1_skew I r2_skew]
+	//     [ 0       -1 0       1]
+	// r_skew = [-ry; rx]
+
+	// Matlab
+	// K = [ mA+r1y^2*iA+mB+r2y^2*iB,  -r1y*iA*r1x-r2y*iB*r2x,          -r1y*iA-r2y*iB]
+	//     [  -r1y*iA*r1x-r2y*iB*r2x, mA+r1x^2*iA+mB+r2x^2*iB,           r1x*iA+r2x*iB]
+	//     [          -r1y*iA-r2y*iB,           r1x*iA+r2x*iB,                   iA+iB]
+
+	float mA = m_invMassA, mB = m_invMassB;
+	float iA = m_invIA, iB = m_invIB;
+
+	b2Mat33 K;
+	K.ex.x = mA + mB + m_rA.y * m_rA.y * iA + m_rB.y * m_rB.y * iB;
+	K.ey.x = -m_rA.y * m_rA.x * iA - m_rB.y * m_rB.x * iB;
+	K.ez.x = -m_rA.y * iA - m_rB.y * iB;
+	K.ex.y = K.ey.x;
+	K.ey.y = mA + mB + m_rA.x * m_rA.x * iA + m_rB.x * m_rB.x * iB;
+	K.ez.y = m_rA.x * iA + m_rB.x * iB;
+	K.ex.z = K.ez.x;
+	K.ey.z = K.ez.y;
+	K.ez.z = iA + iB;
+
+	if (m_stiffness > 0.0f)
+	{
+		K.GetInverse22(&m_mass);
+
+		float invM = iA + iB;
+
+		float C = aB - aA - m_referenceAngle;
+
+		// Damping coefficient
+		float d = m_damping;
+
+		// Spring stiffness
+		float k = m_stiffness;
+
+		// magic formulas
+		float h = data.step.dt;
+		m_gamma = h * (d + h * k);
+		m_gamma = m_gamma != 0.0f ? 1.0f / m_gamma : 0.0f;
+		m_bias = C * h * k * m_gamma;
+
+		invM += m_gamma;
+		m_mass.ez.z = invM != 0.0f ? 1.0f / invM : 0.0f;
+	}
+	else if (K.ez.z == 0.0f)
+	{
+		K.GetInverse22(&m_mass);
+		m_gamma = 0.0f;
+		m_bias = 0.0f;
+	}
+	else
+	{
+		K.GetSymInverse33(&m_mass);
+		m_gamma = 0.0f;
+		m_bias = 0.0f;
+	}
+
+	if (data.step.warmStarting)
+	{
+		// Scale impulses to support a variable time step.
+		m_impulse *= data.step.dtRatio;
+
+		b2Vec2 P(m_impulse.x, m_impulse.y);
+
+		vA -= mA * P;
+		wA -= iA * (b2Cross(m_rA, P) + m_impulse.z);
+
+		vB += mB * P;
+		wB += iB * (b2Cross(m_rB, P) + m_impulse.z);
+	}
+	else
+	{
+		m_impulse.SetZero();
+	}
+
+	data.velocities[m_indexA].v = vA;
+	data.velocities[m_indexA].w = wA;
+	data.velocities[m_indexB].v = vB;
+	data.velocities[m_indexB].w = wB;
+}
+
+void b2WeldJoint::SolveVelocityConstraints(const b2SolverData& data)
+{
+	b2Vec2 vA = data.velocities[m_indexA].v;
+	float wA = data.velocities[m_indexA].w;
+	b2Vec2 vB = data.velocities[m_indexB].v;
+	float wB = data.velocities[m_indexB].w;
+
+	float mA = m_invMassA, mB = m_invMassB;
+	float iA = m_invIA, iB = m_invIB;
+
+	if (m_stiffness > 0.0f)
+	{
+		float Cdot2 = wB - wA;
+
+		float impulse2 = -m_mass.ez.z * (Cdot2 + m_bias + m_gamma * m_impulse.z);
+		m_impulse.z += impulse2;
+
+		wA -= iA * impulse2;
+		wB += iB * impulse2;
+
+		b2Vec2 Cdot1 = vB + b2Cross(wB, m_rB) - vA - b2Cross(wA, m_rA);
+
+		b2Vec2 impulse1 = -b2Mul22(m_mass, Cdot1);
+		m_impulse.x += impulse1.x;
+		m_impulse.y += impulse1.y;
+
+		b2Vec2 P = impulse1;
+
+		vA -= mA * P;
+		wA -= iA * b2Cross(m_rA, P);
+
+		vB += mB * P;
+		wB += iB * b2Cross(m_rB, P);
+	}
+	else
+	{
+		b2Vec2 Cdot1 = vB + b2Cross(wB, m_rB) - vA - b2Cross(wA, m_rA);
+		float Cdot2 = wB - wA;
+		b2Vec3 Cdot(Cdot1.x, Cdot1.y, Cdot2);
+
+		b2Vec3 impulse = -b2Mul(m_mass, Cdot);
+		m_impulse += impulse;
+
+		b2Vec2 P(impulse.x, impulse.y);
+
+		vA -= mA * P;
+		wA -= iA * (b2Cross(m_rA, P) + impulse.z);
+
+		vB += mB * P;
+		wB += iB * (b2Cross(m_rB, P) + impulse.z);
+	}
+
+	data.velocities[m_indexA].v = vA;
+	data.velocities[m_indexA].w = wA;
+	data.velocities[m_indexB].v = vB;
+	data.velocities[m_indexB].w = wB;
+}
+
+bool b2WeldJoint::SolvePositionConstraints(const b2SolverData& data)
+{
+	b2Vec2 cA = data.positions[m_indexA].c;
+	float aA = data.positions[m_indexA].a;
+	b2Vec2 cB = data.positions[m_indexB].c;
+	float aB = data.positions[m_indexB].a;
+
+	b2Rot qA(aA), qB(aB);
+
+	float mA = m_invMassA, mB = m_invMassB;
+	float iA = m_invIA, iB = m_invIB;
+
+	b2Vec2 rA = b2Mul(qA, m_localAnchorA - m_localCenterA);
+	b2Vec2 rB = b2Mul(qB, m_localAnchorB - m_localCenterB);
+
+	float positionError, angularError;
+
+	b2Mat33 K;
+	K.ex.x = mA + mB + rA.y * rA.y * iA + rB.y * rB.y * iB;
+	K.ey.x = -rA.y * rA.x * iA - rB.y * rB.x * iB;
+	K.ez.x = -rA.y * iA - rB.y * iB;
+	K.ex.y = K.ey.x;
+	K.ey.y = mA + mB + rA.x * rA.x * iA + rB.x * rB.x * iB;
+	K.ez.y = rA.x * iA + rB.x * iB;
+	K.ex.z = K.ez.x;
+	K.ey.z = K.ez.y;
+	K.ez.z = iA + iB;
+
+	if (m_stiffness > 0.0f)
+	{
+		b2Vec2 C1 =  cB + rB - cA - rA;
+
+		positionError = C1.Length();
+		angularError = 0.0f;
+
+		b2Vec2 P = -K.Solve22(C1);
+
+		cA -= mA * P;
+		aA -= iA * b2Cross(rA, P);
+
+		cB += mB * P;
+		aB += iB * b2Cross(rB, P);
+	}
+	else
+	{
+		b2Vec2 C1 =  cB + rB - cA - rA;
+		float C2 = aB - aA - m_referenceAngle;
+
+		positionError = C1.Length();
+		angularError = b2Abs(C2);
+
+		b2Vec3 C(C1.x, C1.y, C2);
+	
+		b2Vec3 impulse;
+		if (K.ez.z > 0.0f)
+		{
+			impulse = -K.Solve33(C);
+		}
+		else
+		{
+			b2Vec2 impulse2 = -K.Solve22(C1);
+			impulse.Set(impulse2.x, impulse2.y, 0.0f);
+		}
+
+		b2Vec2 P(impulse.x, impulse.y);
+
+		cA -= mA * P;
+		aA -= iA * (b2Cross(rA, P) + impulse.z);
+
+		cB += mB * P;
+		aB += iB * (b2Cross(rB, P) + impulse.z);
+	}
+
+	data.positions[m_indexA].c = cA;
+	data.positions[m_indexA].a = aA;
+	data.positions[m_indexB].c = cB;
+	data.positions[m_indexB].a = aB;
+
+	return positionError <= b2_linearSlop && angularError <= b2_angularSlop;
+}
+
+b2Vec2 b2WeldJoint::GetAnchorA() const
+{
+	return m_bodyA->GetWorldPoint(m_localAnchorA);
+}
+
+b2Vec2 b2WeldJoint::GetAnchorB() const
+{
+	return m_bodyB->GetWorldPoint(m_localAnchorB);
+}
+
+b2Vec2 b2WeldJoint::GetReactionForce(float inv_dt) const
+{
+	b2Vec2 P(m_impulse.x, m_impulse.y);
+	return inv_dt * P;
+}
+
+float b2WeldJoint::GetReactionTorque(float inv_dt) const
+{
+	return inv_dt * m_impulse.z;
+}
+
+void b2WeldJoint::Dump()
+{
+	int32 indexA = m_bodyA->m_islandIndex;
+	int32 indexB = m_bodyB->m_islandIndex;
+
+	b2Dump("  b2WeldJointDef jd;\n");
+	b2Dump("  jd.bodyA = bodies[%d];\n", indexA);
+	b2Dump("  jd.bodyB = bodies[%d];\n", indexB);
+	b2Dump("  jd.collideConnected = bool(%d);\n", m_collideConnected);
+	b2Dump("  jd.localAnchorA.Set(%.9g, %.9g);\n", m_localAnchorA.x, m_localAnchorA.y);
+	b2Dump("  jd.localAnchorB.Set(%.9g, %.9g);\n", m_localAnchorB.x, m_localAnchorB.y);
+	b2Dump("  jd.referenceAngle = %.9g;\n", m_referenceAngle);
+	b2Dump("  jd.stiffness = %.9g;\n", m_stiffness);
+	b2Dump("  jd.damping = %.9g;\n", m_damping);
+	b2Dump("  joints[%d] = m_world->CreateJoint(&jd);\n", m_index);
+}

3rd/box2d/src/dynamics/b2_wheel_joint.cpp

@@ -0,0 +1,672 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#include "box2d/b2_body.h"
+#include "box2d/b2_draw.h"
+#include "box2d/b2_wheel_joint.h"
+#include "box2d/b2_time_step.h"
+
+// Linear constraint (point-to-line)
+// d = pB - pA = xB + rB - xA - rA
+// C = dot(ay, d)
+// Cdot = dot(d, cross(wA, ay)) + dot(ay, vB + cross(wB, rB) - vA - cross(wA, rA))
+//      = -dot(ay, vA) - dot(cross(d + rA, ay), wA) + dot(ay, vB) + dot(cross(rB, ay), vB)
+// J = [-ay, -cross(d + rA, ay), ay, cross(rB, ay)]
+
+// Spring linear constraint
+// C = dot(ax, d)
+// Cdot = = -dot(ax, vA) - dot(cross(d + rA, ax), wA) + dot(ax, vB) + dot(cross(rB, ax), vB)
+// J = [-ax -cross(d+rA, ax) ax cross(rB, ax)]
+
+// Motor rotational constraint
+// Cdot = wB - wA
+// J = [0 0 -1 0 0 1]
+
+void b2WheelJointDef::Initialize(b2Body* bA, b2Body* bB, const b2Vec2& anchor, const b2Vec2& axis)
+{
+	bodyA = bA;
+	bodyB = bB;
+	localAnchorA = bodyA->GetLocalPoint(anchor);
+	localAnchorB = bodyB->GetLocalPoint(anchor);
+	localAxisA = bodyA->GetLocalVector(axis);
+}
+
+b2WheelJoint::b2WheelJoint(const b2WheelJointDef* def)
+: b2Joint(def)
+{
+	m_localAnchorA = def->localAnchorA;
+	m_localAnchorB = def->localAnchorB;
+	m_localXAxisA = def->localAxisA;
+	m_localYAxisA = b2Cross(1.0f, m_localXAxisA);
+
+	m_mass = 0.0f;
+	m_impulse = 0.0f;
+	m_motorMass = 0.0f;
+	m_motorImpulse = 0.0f;
+	m_springMass = 0.0f;
+	m_springImpulse = 0.0f;
+
+	m_axialMass = 0.0f;
+	m_lowerImpulse = 0.0f;
+	m_upperImpulse = 0.0f;
+	m_lowerTranslation = def->lowerTranslation;
+	m_upperTranslation = def->upperTranslation;
+	m_enableLimit = def->enableLimit;
+
+	m_maxMotorTorque = def->maxMotorTorque;
+	m_motorSpeed = def->motorSpeed;
+	m_enableMotor = def->enableMotor;
+
+	m_bias = 0.0f;
+	m_gamma = 0.0f;
+
+	m_ax.SetZero();
+	m_ay.SetZero();
+
+	m_stiffness = def->stiffness;
+	m_damping = def->damping;
+}
+
+void b2WheelJoint::InitVelocityConstraints(const b2SolverData& data)
+{
+	m_indexA = m_bodyA->m_islandIndex;
+	m_indexB = m_bodyB->m_islandIndex;
+	m_localCenterA = m_bodyA->m_sweep.localCenter;
+	m_localCenterB = m_bodyB->m_sweep.localCenter;
+	m_invMassA = m_bodyA->m_invMass;
+	m_invMassB = m_bodyB->m_invMass;
+	m_invIA = m_bodyA->m_invI;
+	m_invIB = m_bodyB->m_invI;
+
+	float mA = m_invMassA, mB = m_invMassB;
+	float iA = m_invIA, iB = m_invIB;
+
+	b2Vec2 cA = data.positions[m_indexA].c;
+	float aA = data.positions[m_indexA].a;
+	b2Vec2 vA = data.velocities[m_indexA].v;
+	float wA = data.velocities[m_indexA].w;
+
+	b2Vec2 cB = data.positions[m_indexB].c;
+	float aB = data.positions[m_indexB].a;
+	b2Vec2 vB = data.velocities[m_indexB].v;
+	float wB = data.velocities[m_indexB].w;
+
+	b2Rot qA(aA), qB(aB);
+
+	// Compute the effective masses.
+	b2Vec2 rA = b2Mul(qA, m_localAnchorA - m_localCenterA);
+	b2Vec2 rB = b2Mul(qB, m_localAnchorB - m_localCenterB);
+	b2Vec2 d = cB + rB - cA - rA;
+
+	// Point to line constraint
+	{
+		m_ay = b2Mul(qA, m_localYAxisA);
+		m_sAy = b2Cross(d + rA, m_ay);
+		m_sBy = b2Cross(rB, m_ay);
+
+		m_mass = mA + mB + iA * m_sAy * m_sAy + iB * m_sBy * m_sBy;
+
+		if (m_mass > 0.0f)
+		{
+			m_mass = 1.0f / m_mass;
+		}
+	}
+
+	// Spring constraint
+	m_ax = b2Mul(qA, m_localXAxisA);
+	m_sAx = b2Cross(d + rA, m_ax);
+	m_sBx = b2Cross(rB, m_ax);
+
+	const float invMass = mA + mB + iA * m_sAx * m_sAx + iB * m_sBx * m_sBx;
+	if (invMass > 0.0f)
+	{
+		m_axialMass = 1.0f / invMass;
+	}
+	else
+	{
+		m_axialMass = 0.0f;
+	}
+
+	m_springMass = 0.0f;
+	m_bias = 0.0f;
+	m_gamma = 0.0f;
+
+	if (m_stiffness > 0.0f && invMass > 0.0f)
+	{
+		m_springMass = 1.0f / invMass;
+
+		float C = b2Dot(d, m_ax);
+
+		// magic formulas
+		float h = data.step.dt;
+		m_gamma = h * (m_damping + h * m_stiffness);
+		if (m_gamma > 0.0f)
+		{
+			m_gamma = 1.0f / m_gamma;
+		}
+
+		m_bias = C * h * m_stiffness * m_gamma;
+
+		m_springMass = invMass + m_gamma;
+		if (m_springMass > 0.0f)
+		{
+			m_springMass = 1.0f / m_springMass;
+		}
+	}
+	else
+	{
+		m_springImpulse = 0.0f;
+	}
+
+	if (m_enableLimit)
+	{
+		m_translation = b2Dot(m_ax, d);
+	}
+	else
+	{
+		m_lowerImpulse = 0.0f;
+		m_upperImpulse = 0.0f;
+	}
+
+	if (m_enableMotor)
+	{
+		m_motorMass = iA + iB;
+		if (m_motorMass > 0.0f)
+		{
+			m_motorMass = 1.0f / m_motorMass;
+		}
+	}
+	else
+	{
+		m_motorMass = 0.0f;
+		m_motorImpulse = 0.0f;
+	}
+
+	if (data.step.warmStarting)
+	{
+		// Account for variable time step.
+		m_impulse *= data.step.dtRatio;
+		m_springImpulse *= data.step.dtRatio;
+		m_motorImpulse *= data.step.dtRatio;
+
+		float axialImpulse = m_springImpulse + m_lowerImpulse - m_upperImpulse;
+		b2Vec2 P = m_impulse * m_ay + axialImpulse * m_ax;
+		float LA = m_impulse * m_sAy + axialImpulse * m_sAx + m_motorImpulse;
+		float LB = m_impulse * m_sBy + axialImpulse * m_sBx + m_motorImpulse;
+
+		vA -= m_invMassA * P;
+		wA -= m_invIA * LA;
+
+		vB += m_invMassB * P;
+		wB += m_invIB * LB;
+	}
+	else
+	{
+		m_impulse = 0.0f;
+		m_springImpulse = 0.0f;
+		m_motorImpulse = 0.0f;
+		m_lowerImpulse = 0.0f;
+		m_upperImpulse = 0.0f;
+	}
+
+	data.velocities[m_indexA].v = vA;
+	data.velocities[m_indexA].w = wA;
+	data.velocities[m_indexB].v = vB;
+	data.velocities[m_indexB].w = wB;
+}
+
+void b2WheelJoint::SolveVelocityConstraints(const b2SolverData& data)
+{
+	float mA = m_invMassA, mB = m_invMassB;
+	float iA = m_invIA, iB = m_invIB;
+
+	b2Vec2 vA = data.velocities[m_indexA].v;
+	float wA = data.velocities[m_indexA].w;
+	b2Vec2 vB = data.velocities[m_indexB].v;
+	float wB = data.velocities[m_indexB].w;
+
+	// Solve spring constraint
+	{
+		float Cdot = b2Dot(m_ax, vB - vA) + m_sBx * wB - m_sAx * wA;
+		float impulse = -m_springMass * (Cdot + m_bias + m_gamma * m_springImpulse);
+		m_springImpulse += impulse;
+
+		b2Vec2 P = impulse * m_ax;
+		float LA = impulse * m_sAx;
+		float LB = impulse * m_sBx;
+
+		vA -= mA * P;
+		wA -= iA * LA;
+
+		vB += mB * P;
+		wB += iB * LB;
+	}
+
+	// Solve rotational motor constraint
+	{
+		float Cdot = wB - wA - m_motorSpeed;
+		float impulse = -m_motorMass * Cdot;
+
+		float oldImpulse = m_motorImpulse;
+		float maxImpulse = data.step.dt * m_maxMotorTorque;
+		m_motorImpulse = b2Clamp(m_motorImpulse + impulse, -maxImpulse, maxImpulse);
+		impulse = m_motorImpulse - oldImpulse;
+
+		wA -= iA * impulse;
+		wB += iB * impulse;
+	}
+
+	if (m_enableLimit)
+	{
+		// Lower limit
+		{
+			float C = m_translation - m_lowerTranslation;
+			float Cdot = b2Dot(m_ax, vB - vA) + m_sBx * wB - m_sAx * wA;
+			float impulse = -m_axialMass * (Cdot + b2Max(C, 0.0f) * data.step.inv_dt);
+			float oldImpulse = m_lowerImpulse;
+			m_lowerImpulse = b2Max(m_lowerImpulse + impulse, 0.0f);
+			impulse = m_lowerImpulse - oldImpulse;
+
+			b2Vec2 P = impulse * m_ax;
+			float LA = impulse * m_sAx;
+			float LB = impulse * m_sBx;
+
+			vA -= mA * P;
+			wA -= iA * LA;
+			vB += mB * P;
+			wB += iB * LB;
+		}
+
+		// Upper limit
+		// Note: signs are flipped to keep C positive when the constraint is satisfied.
+		// This also keeps the impulse positive when the limit is active.
+		{
+			float C = m_upperTranslation - m_translation;
+			float Cdot = b2Dot(m_ax, vA - vB) + m_sAx * wA - m_sBx * wB;
+			float impulse = -m_axialMass * (Cdot + b2Max(C, 0.0f) * data.step.inv_dt);
+			float oldImpulse = m_upperImpulse;
+			m_upperImpulse = b2Max(m_upperImpulse + impulse, 0.0f);
+			impulse = m_upperImpulse - oldImpulse;
+
+			b2Vec2 P = impulse * m_ax;
+			float LA = impulse * m_sAx;
+			float LB = impulse * m_sBx;
+
+			vA += mA * P;
+			wA += iA * LA;
+			vB -= mB * P;
+			wB -= iB * LB;
+		}
+	}
+
+	// Solve point to line constraint
+	{
+		float Cdot = b2Dot(m_ay, vB - vA) + m_sBy * wB - m_sAy * wA;
+		float impulse = -m_mass * Cdot;
+		m_impulse += impulse;
+
+		b2Vec2 P = impulse * m_ay;
+		float LA = impulse * m_sAy;
+		float LB = impulse * m_sBy;
+
+		vA -= mA * P;
+		wA -= iA * LA;
+
+		vB += mB * P;
+		wB += iB * LB;
+	}
+
+	data.velocities[m_indexA].v = vA;
+	data.velocities[m_indexA].w = wA;
+	data.velocities[m_indexB].v = vB;
+	data.velocities[m_indexB].w = wB;
+}
+
+bool b2WheelJoint::SolvePositionConstraints(const b2SolverData& data)
+{
+	b2Vec2 cA = data.positions[m_indexA].c;
+	float aA = data.positions[m_indexA].a;
+	b2Vec2 cB = data.positions[m_indexB].c;
+	float aB = data.positions[m_indexB].a;
+
+	float linearError = 0.0f;
+
+	if (m_enableLimit)
+	{
+		b2Rot qA(aA), qB(aB);
+
+		b2Vec2 rA = b2Mul(qA, m_localAnchorA - m_localCenterA);
+		b2Vec2 rB = b2Mul(qB, m_localAnchorB - m_localCenterB);
+		b2Vec2 d = (cB - cA) + rB - rA;
+
+		b2Vec2 ax = b2Mul(qA, m_localXAxisA);
+		float sAx = b2Cross(d + rA, m_ax);
+		float sBx = b2Cross(rB, m_ax);
+
+		float C = 0.0f;
+		float translation = b2Dot(ax, d);
+		if (b2Abs(m_upperTranslation - m_lowerTranslation) < 2.0f * b2_linearSlop)
+		{
+			C = translation;
+		}
+		else if (translation <= m_lowerTranslation)
+		{
+			C = b2Min(translation - m_lowerTranslation, 0.0f);
+		}
+		else if (translation >= m_upperTranslation)
+		{
+			C = b2Max(translation - m_upperTranslation, 0.0f);
+		}
+
+		if (C != 0.0f)
+		{
+
+			float invMass = m_invMassA + m_invMassB + m_invIA * sAx * sAx + m_invIB * sBx * sBx;
+			float impulse = 0.0f;
+			if (invMass != 0.0f)
+			{
+				impulse = -C / invMass;
+			}
+
+			b2Vec2 P = impulse * ax;
+			float LA = impulse * sAx;
+			float LB = impulse * sBx;
+
+			cA -= m_invMassA * P;
+			aA -= m_invIA * LA;
+			cB += m_invMassB * P;
+			aB += m_invIB * LB;
+
+			linearError = b2Abs(C);
+		}
+	}
+
+	// Solve perpendicular constraint
+	{
+		b2Rot qA(aA), qB(aB);
+
+		b2Vec2 rA = b2Mul(qA, m_localAnchorA - m_localCenterA);
+		b2Vec2 rB = b2Mul(qB, m_localAnchorB - m_localCenterB);
+		b2Vec2 d = (cB - cA) + rB - rA;
+
+		b2Vec2 ay = b2Mul(qA, m_localYAxisA);
+
+		float sAy = b2Cross(d + rA, ay);
+		float sBy = b2Cross(rB, ay);
+
+		float C = b2Dot(d, ay);
+
+		float invMass = m_invMassA + m_invMassB + m_invIA * m_sAy * m_sAy + m_invIB * m_sBy * m_sBy;
+
+		float impulse = 0.0f;
+		if (invMass != 0.0f)
+		{
+			impulse = - C / invMass;
+		}
+
+		b2Vec2 P = impulse * ay;
+		float LA = impulse * sAy;
+		float LB = impulse * sBy;
+
+		cA -= m_invMassA * P;
+		aA -= m_invIA * LA;
+		cB += m_invMassB * P;
+		aB += m_invIB * LB;
+
+		linearError = b2Max(linearError, b2Abs(C));
+	}
+
+	data.positions[m_indexA].c = cA;
+	data.positions[m_indexA].a = aA;
+	data.positions[m_indexB].c = cB;
+	data.positions[m_indexB].a = aB;
+
+	return linearError <= b2_linearSlop;
+}
+
+b2Vec2 b2WheelJoint::GetAnchorA() const
+{
+	return m_bodyA->GetWorldPoint(m_localAnchorA);
+}
+
+b2Vec2 b2WheelJoint::GetAnchorB() const
+{
+	return m_bodyB->GetWorldPoint(m_localAnchorB);
+}
+
+b2Vec2 b2WheelJoint::GetReactionForce(float inv_dt) const
+{
+	return inv_dt * (m_impulse * m_ay + (m_springImpulse + m_lowerImpulse - m_upperImpulse) * m_ax);
+}
+
+float b2WheelJoint::GetReactionTorque(float inv_dt) const
+{
+	return inv_dt * m_motorImpulse;
+}
+
+float b2WheelJoint::GetJointTranslation() const
+{
+	b2Body* bA = m_bodyA;
+	b2Body* bB = m_bodyB;
+
+	b2Vec2 pA = bA->GetWorldPoint(m_localAnchorA);
+	b2Vec2 pB = bB->GetWorldPoint(m_localAnchorB);
+	b2Vec2 d = pB - pA;
+	b2Vec2 axis = bA->GetWorldVector(m_localXAxisA);
+
+	float translation = b2Dot(d, axis);
+	return translation;
+}
+
+float b2WheelJoint::GetJointLinearSpeed() const
+{
+	b2Body* bA = m_bodyA;
+	b2Body* bB = m_bodyB;
+
+	b2Vec2 rA = b2Mul(bA->m_xf.q, m_localAnchorA - bA->m_sweep.localCenter);
+	b2Vec2 rB = b2Mul(bB->m_xf.q, m_localAnchorB - bB->m_sweep.localCenter);
+	b2Vec2 p1 = bA->m_sweep.c + rA;
+	b2Vec2 p2 = bB->m_sweep.c + rB;
+	b2Vec2 d = p2 - p1;
+	b2Vec2 axis = b2Mul(bA->m_xf.q, m_localXAxisA);
+
+	b2Vec2 vA = bA->m_linearVelocity;
+	b2Vec2 vB = bB->m_linearVelocity;
+	float wA = bA->m_angularVelocity;
+	float wB = bB->m_angularVelocity;
+
+	float speed = b2Dot(d, b2Cross(wA, axis)) + b2Dot(axis, vB + b2Cross(wB, rB) - vA - b2Cross(wA, rA));
+	return speed;
+}
+
+float b2WheelJoint::GetJointAngle() const
+{
+	b2Body* bA = m_bodyA;
+	b2Body* bB = m_bodyB;
+	return bB->m_sweep.a - bA->m_sweep.a;
+}
+
+float b2WheelJoint::GetJointAngularSpeed() const
+{
+	float wA = m_bodyA->m_angularVelocity;
+	float wB = m_bodyB->m_angularVelocity;
+	return wB - wA;
+}
+
+bool b2WheelJoint::IsLimitEnabled() const
+{
+	return m_enableLimit;
+}
+
+void b2WheelJoint::EnableLimit(bool flag)
+{
+	if (flag != m_enableLimit)
+	{
+		m_bodyA->SetAwake(true);
+		m_bodyB->SetAwake(true);
+		m_enableLimit = flag;
+		m_lowerImpulse = 0.0f;
+		m_upperImpulse = 0.0f;
+	}
+}
+
+float b2WheelJoint::GetLowerLimit() const
+{
+	return m_lowerTranslation;
+}
+
+float b2WheelJoint::GetUpperLimit() const
+{
+	return m_upperTranslation;
+}
+
+void b2WheelJoint::SetLimits(float lower, float upper)
+{
+	b2Assert(lower <= upper);
+	if (lower != m_lowerTranslation || upper != m_upperTranslation)
+	{
+		m_bodyA->SetAwake(true);
+		m_bodyB->SetAwake(true);
+		m_lowerTranslation = lower;
+		m_upperTranslation = upper;
+		m_lowerImpulse = 0.0f;
+		m_upperImpulse = 0.0f;
+	}
+}
+
+bool b2WheelJoint::IsMotorEnabled() const
+{
+	return m_enableMotor;
+}
+
+void b2WheelJoint::EnableMotor(bool flag)
+{
+	if (flag != m_enableMotor)
+	{
+		m_bodyA->SetAwake(true);
+		m_bodyB->SetAwake(true);
+		m_enableMotor = flag;
+	}
+}
+
+void b2WheelJoint::SetMotorSpeed(float speed)
+{
+	if (speed != m_motorSpeed)
+	{
+		m_bodyA->SetAwake(true);
+		m_bodyB->SetAwake(true);
+		m_motorSpeed = speed;
+	}
+}
+
+void b2WheelJoint::SetMaxMotorTorque(float torque)
+{
+	if (torque != m_maxMotorTorque)
+	{
+		m_bodyA->SetAwake(true);
+		m_bodyB->SetAwake(true);
+		m_maxMotorTorque = torque;
+	}
+}
+
+float b2WheelJoint::GetMotorTorque(float inv_dt) const
+{
+	return inv_dt * m_motorImpulse;
+}
+
+void b2WheelJoint::SetStiffness(float stiffness)
+{
+	m_stiffness = stiffness;
+}
+
+float b2WheelJoint::GetStiffness() const
+{
+	return m_stiffness;
+}
+
+void b2WheelJoint::SetDamping(float damping)
+{
+	m_damping = damping;
+}
+
+float b2WheelJoint::GetDamping() const
+{
+	return m_damping;
+}
+
+void b2WheelJoint::Dump()
+{
+	// FLT_DECIMAL_DIG == 9
+
+	int32 indexA = m_bodyA->m_islandIndex;
+	int32 indexB = m_bodyB->m_islandIndex;
+
+	b2Dump("  b2WheelJointDef jd;\n");
+	b2Dump("  jd.bodyA = bodies[%d];\n", indexA);
+	b2Dump("  jd.bodyB = bodies[%d];\n", indexB);
+	b2Dump("  jd.collideConnected = bool(%d);\n", m_collideConnected);
+	b2Dump("  jd.localAnchorA.Set(%.9g, %.9g);\n", m_localAnchorA.x, m_localAnchorA.y);
+	b2Dump("  jd.localAnchorB.Set(%.9g, %.9g);\n", m_localAnchorB.x, m_localAnchorB.y);
+	b2Dump("  jd.localAxisA.Set(%.9g, %.9g);\n", m_localXAxisA.x, m_localXAxisA.y);
+	b2Dump("  jd.enableMotor = bool(%d);\n", m_enableMotor);
+	b2Dump("  jd.motorSpeed = %.9g;\n", m_motorSpeed);
+	b2Dump("  jd.maxMotorTorque = %.9g;\n", m_maxMotorTorque);
+	b2Dump("  jd.stiffness = %.9g;\n", m_stiffness);
+	b2Dump("  jd.damping = %.9g;\n", m_damping);
+	b2Dump("  joints[%d] = m_world->CreateJoint(&jd);\n", m_index);
+}
+
+///
+void b2WheelJoint::Draw(b2Draw* draw) const
+{
+	const b2Transform& xfA = m_bodyA->GetTransform();
+	const b2Transform& xfB = m_bodyB->GetTransform();
+	b2Vec2 pA = b2Mul(xfA, m_localAnchorA);
+	b2Vec2 pB = b2Mul(xfB, m_localAnchorB);
+
+	b2Vec2 axis = b2Mul(xfA.q, m_localXAxisA);
+
+	b2Color c1(0.7f, 0.7f, 0.7f);
+	b2Color c2(0.3f, 0.9f, 0.3f);
+	b2Color c3(0.9f, 0.3f, 0.3f);
+	b2Color c4(0.3f, 0.3f, 0.9f);
+	b2Color c5(0.4f, 0.4f, 0.4f);
+
+	draw->DrawSegment(pA, pB, c5);
+
+	if (m_enableLimit)
+	{
+		b2Vec2 lower = pA + m_lowerTranslation * axis;
+		b2Vec2 upper = pA + m_upperTranslation * axis;
+		b2Vec2 perp = b2Mul(xfA.q, m_localYAxisA);
+		draw->DrawSegment(lower, upper, c1);
+		draw->DrawSegment(lower - 0.5f * perp, lower + 0.5f * perp, c2);
+		draw->DrawSegment(upper - 0.5f * perp, upper + 0.5f * perp, c3);
+	}
+	else
+	{
+		draw->DrawSegment(pA - 1.0f * axis, pA + 1.0f * axis, c1);
+	}
+
+	draw->DrawPoint(pA, 5.0f, c1);
+	draw->DrawPoint(pB, 5.0f, c4);
+}

3rd/box2d/src/dynamics/b2_world.cpp

@@ -0,0 +1,1322 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#include "b2_contact_solver.h"
+#include "b2_island.h"
+
+#include "box2d/b2_body.h"
+#include "box2d/b2_broad_phase.h"
+#include "box2d/b2_chain_shape.h"
+#include "box2d/b2_circle_shape.h"
+#include "box2d/b2_collision.h"
+#include "box2d/b2_contact.h"
+#include "box2d/b2_draw.h"
+#include "box2d/b2_edge_shape.h"
+#include "box2d/b2_fixture.h"
+#include "box2d/b2_polygon_shape.h"
+#include "box2d/b2_pulley_joint.h"
+#include "box2d/b2_time_of_impact.h"
+#include "box2d/b2_timer.h"
+#include "box2d/b2_world.h"
+
+#include <new>
+
+b2World::b2World(const b2Vec2& gravity)
+{
+	m_destructionListener = nullptr;
+	m_debugDraw = nullptr;
+
+	m_bodyList = nullptr;
+	m_jointList = nullptr;
+
+	m_bodyCount = 0;
+	m_jointCount = 0;
+
+	m_warmStarting = true;
+	m_continuousPhysics = true;
+	m_subStepping = false;
+
+	m_stepComplete = true;
+
+	m_allowSleep = true;
+	m_gravity = gravity;
+
+	m_newContacts = false;
+	m_locked = false;
+	m_clearForces = true;
+
+	m_inv_dt0 = 0.0f;
+
+	m_contactManager.m_allocator = &m_blockAllocator;
+
+	memset(&m_profile, 0, sizeof(b2Profile));
+}
+
+b2World::~b2World()
+{
+	// Some shapes allocate using b2Alloc.
+	b2Body* b = m_bodyList;
+	while (b)
+	{
+		b2Body* bNext = b->m_next;
+
+		b2Fixture* f = b->m_fixtureList;
+		while (f)
+		{
+			b2Fixture* fNext = f->m_next;
+			f->m_proxyCount = 0;
+			f->Destroy(&m_blockAllocator);
+			f = fNext;
+		}
+
+		b = bNext;
+	}
+}
+
+void b2World::SetDestructionListener(b2DestructionListener* listener)
+{
+	m_destructionListener = listener;
+}
+
+void b2World::SetContactFilter(b2ContactFilter* filter)
+{
+	m_contactManager.m_contactFilter = filter;
+}
+
+void b2World::SetContactListener(b2ContactListener* listener)
+{
+	m_contactManager.m_contactListener = listener;
+}
+
+void b2World::SetDebugDraw(b2Draw* debugDraw)
+{
+	m_debugDraw = debugDraw;
+}
+
+b2Body* b2World::CreateBody(const b2BodyDef* def)
+{
+	b2Assert(IsLocked() == false);
+	if (IsLocked())
+	{
+		return nullptr;
+	}
+
+	void* mem = m_blockAllocator.Allocate(sizeof(b2Body));
+	b2Body* b = new (mem) b2Body(def, this);
+
+	// Add to world doubly linked list.
+	b->m_prev = nullptr;
+	b->m_next = m_bodyList;
+	if (m_bodyList)
+	{
+		m_bodyList->m_prev = b;
+	}
+	m_bodyList = b;
+	++m_bodyCount;
+
+	return b;
+}
+
+void b2World::DestroyBody(b2Body* b)
+{
+	b2Assert(m_bodyCount > 0);
+	b2Assert(IsLocked() == false);
+	if (IsLocked())
+	{
+		return;
+	}
+
+	// Delete the attached joints.
+	b2JointEdge* je = b->m_jointList;
+	while (je)
+	{
+		b2JointEdge* je0 = je;
+		je = je->next;
+
+		if (m_destructionListener)
+		{
+			m_destructionListener->SayGoodbye(je0->joint);
+		}
+
+		DestroyJoint(je0->joint);
+
+		b->m_jointList = je;
+	}
+	b->m_jointList = nullptr;
+
+	// Delete the attached contacts.
+	b2ContactEdge* ce = b->m_contactList;
+	while (ce)
+	{
+		b2ContactEdge* ce0 = ce;
+		ce = ce->next;
+		m_contactManager.Destroy(ce0->contact);
+	}
+	b->m_contactList = nullptr;
+
+	// Delete the attached fixtures. This destroys broad-phase proxies.
+	b2Fixture* f = b->m_fixtureList;
+	while (f)
+	{
+		b2Fixture* f0 = f;
+		f = f->m_next;
+
+		if (m_destructionListener)
+		{
+			m_destructionListener->SayGoodbye(f0);
+		}
+
+		f0->DestroyProxies(&m_contactManager.m_broadPhase);
+		f0->Destroy(&m_blockAllocator);
+		f0->~b2Fixture();
+		m_blockAllocator.Free(f0, sizeof(b2Fixture));
+
+		b->m_fixtureList = f;
+		b->m_fixtureCount -= 1;
+	}
+	b->m_fixtureList = nullptr;
+	b->m_fixtureCount = 0;
+
+	// Remove world body list.
+	if (b->m_prev)
+	{
+		b->m_prev->m_next = b->m_next;
+	}
+
+	if (b->m_next)
+	{
+		b->m_next->m_prev = b->m_prev;
+	}
+
+	if (b == m_bodyList)
+	{
+		m_bodyList = b->m_next;
+	}
+
+	--m_bodyCount;
+	b->~b2Body();
+	m_blockAllocator.Free(b, sizeof(b2Body));
+}
+
+b2Joint* b2World::CreateJoint(const b2JointDef* def)
+{
+	b2Assert(IsLocked() == false);
+	if (IsLocked())
+	{
+		return nullptr;
+	}
+
+	b2Joint* j = b2Joint::Create(def, &m_blockAllocator);
+
+	// Connect to the world list.
+	j->m_prev = nullptr;
+	j->m_next = m_jointList;
+	if (m_jointList)
+	{
+		m_jointList->m_prev = j;
+	}
+	m_jointList = j;
+	++m_jointCount;
+
+	// Connect to the bodies' doubly linked lists.
+	j->m_edgeA.joint = j;
+	j->m_edgeA.other = j->m_bodyB;
+	j->m_edgeA.prev = nullptr;
+	j->m_edgeA.next = j->m_bodyA->m_jointList;
+	if (j->m_bodyA->m_jointList) j->m_bodyA->m_jointList->prev = &j->m_edgeA;
+	j->m_bodyA->m_jointList = &j->m_edgeA;
+
+	j->m_edgeB.joint = j;
+	j->m_edgeB.other = j->m_bodyA;
+	j->m_edgeB.prev = nullptr;
+	j->m_edgeB.next = j->m_bodyB->m_jointList;
+	if (j->m_bodyB->m_jointList) j->m_bodyB->m_jointList->prev = &j->m_edgeB;
+	j->m_bodyB->m_jointList = &j->m_edgeB;
+
+	b2Body* bodyA = def->bodyA;
+	b2Body* bodyB = def->bodyB;
+
+	// If the joint prevents collisions, then flag any contacts for filtering.
+	if (def->collideConnected == false)
+	{
+		b2ContactEdge* edge = bodyB->GetContactList();
+		while (edge)
+		{
+			if (edge->other == bodyA)
+			{
+				// Flag the contact for filtering at the next time step (where either
+				// body is awake).
+				edge->contact->FlagForFiltering();
+			}
+
+			edge = edge->next;
+		}
+	}
+
+	// Note: creating a joint doesn't wake the bodies.
+
+	return j;
+}
+
+void b2World::DestroyJoint(b2Joint* j)
+{
+	b2Assert(IsLocked() == false);
+	if (IsLocked())
+	{
+		return;
+	}
+
+	bool collideConnected = j->m_collideConnected;
+
+	// Remove from the doubly linked list.
+	if (j->m_prev)
+	{
+		j->m_prev->m_next = j->m_next;
+	}
+
+	if (j->m_next)
+	{
+		j->m_next->m_prev = j->m_prev;
+	}
+
+	if (j == m_jointList)
+	{
+		m_jointList = j->m_next;
+	}
+
+	// Disconnect from island graph.
+	b2Body* bodyA = j->m_bodyA;
+	b2Body* bodyB = j->m_bodyB;
+
+	// Wake up connected bodies.
+	bodyA->SetAwake(true);
+	bodyB->SetAwake(true);
+
+	// Remove from body 1.
+	if (j->m_edgeA.prev)
+	{
+		j->m_edgeA.prev->next = j->m_edgeA.next;
+	}
+
+	if (j->m_edgeA.next)
+	{
+		j->m_edgeA.next->prev = j->m_edgeA.prev;
+	}
+
+	if (&j->m_edgeA == bodyA->m_jointList)
+	{
+		bodyA->m_jointList = j->m_edgeA.next;
+	}
+
+	j->m_edgeA.prev = nullptr;
+	j->m_edgeA.next = nullptr;
+
+	// Remove from body 2
+	if (j->m_edgeB.prev)
+	{
+		j->m_edgeB.prev->next = j->m_edgeB.next;
+	}
+
+	if (j->m_edgeB.next)
+	{
+		j->m_edgeB.next->prev = j->m_edgeB.prev;
+	}
+
+	if (&j->m_edgeB == bodyB->m_jointList)
+	{
+		bodyB->m_jointList = j->m_edgeB.next;
+	}
+
+	j->m_edgeB.prev = nullptr;
+	j->m_edgeB.next = nullptr;
+
+	b2Joint::Destroy(j, &m_blockAllocator);
+
+	b2Assert(m_jointCount > 0);
+	--m_jointCount;
+
+	// If the joint prevents collisions, then flag any contacts for filtering.
+	if (collideConnected == false)
+	{
+		b2ContactEdge* edge = bodyB->GetContactList();
+		while (edge)
+		{
+			if (edge->other == bodyA)
+			{
+				// Flag the contact for filtering at the next time step (where either
+				// body is awake).
+				edge->contact->FlagForFiltering();
+			}
+
+			edge = edge->next;
+		}
+	}
+}
+
+//
+void b2World::SetAllowSleeping(bool flag)
+{
+	if (flag == m_allowSleep)
+	{
+		return;
+	}
+
+	m_allowSleep = flag;
+	if (m_allowSleep == false)
+	{
+		for (b2Body* b = m_bodyList; b; b = b->m_next)
+		{
+			b->SetAwake(true);
+		}
+	}
+}
+
+// Find islands, integrate and solve constraints, solve position constraints
+void b2World::Solve(const b2TimeStep& step)
+{
+	m_profile.solveInit = 0.0f;
+	m_profile.solveVelocity = 0.0f;
+	m_profile.solvePosition = 0.0f;
+
+	// Size the island for the worst case.
+	b2Island island(m_bodyCount,
+					m_contactManager.m_contactCount,
+					m_jointCount,
+					&m_stackAllocator,
+					m_contactManager.m_contactListener);
+
+	// Clear all the island flags.
+	for (b2Body* b = m_bodyList; b; b = b->m_next)
+	{
+		b->m_flags &= ~b2Body::e_islandFlag;
+	}
+	for (b2Contact* c = m_contactManager.m_contactList; c; c = c->m_next)
+	{
+		c->m_flags &= ~b2Contact::e_islandFlag;
+	}
+	for (b2Joint* j = m_jointList; j; j = j->m_next)
+	{
+		j->m_islandFlag = false;
+	}
+
+	// Build and simulate all awake islands.
+	int32 stackSize = m_bodyCount;
+	b2Body** stack = (b2Body**)m_stackAllocator.Allocate(stackSize * sizeof(b2Body*));
+	for (b2Body* seed = m_bodyList; seed; seed = seed->m_next)
+	{
+		if (seed->m_flags & b2Body::e_islandFlag)
+		{
+			continue;
+		}
+
+		if (seed->IsAwake() == false || seed->IsEnabled() == false)
+		{
+			continue;
+		}
+
+		// The seed can be dynamic or kinematic.
+		if (seed->GetType() == b2_staticBody)
+		{
+			continue;
+		}
+
+		// Reset island and stack.
+		island.Clear();
+		int32 stackCount = 0;
+		stack[stackCount++] = seed;
+		seed->m_flags |= b2Body::e_islandFlag;
+
+		// Perform a depth first search (DFS) on the constraint graph.
+		while (stackCount > 0)
+		{
+			// Grab the next body off the stack and add it to the island.
+			b2Body* b = stack[--stackCount];
+			b2Assert(b->IsEnabled() == true);
+			island.Add(b);
+
+			// To keep islands as small as possible, we don't
+			// propagate islands across static bodies.
+			if (b->GetType() == b2_staticBody)
+			{
+				continue;
+			}
+
+			// Make sure the body is awake (without resetting sleep timer).
+			b->m_flags |= b2Body::e_awakeFlag;
+
+			// Search all contacts connected to this body.
+			for (b2ContactEdge* ce = b->m_contactList; ce; ce = ce->next)
+			{
+				b2Contact* contact = ce->contact;
+
+				// Has this contact already been added to an island?
+				if (contact->m_flags & b2Contact::e_islandFlag)
+				{
+					continue;
+				}
+
+				// Is this contact solid and touching?
+				if (contact->IsEnabled() == false ||
+					contact->IsTouching() == false)
+				{
+					continue;
+				}
+
+				// Skip sensors.
+				bool sensorA = contact->m_fixtureA->m_isSensor;
+				bool sensorB = contact->m_fixtureB->m_isSensor;
+				if (sensorA || sensorB)
+				{
+					continue;
+				}
+
+				island.Add(contact);
+				contact->m_flags |= b2Contact::e_islandFlag;
+
+				b2Body* other = ce->other;
+
+				// Was the other body already added to this island?
+				if (other->m_flags & b2Body::e_islandFlag)
+				{
+					continue;
+				}
+
+				b2Assert(stackCount < stackSize);
+				stack[stackCount++] = other;
+				other->m_flags |= b2Body::e_islandFlag;
+			}
+
+			// Search all joints connect to this body.
+			for (b2JointEdge* je = b->m_jointList; je; je = je->next)
+			{
+				if (je->joint->m_islandFlag == true)
+				{
+					continue;
+				}
+
+				b2Body* other = je->other;
+
+				// Don't simulate joints connected to disabled bodies.
+				if (other->IsEnabled() == false)
+				{
+					continue;
+				}
+
+				island.Add(je->joint);
+				je->joint->m_islandFlag = true;
+
+				if (other->m_flags & b2Body::e_islandFlag)
+				{
+					continue;
+				}
+
+				b2Assert(stackCount < stackSize);
+				stack[stackCount++] = other;
+				other->m_flags |= b2Body::e_islandFlag;
+			}
+		}
+
+		b2Profile profile;
+		island.Solve(&profile, step, m_gravity, m_allowSleep);
+		m_profile.solveInit += profile.solveInit;
+		m_profile.solveVelocity += profile.solveVelocity;
+		m_profile.solvePosition += profile.solvePosition;
+
+		// Post solve cleanup.
+		for (int32 i = 0; i < island.m_bodyCount; ++i)
+		{
+			// Allow static bodies to participate in other islands.
+			b2Body* b = island.m_bodies[i];
+			if (b->GetType() == b2_staticBody)
+			{
+				b->m_flags &= ~b2Body::e_islandFlag;
+			}
+		}
+	}
+
+	m_stackAllocator.Free(stack);
+
+	{
+		b2Timer timer;
+		// Synchronize fixtures, check for out of range bodies.
+		for (b2Body* b = m_bodyList; b; b = b->GetNext())
+		{
+			// If a body was not in an island then it did not move.
+			if ((b->m_flags & b2Body::e_islandFlag) == 0)
+			{
+				continue;
+			}
+
+			if (b->GetType() == b2_staticBody)
+			{
+				continue;
+			}
+
+			// Update fixtures (for broad-phase).
+			b->SynchronizeFixtures();
+		}
+
+		// Look for new contacts.
+		m_contactManager.FindNewContacts();
+		m_profile.broadphase = timer.GetMilliseconds();
+	}
+}
+
+// Find TOI contacts and solve them.
+void b2World::SolveTOI(const b2TimeStep& step)
+{
+	b2Island island(2 * b2_maxTOIContacts, b2_maxTOIContacts, 0, &m_stackAllocator, m_contactManager.m_contactListener);
+
+	if (m_stepComplete)
+	{
+		for (b2Body* b = m_bodyList; b; b = b->m_next)
+		{
+			b->m_flags &= ~b2Body::e_islandFlag;
+			b->m_sweep.alpha0 = 0.0f;
+		}
+
+		for (b2Contact* c = m_contactManager.m_contactList; c; c = c->m_next)
+		{
+			// Invalidate TOI
+			c->m_flags &= ~(b2Contact::e_toiFlag | b2Contact::e_islandFlag);
+			c->m_toiCount = 0;
+			c->m_toi = 1.0f;
+		}
+	}
+
+	// Find TOI events and solve them.
+	for (;;)
+	{
+		// Find the first TOI.
+		b2Contact* minContact = nullptr;
+		float minAlpha = 1.0f;
+
+		for (b2Contact* c = m_contactManager.m_contactList; c; c = c->m_next)
+		{
+			// Is this contact disabled?
+			if (c->IsEnabled() == false)
+			{
+				continue;
+			}
+
+			// Prevent excessive sub-stepping.
+			if (c->m_toiCount > b2_maxSubSteps)
+			{
+				continue;
+			}
+
+			float alpha = 1.0f;
+			if (c->m_flags & b2Contact::e_toiFlag)
+			{
+				// This contact has a valid cached TOI.
+				alpha = c->m_toi;
+			}
+			else
+			{
+				b2Fixture* fA = c->GetFixtureA();
+				b2Fixture* fB = c->GetFixtureB();
+
+				// Is there a sensor?
+				if (fA->IsSensor() || fB->IsSensor())
+				{
+					continue;
+				}
+
+				b2Body* bA = fA->GetBody();
+				b2Body* bB = fB->GetBody();
+
+				b2BodyType typeA = bA->m_type;
+				b2BodyType typeB = bB->m_type;
+				b2Assert(typeA == b2_dynamicBody || typeB == b2_dynamicBody);
+
+				bool activeA = bA->IsAwake() && typeA != b2_staticBody;
+				bool activeB = bB->IsAwake() && typeB != b2_staticBody;
+
+				// Is at least one body active (awake and dynamic or kinematic)?
+				if (activeA == false && activeB == false)
+				{
+					continue;
+				}
+
+				bool collideA = bA->IsBullet() || typeA != b2_dynamicBody;
+				bool collideB = bB->IsBullet() || typeB != b2_dynamicBody;
+
+				// Are these two non-bullet dynamic bodies?
+				if (collideA == false && collideB == false)
+				{
+					continue;
+				}
+
+				// Compute the TOI for this contact.
+				// Put the sweeps onto the same time interval.
+				float alpha0 = bA->m_sweep.alpha0;
+
+				if (bA->m_sweep.alpha0 < bB->m_sweep.alpha0)
+				{
+					alpha0 = bB->m_sweep.alpha0;
+					bA->m_sweep.Advance(alpha0);
+				}
+				else if (bB->m_sweep.alpha0 < bA->m_sweep.alpha0)
+				{
+					alpha0 = bA->m_sweep.alpha0;
+					bB->m_sweep.Advance(alpha0);
+				}
+
+				b2Assert(alpha0 < 1.0f);
+
+				int32 indexA = c->GetChildIndexA();
+				int32 indexB = c->GetChildIndexB();
+
+				// Compute the time of impact in interval [0, minTOI]
+				b2TOIInput input;
+				input.proxyA.Set(fA->GetShape(), indexA);
+				input.proxyB.Set(fB->GetShape(), indexB);
+				input.sweepA = bA->m_sweep;
+				input.sweepB = bB->m_sweep;
+				input.tMax = 1.0f;
+
+				b2TOIOutput output;
+				b2TimeOfImpact(&output, &input);
+
+				// Beta is the fraction of the remaining portion of the .
+				float beta = output.t;
+				if (output.state == b2TOIOutput::e_touching)
+				{
+					alpha = b2Min(alpha0 + (1.0f - alpha0) * beta, 1.0f);
+				}
+				else
+				{
+					alpha = 1.0f;
+				}
+
+				c->m_toi = alpha;
+				c->m_flags |= b2Contact::e_toiFlag;
+			}
+
+			if (alpha < minAlpha)
+			{
+				// This is the minimum TOI found so far.
+				minContact = c;
+				minAlpha = alpha;
+			}
+		}
+
+		if (minContact == nullptr || 1.0f - 10.0f * b2_epsilon < minAlpha)
+		{
+			// No more TOI events. Done!
+			m_stepComplete = true;
+			break;
+		}
+
+		// Advance the bodies to the TOI.
+		b2Fixture* fA = minContact->GetFixtureA();
+		b2Fixture* fB = minContact->GetFixtureB();
+		b2Body* bA = fA->GetBody();
+		b2Body* bB = fB->GetBody();
+
+		b2Sweep backup1 = bA->m_sweep;
+		b2Sweep backup2 = bB->m_sweep;
+
+		bA->Advance(minAlpha);
+		bB->Advance(minAlpha);
+
+		// The TOI contact likely has some new contact points.
+		minContact->Update(m_contactManager.m_contactListener);
+		minContact->m_flags &= ~b2Contact::e_toiFlag;
+		++minContact->m_toiCount;
+
+		// Is the contact solid?
+		if (minContact->IsEnabled() == false || minContact->IsTouching() == false)
+		{
+			// Restore the sweeps.
+			minContact->SetEnabled(false);
+			bA->m_sweep = backup1;
+			bB->m_sweep = backup2;
+			bA->SynchronizeTransform();
+			bB->SynchronizeTransform();
+			continue;
+		}
+
+		bA->SetAwake(true);
+		bB->SetAwake(true);
+
+		// Build the island
+		island.Clear();
+		island.Add(bA);
+		island.Add(bB);
+		island.Add(minContact);
+
+		bA->m_flags |= b2Body::e_islandFlag;
+		bB->m_flags |= b2Body::e_islandFlag;
+		minContact->m_flags |= b2Contact::e_islandFlag;
+
+		// Get contacts on bodyA and bodyB.
+		b2Body* bodies[2] = {bA, bB};
+		for (int32 i = 0; i < 2; ++i)
+		{
+			b2Body* body = bodies[i];
+			if (body->m_type == b2_dynamicBody)
+			{
+				for (b2ContactEdge* ce = body->m_contactList; ce; ce = ce->next)
+				{
+					if (island.m_bodyCount == island.m_bodyCapacity)
+					{
+						break;
+					}
+
+					if (island.m_contactCount == island.m_contactCapacity)
+					{
+						break;
+					}
+
+					b2Contact* contact = ce->contact;
+
+					// Has this contact already been added to the island?
+					if (contact->m_flags & b2Contact::e_islandFlag)
+					{
+						continue;
+					}
+
+					// Only add static, kinematic, or bullet bodies.
+					b2Body* other = ce->other;
+					if (other->m_type == b2_dynamicBody &&
+						body->IsBullet() == false && other->IsBullet() == false)
+					{
+						continue;
+					}
+
+					// Skip sensors.
+					bool sensorA = contact->m_fixtureA->m_isSensor;
+					bool sensorB = contact->m_fixtureB->m_isSensor;
+					if (sensorA || sensorB)
+					{
+						continue;
+					}
+
+					// Tentatively advance the body to the TOI.
+					b2Sweep backup = other->m_sweep;
+					if ((other->m_flags & b2Body::e_islandFlag) == 0)
+					{
+						other->Advance(minAlpha);
+					}
+
+					// Update the contact points
+					contact->Update(m_contactManager.m_contactListener);
+
+					// Was the contact disabled by the user?
+					if (contact->IsEnabled() == false)
+					{
+						other->m_sweep = backup;
+						other->SynchronizeTransform();
+						continue;
+					}
+
+					// Are there contact points?
+					if (contact->IsTouching() == false)
+					{
+						other->m_sweep = backup;
+						other->SynchronizeTransform();
+						continue;
+					}
+
+					// Add the contact to the island
+					contact->m_flags |= b2Contact::e_islandFlag;
+					island.Add(contact);
+
+					// Has the other body already been added to the island?
+					if (other->m_flags & b2Body::e_islandFlag)
+					{
+						continue;
+					}
+					
+					// Add the other body to the island.
+					other->m_flags |= b2Body::e_islandFlag;
+
+					if (other->m_type != b2_staticBody)
+					{
+						other->SetAwake(true);
+					}
+
+					island.Add(other);
+				}
+			}
+		}
+
+		b2TimeStep subStep;
+		subStep.dt = (1.0f - minAlpha) * step.dt;
+		subStep.inv_dt = 1.0f / subStep.dt;
+		subStep.dtRatio = 1.0f;
+		subStep.positionIterations = 20;
+		subStep.velocityIterations = step.velocityIterations;
+		subStep.warmStarting = false;
+		island.SolveTOI(subStep, bA->m_islandIndex, bB->m_islandIndex);
+
+		// Reset island flags and synchronize broad-phase proxies.
+		for (int32 i = 0; i < island.m_bodyCount; ++i)
+		{
+			b2Body* body = island.m_bodies[i];
+			body->m_flags &= ~b2Body::e_islandFlag;
+
+			if (body->m_type != b2_dynamicBody)
+			{
+				continue;
+			}
+
+			body->SynchronizeFixtures();
+
+			// Invalidate all contact TOIs on this displaced body.
+			for (b2ContactEdge* ce = body->m_contactList; ce; ce = ce->next)
+			{
+				ce->contact->m_flags &= ~(b2Contact::e_toiFlag | b2Contact::e_islandFlag);
+			}
+		}
+
+		// Commit fixture proxy movements to the broad-phase so that new contacts are created.
+		// Also, some contacts can be destroyed.
+		m_contactManager.FindNewContacts();
+
+		if (m_subStepping)
+		{
+			m_stepComplete = false;
+			break;
+		}
+	}
+}
+
+void b2World::Step(float dt, int32 velocityIterations, int32 positionIterations)
+{
+	b2Timer stepTimer;
+
+	// If new fixtures were added, we need to find the new contacts.
+	if (m_newContacts)
+	{
+		m_contactManager.FindNewContacts();
+		m_newContacts = false;
+	}
+
+	m_locked = true;
+
+	b2TimeStep step;
+	step.dt = dt;
+	step.velocityIterations	= velocityIterations;
+	step.positionIterations = positionIterations;
+	if (dt > 0.0f)
+	{
+		step.inv_dt = 1.0f / dt;
+	}
+	else
+	{
+		step.inv_dt = 0.0f;
+	}
+
+	step.dtRatio = m_inv_dt0 * dt;
+
+	step.warmStarting = m_warmStarting;
+	
+	// Update contacts. This is where some contacts are destroyed.
+	{
+		b2Timer timer;
+		m_contactManager.Collide();
+		m_profile.collide = timer.GetMilliseconds();
+	}
+
+	// Integrate velocities, solve velocity constraints, and integrate positions.
+	if (m_stepComplete && step.dt > 0.0f)
+	{
+		b2Timer timer;
+		Solve(step);
+		m_profile.solve = timer.GetMilliseconds();
+	}
+
+	// Handle TOI events.
+	if (m_continuousPhysics && step.dt > 0.0f)
+	{
+		b2Timer timer;
+		SolveTOI(step);
+		m_profile.solveTOI = timer.GetMilliseconds();
+	}
+
+	if (step.dt > 0.0f)
+	{
+		m_inv_dt0 = step.inv_dt;
+	}
+
+	if (m_clearForces)
+	{
+		ClearForces();
+	}
+
+	m_locked = false;
+
+	m_profile.step = stepTimer.GetMilliseconds();
+}
+
+void b2World::ClearForces()
+{
+	for (b2Body* body = m_bodyList; body; body = body->GetNext())
+	{
+		body->m_force.SetZero();
+		body->m_torque = 0.0f;
+	}
+}
+
+struct b2WorldQueryWrapper
+{
+	bool QueryCallback(int32 proxyId)
+	{
+		b2FixtureProxy* proxy = (b2FixtureProxy*)broadPhase->GetUserData(proxyId);
+		return callback->ReportFixture(proxy->fixture);
+	}
+
+	const b2BroadPhase* broadPhase;
+	b2QueryCallback* callback;
+};
+
+void b2World::QueryAABB(b2QueryCallback* callback, const b2AABB& aabb) const
+{
+	b2WorldQueryWrapper wrapper;
+	wrapper.broadPhase = &m_contactManager.m_broadPhase;
+	wrapper.callback = callback;
+	m_contactManager.m_broadPhase.Query(&wrapper, aabb);
+}
+
+struct b2WorldRayCastWrapper
+{
+	float RayCastCallback(const b2RayCastInput& input, int32 proxyId)
+	{
+		void* userData = broadPhase->GetUserData(proxyId);
+		b2FixtureProxy* proxy = (b2FixtureProxy*)userData;
+		b2Fixture* fixture = proxy->fixture;
+		int32 index = proxy->childIndex;
+		b2RayCastOutput output;
+		bool hit = fixture->RayCast(&output, input, index);
+
+		if (hit)
+		{
+			float fraction = output.fraction;
+			b2Vec2 point = (1.0f - fraction) * input.p1 + fraction * input.p2;
+			return callback->ReportFixture(fixture, point, output.normal, fraction);
+		}
+
+		return input.maxFraction;
+	}
+
+	const b2BroadPhase* broadPhase;
+	b2RayCastCallback* callback;
+};
+
+void b2World::RayCast(b2RayCastCallback* callback, const b2Vec2& point1, const b2Vec2& point2) const
+{
+	b2WorldRayCastWrapper wrapper;
+	wrapper.broadPhase = &m_contactManager.m_broadPhase;
+	wrapper.callback = callback;
+	b2RayCastInput input;
+	input.maxFraction = 1.0f;
+	input.p1 = point1;
+	input.p2 = point2;
+	m_contactManager.m_broadPhase.RayCast(&wrapper, input);
+}
+
+void b2World::DrawShape(b2Fixture* fixture, const b2Transform& xf, const b2Color& color)
+{
+	switch (fixture->GetType())
+	{
+	case b2Shape::e_circle:
+		{
+			b2CircleShape* circle = (b2CircleShape*)fixture->GetShape();
+
+			b2Vec2 center = b2Mul(xf, circle->m_p);
+			float radius = circle->m_radius;
+			b2Vec2 axis = b2Mul(xf.q, b2Vec2(1.0f, 0.0f));
+
+			m_debugDraw->DrawSolidCircle(center, radius, axis, color);
+		}
+		break;
+
+	case b2Shape::e_edge:
+		{
+			b2EdgeShape* edge = (b2EdgeShape*)fixture->GetShape();
+			b2Vec2 v1 = b2Mul(xf, edge->m_vertex1);
+			b2Vec2 v2 = b2Mul(xf, edge->m_vertex2);
+			m_debugDraw->DrawSegment(v1, v2, color);
+
+			if (edge->m_oneSided == false)
+			{
+				m_debugDraw->DrawPoint(v1, 4.0f, color);
+				m_debugDraw->DrawPoint(v2, 4.0f, color);
+			}
+		}
+		break;
+
+	case b2Shape::e_chain:
+		{
+			b2ChainShape* chain = (b2ChainShape*)fixture->GetShape();
+			int32 count = chain->m_count;
+			const b2Vec2* vertices = chain->m_vertices;
+
+			b2Vec2 v1 = b2Mul(xf, vertices[0]);
+			for (int32 i = 1; i < count; ++i)
+			{
+				b2Vec2 v2 = b2Mul(xf, vertices[i]);
+				m_debugDraw->DrawSegment(v1, v2, color);
+				v1 = v2;
+			}
+		}
+		break;
+
+	case b2Shape::e_polygon:
+		{
+			b2PolygonShape* poly = (b2PolygonShape*)fixture->GetShape();
+			int32 vertexCount = poly->m_count;
+			b2Assert(vertexCount <= b2_maxPolygonVertices);
+			b2Vec2 vertices[b2_maxPolygonVertices];
+
+			for (int32 i = 0; i < vertexCount; ++i)
+			{
+				vertices[i] = b2Mul(xf, poly->m_vertices[i]);
+			}
+
+			m_debugDraw->DrawSolidPolygon(vertices, vertexCount, color);
+		}
+		break;
+
+	default:
+	break;
+	}
+}
+
+void b2World::DebugDraw()
+{
+	if (m_debugDraw == nullptr)
+	{
+		return;
+	}
+
+	uint32 flags = m_debugDraw->GetFlags();
+
+	if (flags & b2Draw::e_shapeBit)
+	{
+		for (b2Body* b = m_bodyList; b; b = b->GetNext())
+		{
+			const b2Transform& xf = b->GetTransform();
+			for (b2Fixture* f = b->GetFixtureList(); f; f = f->GetNext())
+			{
+				if (b->GetType() == b2_dynamicBody && b->m_mass == 0.0f)
+				{
+					// Bad body
+					DrawShape(f, xf, b2Color(1.0f, 0.0f, 0.0f));
+				}
+				else if (b->IsEnabled() == false)
+				{
+					DrawShape(f, xf, b2Color(0.5f, 0.5f, 0.3f));
+				}
+				else if (b->GetType() == b2_staticBody)
+				{
+					DrawShape(f, xf, b2Color(0.5f, 0.9f, 0.5f));
+				}
+				else if (b->GetType() == b2_kinematicBody)
+				{
+					DrawShape(f, xf, b2Color(0.5f, 0.5f, 0.9f));
+				}
+				else if (b->IsAwake() == false)
+				{
+					DrawShape(f, xf, b2Color(0.6f, 0.6f, 0.6f));
+				}
+				else
+				{
+					DrawShape(f, xf, b2Color(0.9f, 0.7f, 0.7f));
+				}
+			}
+		}
+	}
+
+	if (flags & b2Draw::e_jointBit)
+	{
+		for (b2Joint* j = m_jointList; j; j = j->GetNext())
+		{
+			j->Draw(m_debugDraw);
+		}
+	}
+
+	if (flags & b2Draw::e_pairBit)
+	{
+		b2Color color(0.3f, 0.9f, 0.9f);
+		for (b2Contact* c = m_contactManager.m_contactList; c; c = c->GetNext())
+		{
+			b2Fixture* fixtureA = c->GetFixtureA();
+			b2Fixture* fixtureB = c->GetFixtureB();
+			int32 indexA = c->GetChildIndexA();
+			int32 indexB = c->GetChildIndexB();
+			b2Vec2 cA = fixtureA->GetAABB(indexA).GetCenter();
+			b2Vec2 cB = fixtureB->GetAABB(indexB).GetCenter();
+
+			m_debugDraw->DrawSegment(cA, cB, color);
+		}
+	}
+
+	if (flags & b2Draw::e_aabbBit)
+	{
+		b2Color color(0.9f, 0.3f, 0.9f);
+		b2BroadPhase* bp = &m_contactManager.m_broadPhase;
+
+		for (b2Body* b = m_bodyList; b; b = b->GetNext())
+		{
+			if (b->IsEnabled() == false)
+			{
+				continue;
+			}
+
+			for (b2Fixture* f = b->GetFixtureList(); f; f = f->GetNext())
+			{
+				for (int32 i = 0; i < f->m_proxyCount; ++i)
+				{
+					b2FixtureProxy* proxy = f->m_proxies + i;
+					b2AABB aabb = bp->GetFatAABB(proxy->proxyId);
+					b2Vec2 vs[4];
+					vs[0].Set(aabb.lowerBound.x, aabb.lowerBound.y);
+					vs[1].Set(aabb.upperBound.x, aabb.lowerBound.y);
+					vs[2].Set(aabb.upperBound.x, aabb.upperBound.y);
+					vs[3].Set(aabb.lowerBound.x, aabb.upperBound.y);
+
+					m_debugDraw->DrawPolygon(vs, 4, color);
+				}
+			}
+		}
+	}
+
+	if (flags & b2Draw::e_centerOfMassBit)
+	{
+		for (b2Body* b = m_bodyList; b; b = b->GetNext())
+		{
+			b2Transform xf = b->GetTransform();
+			xf.p = b->GetWorldCenter();
+			m_debugDraw->DrawTransform(xf);
+		}
+	}
+}
+
+int32 b2World::GetProxyCount() const
+{
+	return m_contactManager.m_broadPhase.GetProxyCount();
+}
+
+int32 b2World::GetTreeHeight() const
+{
+	return m_contactManager.m_broadPhase.GetTreeHeight();
+}
+
+int32 b2World::GetTreeBalance() const
+{
+	return m_contactManager.m_broadPhase.GetTreeBalance();
+}
+
+float b2World::GetTreeQuality() const
+{
+	return m_contactManager.m_broadPhase.GetTreeQuality();
+}
+
+void b2World::ShiftOrigin(const b2Vec2& newOrigin)
+{
+	b2Assert(m_locked == false);
+	if (m_locked)
+	{
+		return;
+	}
+
+	for (b2Body* b = m_bodyList; b; b = b->m_next)
+	{
+		b->m_xf.p -= newOrigin;
+		b->m_sweep.c0 -= newOrigin;
+		b->m_sweep.c -= newOrigin;
+	}
+
+	for (b2Joint* j = m_jointList; j; j = j->m_next)
+	{
+		j->ShiftOrigin(newOrigin);
+	}
+
+	m_contactManager.m_broadPhase.ShiftOrigin(newOrigin);
+}
+
+void b2World::Dump()
+{
+	if (m_locked)
+	{
+		return;
+	}
+
+	b2OpenDump("box2d_dump.inl");
+
+	b2Dump("b2Vec2 g(%.9g, %.9g);\n", m_gravity.x, m_gravity.y);
+	b2Dump("m_world->SetGravity(g);\n");
+
+	b2Dump("b2Body** bodies = (b2Body**)b2Alloc(%d * sizeof(b2Body*));\n", m_bodyCount);
+	b2Dump("b2Joint** joints = (b2Joint**)b2Alloc(%d * sizeof(b2Joint*));\n", m_jointCount);
+
+	int32 i = 0;
+	for (b2Body* b = m_bodyList; b; b = b->m_next)
+	{
+		b->m_islandIndex = i;
+		b->Dump();
+		++i;
+	}
+
+	i = 0;
+	for (b2Joint* j = m_jointList; j; j = j->m_next)
+	{
+		j->m_index = i;
+		++i;
+	}
+
+	// First pass on joints, skip gear joints.
+	for (b2Joint* j = m_jointList; j; j = j->m_next)
+	{
+		if (j->m_type == e_gearJoint)
+		{
+			continue;
+		}
+
+		b2Dump("{\n");
+		j->Dump();
+		b2Dump("}\n");
+	}
+
+	// Second pass on joints, only gear joints.
+	for (b2Joint* j = m_jointList; j; j = j->m_next)
+	{
+		if (j->m_type != e_gearJoint)
+		{
+			continue;
+		}
+
+		b2Dump("{\n");
+		j->Dump();
+		b2Dump("}\n");
+	}
+
+	b2Dump("b2Free(joints);\n");
+	b2Dump("b2Free(bodies);\n");
+	b2Dump("joints = nullptr;\n");
+	b2Dump("bodies = nullptr;\n");
+
+	b2CloseDump();
+}

3rd/box2d/src/dynamics/b2_world_callbacks.cpp

@@ -0,0 +1,40 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#include "box2d/b2_fixture.h"
+#include "box2d/b2_world_callbacks.h"
+
+// Return true if contact calculations should be performed between these two shapes.
+// If you implement your own collision filter you may want to build from this implementation.
+bool b2ContactFilter::ShouldCollide(b2Fixture* fixtureA, b2Fixture* fixtureB)
+{
+	const b2Filter& filterA = fixtureA->GetFilterData();
+	const b2Filter& filterB = fixtureB->GetFilterData();
+
+	if (filterA.groupIndex == filterB.groupIndex && filterA.groupIndex != 0)
+	{
+		return filterA.groupIndex > 0;
+	}
+
+	bool collide = (filterA.maskBits & filterB.categoryBits) != 0 && (filterA.categoryBits & filterB.maskBits) != 0;
+	return collide;
+}

3rd/box2d/src/rope/b2_rope.cpp

@@ -0,0 +1,809 @@
+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#include "box2d/b2_draw.h"
+#include "box2d/b2_rope.h"
+
+#include <stdio.h>
+
+struct b2RopeStretch
+{
+	int32 i1, i2;
+	float invMass1, invMass2;
+	float L;
+	float lambda;
+	float spring;
+	float damper;
+};
+
+struct b2RopeBend
+{
+	int32 i1, i2, i3;
+	float invMass1, invMass2, invMass3;
+	float invEffectiveMass;
+	float lambda;
+	float L1, L2;
+	float alpha1, alpha2;
+	float spring;
+	float damper;
+};
+
+b2Rope::b2Rope()
+{
+	m_position.SetZero();
+	m_count = 0;
+	m_stretchCount = 0;
+	m_bendCount = 0;
+	m_stretchConstraints = nullptr;
+	m_bendConstraints = nullptr;
+	m_bindPositions = nullptr;
+	m_ps = nullptr;
+	m_p0s = nullptr;
+	m_vs = nullptr;
+	m_invMasses = nullptr;
+	m_gravity.SetZero();
+}
+
+b2Rope::~b2Rope()
+{
+	b2Free(m_stretchConstraints);
+	b2Free(m_bendConstraints);
+	b2Free(m_bindPositions);
+	b2Free(m_ps);
+	b2Free(m_p0s);
+	b2Free(m_vs);
+	b2Free(m_invMasses);
+}
+
+void b2Rope::Create(const b2RopeDef& def)
+{
+	b2Assert(def.count >= 3);
+	m_position = def.position;
+	m_count = def.count;
+	m_bindPositions = (b2Vec2*)b2Alloc(m_count * sizeof(b2Vec2));
+	m_ps = (b2Vec2*)b2Alloc(m_count * sizeof(b2Vec2));
+	m_p0s = (b2Vec2*)b2Alloc(m_count * sizeof(b2Vec2));
+	m_vs = (b2Vec2*)b2Alloc(m_count * sizeof(b2Vec2));
+	m_invMasses = (float*)b2Alloc(m_count * sizeof(float));
+
+	for (int32 i = 0; i < m_count; ++i)
+	{
+		m_bindPositions[i] = def.vertices[i];
+		m_ps[i] = def.vertices[i] + m_position;
+		m_p0s[i] = def.vertices[i] + m_position;
+		m_vs[i].SetZero();
+
+		float m = def.masses[i];
+		if (m > 0.0f)
+		{
+			m_invMasses[i] = 1.0f / m;
+		}
+		else
+		{
+			m_invMasses[i] = 0.0f;
+		}
+	}
+
+	m_stretchCount = m_count - 1;
+	m_bendCount = m_count - 2;
+
+	m_stretchConstraints = (b2RopeStretch*)b2Alloc(m_stretchCount * sizeof(b2RopeStretch));
+	m_bendConstraints = (b2RopeBend*)b2Alloc(m_bendCount * sizeof(b2RopeBend));
+
+	for (int32 i = 0; i < m_stretchCount; ++i)
+	{
+		b2RopeStretch& c = m_stretchConstraints[i];
+
+		b2Vec2 p1 = m_ps[i];
+		b2Vec2 p2 = m_ps[i+1];
+
+		c.i1 = i;
+		c.i2 = i + 1;
+		c.L = b2Distance(p1, p2);
+		c.invMass1 = m_invMasses[i];
+		c.invMass2 = m_invMasses[i + 1];
+		c.lambda = 0.0f;
+		c.damper = 0.0f;
+		c.spring = 0.0f;
+	}
+
+	for (int32 i = 0; i < m_bendCount; ++i)
+	{
+		b2RopeBend& c = m_bendConstraints[i];
+
+		b2Vec2 p1 = m_ps[i];
+		b2Vec2 p2 = m_ps[i + 1];
+		b2Vec2 p3 = m_ps[i + 2];
+
+		c.i1 = i;
+		c.i2 = i + 1;
+		c.i3 = i + 2;
+		c.invMass1 = m_invMasses[i];
+		c.invMass2 = m_invMasses[i + 1];
+		c.invMass3 = m_invMasses[i + 2];
+		c.invEffectiveMass = 0.0f;
+		c.L1 = b2Distance(p1, p2);
+		c.L2 = b2Distance(p2, p3);
+		c.lambda = 0.0f;
+
+		// Pre-compute effective mass (TODO use flattened config)
+		b2Vec2 e1 = p2 - p1;
+		b2Vec2 e2 = p3 - p2;
+		float L1sqr = e1.LengthSquared();
+		float L2sqr = e2.LengthSquared();
+
+		if (L1sqr * L2sqr == 0.0f)
+		{
+			continue;
+		}
+
+		b2Vec2 Jd1 = (-1.0f / L1sqr) * e1.Skew();
+		b2Vec2 Jd2 = (1.0f / L2sqr) * e2.Skew();
+
+		b2Vec2 J1 = -Jd1;
+		b2Vec2 J2 = Jd1 - Jd2;
+		b2Vec2 J3 = Jd2;
+
+		c.invEffectiveMass = c.invMass1 * b2Dot(J1, J1) + c.invMass2 * b2Dot(J2, J2) + c.invMass3 * b2Dot(J3, J3);
+	
+		b2Vec2 r = p3 - p1;
+
+		float rr = r.LengthSquared();
+		if (rr == 0.0f)
+		{
+			continue;
+		}
+
+		// a1 = h2 / (h1 + h2)
+		// a2 = h1 / (h1 + h2)
+		c.alpha1 = b2Dot(e2, r) / rr;
+		c.alpha2 = b2Dot(e1, r) / rr;
+	}
+
+	m_gravity = def.gravity;
+
+	SetTuning(def.tuning);
+}
+
+void b2Rope::SetTuning(const b2RopeTuning& tuning)
+{
+	m_tuning = tuning;
+
+	// Pre-compute spring and damper values based on tuning
+
+	const float bendOmega = 2.0f * b2_pi * m_tuning.bendHertz;
+
+	for (int32 i = 0; i < m_bendCount; ++i)
+	{
+		b2RopeBend& c = m_bendConstraints[i];
+
+		float L1sqr = c.L1 * c.L1;
+		float L2sqr = c.L2 * c.L2;
+
+		if (L1sqr * L2sqr == 0.0f)
+		{
+			c.spring = 0.0f;
+			c.damper = 0.0f;
+			continue;
+		}
+
+		// Flatten the triangle formed by the two edges
+		float J2 = 1.0f / c.L1 + 1.0f / c.L2;
+		float sum = c.invMass1 / L1sqr + c.invMass2 * J2 * J2 + c.invMass3 / L2sqr;
+		if (sum == 0.0f)
+		{
+			c.spring = 0.0f;
+			c.damper = 0.0f;
+			continue;
+		}
+
+		float mass = 1.0f / sum;
+
+		c.spring = mass * bendOmega * bendOmega;
+		c.damper = 2.0f * mass * m_tuning.bendDamping * bendOmega;
+	}
+	
+	const float stretchOmega = 2.0f * b2_pi * m_tuning.stretchHertz;
+
+	for (int32 i = 0; i < m_stretchCount; ++i)
+	{
+		b2RopeStretch& c = m_stretchConstraints[i];
+
+		float sum = c.invMass1 + c.invMass2;
+		if (sum == 0.0f)
+		{
+			continue;
+		}
+
+		float mass = 1.0f / sum;
+
+		c.spring = mass * stretchOmega * stretchOmega;
+		c.damper = 2.0f * mass * m_tuning.stretchDamping * stretchOmega;
+	}
+}
+
+void b2Rope::Step(float dt, int32 iterations, const b2Vec2& position)
+{
+	if (dt == 0.0f)
+	{
+		return;
+	}
+
+	const float inv_dt = 1.0f / dt;
+	float d = expf(- dt * m_tuning.damping);
+
+	// Apply gravity and damping
+	for (int32 i = 0; i < m_count; ++i)
+	{
+		if (m_invMasses[i] > 0.0f)
+		{
+			m_vs[i] *= d;
+			m_vs[i] += dt * m_gravity;
+		}
+		else
+		{
+			m_vs[i] = inv_dt * (m_bindPositions[i] + position - m_p0s[i]);
+		}
+	}
+
+	// Apply bending spring
+	if (m_tuning.bendingModel == b2_springAngleBendingModel)
+	{
+		ApplyBendForces(dt);
+	}
+
+	for (int32 i = 0; i < m_bendCount; ++i)
+	{
+		m_bendConstraints[i].lambda = 0.0f;
+	}
+
+	for (int32 i = 0; i < m_stretchCount; ++i)
+	{
+		m_stretchConstraints[i].lambda = 0.0f;
+	}
+
+	// Update position
+	for (int32 i = 0; i < m_count; ++i)
+	{
+		m_ps[i] += dt * m_vs[i];
+	}
+
+	// Solve constraints
+	for (int32 i = 0; i < iterations; ++i)
+	{
+		if (m_tuning.bendingModel == b2_pbdAngleBendingModel)
+		{
+			SolveBend_PBD_Angle();
+		}
+		else if (m_tuning.bendingModel == b2_xpbdAngleBendingModel)
+		{
+			SolveBend_XPBD_Angle(dt);
+		}
+		else if (m_tuning.bendingModel == b2_pbdDistanceBendingModel)
+		{
+			SolveBend_PBD_Distance();
+		}
+		else if (m_tuning.bendingModel == b2_pbdHeightBendingModel)
+		{
+			SolveBend_PBD_Height();
+		}
+		else if (m_tuning.bendingModel == b2_pbdTriangleBendingModel)
+		{
+			SolveBend_PBD_Triangle();
+		}
+
+		if (m_tuning.stretchingModel == b2_pbdStretchingModel)
+		{
+			SolveStretch_PBD();
+		}
+		else if (m_tuning.stretchingModel == b2_xpbdStretchingModel)
+		{
+			SolveStretch_XPBD(dt);
+		}
+	}
+
+	// Constrain velocity
+	for (int32 i = 0; i < m_count; ++i)
+	{
+		m_vs[i] = inv_dt * (m_ps[i] - m_p0s[i]);
+		m_p0s[i] = m_ps[i];
+	}
+}
+
+void b2Rope::Reset(const b2Vec2& position)
+{
+	m_position = position;
+
+	for (int32 i = 0; i < m_count; ++i)
+	{
+		m_ps[i] = m_bindPositions[i] + m_position;
+		m_p0s[i] = m_bindPositions[i] + m_position;
+		m_vs[i].SetZero();
+	}
+
+	for (int32 i = 0; i < m_bendCount; ++i)
+	{
+		m_bendConstraints[i].lambda = 0.0f;
+	}
+
+	for (int32 i = 0; i < m_stretchCount; ++i)
+	{
+		m_stretchConstraints[i].lambda = 0.0f;
+	}
+}
+
+void b2Rope::SolveStretch_PBD()
+{
+	const float stiffness = m_tuning.stretchStiffness;
+
+	for (int32 i = 0; i < m_stretchCount; ++i)
+	{
+		const b2RopeStretch& c = m_stretchConstraints[i];
+
+		b2Vec2 p1 = m_ps[c.i1];
+		b2Vec2 p2 = m_ps[c.i2];
+
+		b2Vec2 d = p2 - p1;
+		float L = d.Normalize();
+
+		float sum = c.invMass1 + c.invMass2;
+		if (sum == 0.0f)
+		{
+			continue;
+		}
+
+		float s1 = c.invMass1 / sum;
+		float s2 = c.invMass2 / sum;
+
+		p1 -= stiffness * s1 * (c.L - L) * d;
+		p2 += stiffness * s2 * (c.L - L) * d;
+
+		m_ps[c.i1] = p1;
+		m_ps[c.i2] = p2;
+	}
+}
+
+void b2Rope::SolveStretch_XPBD(float dt)
+{
+	b2Assert(dt > 0.0f);
+
+	for (int32 i = 0; i < m_stretchCount; ++i)
+	{
+		b2RopeStretch& c = m_stretchConstraints[i];
+
+		b2Vec2 p1 = m_ps[c.i1];
+		b2Vec2 p2 = m_ps[c.i2];
+
+		b2Vec2 dp1 = p1 - m_p0s[c.i1];
+		b2Vec2 dp2 = p2 - m_p0s[c.i2];
+
+		b2Vec2 u = p2 - p1;
+		float L = u.Normalize();
+
+		b2Vec2 J1 = -u;
+		b2Vec2 J2 = u;
+
+		float sum = c.invMass1 + c.invMass2;
+		if (sum == 0.0f)
+		{
+			continue;
+		}
+
+		const float alpha = 1.0f / (c.spring * dt * dt);	// 1 / kg
+		const float beta = dt * dt * c.damper;				// kg * s
+		const float sigma = alpha * beta / dt;				// non-dimensional
+		float C = L - c.L;
+
+		// This is using the initial velocities
+		float Cdot = b2Dot(J1, dp1) + b2Dot(J2, dp2);
+
+		float B = C + alpha * c.lambda + sigma * Cdot;
+		float sum2 = (1.0f + sigma) * sum + alpha;
+
+		float impulse = -B / sum2;
+
+		p1 += (c.invMass1 * impulse) * J1;
+		p2 += (c.invMass2 * impulse) * J2;
+
+		m_ps[c.i1] = p1;
+		m_ps[c.i2] = p2;
+		c.lambda += impulse;
+	}
+}
+
+void b2Rope::SolveBend_PBD_Angle()
+{
+	const float stiffness = m_tuning.bendStiffness;
+
+	for (int32 i = 0; i < m_bendCount; ++i)
+	{
+		const b2RopeBend& c = m_bendConstraints[i];
+
+		b2Vec2 p1 = m_ps[c.i1];
+		b2Vec2 p2 = m_ps[c.i2];
+		b2Vec2 p3 = m_ps[c.i3];
+
+		b2Vec2 d1 = p2 - p1;
+		b2Vec2 d2 = p3 - p2;
+		float a = b2Cross(d1, d2);
+		float b = b2Dot(d1, d2);
+
+		float angle = b2Atan2(a, b);
+
+		float L1sqr, L2sqr;
+		
+		if (m_tuning.isometric)
+		{
+			L1sqr = c.L1 * c.L1;
+			L2sqr = c.L2 * c.L2;
+		}
+		else
+		{
+			L1sqr = d1.LengthSquared();
+			L2sqr = d2.LengthSquared();
+		}
+
+		if (L1sqr * L2sqr == 0.0f)
+		{
+			continue;
+		}
+
+		b2Vec2 Jd1 = (-1.0f / L1sqr) * d1.Skew();
+		b2Vec2 Jd2 = (1.0f / L2sqr) * d2.Skew();
+
+		b2Vec2 J1 = -Jd1;
+		b2Vec2 J2 = Jd1 - Jd2;
+		b2Vec2 J3 = Jd2;
+
+		float sum;
+		if (m_tuning.fixedEffectiveMass)
+		{
+			sum = c.invEffectiveMass;
+		}
+		else
+		{
+			sum = c.invMass1 * b2Dot(J1, J1) + c.invMass2 * b2Dot(J2, J2) + c.invMass3 * b2Dot(J3, J3);
+		}
+
+		if (sum == 0.0f)
+		{
+			sum = c.invEffectiveMass;
+		}
+
+		float impulse = -stiffness * angle / sum;
+
+		p1 += (c.invMass1 * impulse) * J1;
+		p2 += (c.invMass2 * impulse) * J2;
+		p3 += (c.invMass3 * impulse) * J3;
+
+		m_ps[c.i1] = p1;
+		m_ps[c.i2] = p2;
+		m_ps[c.i3] = p3;
+	}
+}
+
+void b2Rope::SolveBend_XPBD_Angle(float dt)
+{
+	b2Assert(dt > 0.0f);
+
+	for (int32 i = 0; i < m_bendCount; ++i)
+	{
+		b2RopeBend& c = m_bendConstraints[i];
+
+		b2Vec2 p1 = m_ps[c.i1];
+		b2Vec2 p2 = m_ps[c.i2];
+		b2Vec2 p3 = m_ps[c.i3];
+
+		b2Vec2 dp1 = p1 - m_p0s[c.i1];
+		b2Vec2 dp2 = p2 - m_p0s[c.i2];
+		b2Vec2 dp3 = p3 - m_p0s[c.i3];
+
+		b2Vec2 d1 = p2 - p1;
+		b2Vec2 d2 = p3 - p2;
+
+		float L1sqr, L2sqr;
+
+		if (m_tuning.isometric)
+		{
+			L1sqr = c.L1 * c.L1;
+			L2sqr = c.L2 * c.L2;
+		}
+		else
+		{
+			L1sqr = d1.LengthSquared();
+			L2sqr = d2.LengthSquared();
+		}
+
+		if (L1sqr * L2sqr == 0.0f)
+		{
+			continue;
+		}
+
+		float a = b2Cross(d1, d2);
+		float b = b2Dot(d1, d2);
+
+		float angle = b2Atan2(a, b);
+
+		b2Vec2 Jd1 = (-1.0f / L1sqr) * d1.Skew();
+		b2Vec2 Jd2 = (1.0f / L2sqr) * d2.Skew();
+
+		b2Vec2 J1 = -Jd1;
+		b2Vec2 J2 = Jd1 - Jd2;
+		b2Vec2 J3 = Jd2;
+
+		float sum;
+		if (m_tuning.fixedEffectiveMass)
+		{
+			sum = c.invEffectiveMass;
+		}
+		else
+		{
+			sum = c.invMass1 * b2Dot(J1, J1) + c.invMass2 * b2Dot(J2, J2) + c.invMass3 * b2Dot(J3, J3);
+		}
+
+		if (sum == 0.0f)
+		{
+			continue;
+		}
+
+		const float alpha = 1.0f / (c.spring * dt * dt);
+		const float beta = dt * dt * c.damper;
+		const float sigma = alpha * beta / dt;
+		float C = angle;
+
+		// This is using the initial velocities
+		float Cdot = b2Dot(J1, dp1) + b2Dot(J2, dp2) + b2Dot(J3, dp3);
+
+		float B = C + alpha * c.lambda + sigma * Cdot;
+		float sum2 = (1.0f + sigma) * sum + alpha;
+
+		float impulse = -B / sum2;
+
+		p1 += (c.invMass1 * impulse) * J1;
+		p2 += (c.invMass2 * impulse) * J2;
+		p3 += (c.invMass3 * impulse) * J3;
+
+		m_ps[c.i1] = p1;
+		m_ps[c.i2] = p2;
+		m_ps[c.i3] = p3;
+		c.lambda += impulse;
+	}
+}
+
+void b2Rope::ApplyBendForces(float dt)
+{
+	// omega = 2 * pi * hz
+	const float omega = 2.0f * b2_pi * m_tuning.bendHertz;
+
+	for (int32 i = 0; i < m_bendCount; ++i)
+	{
+		const b2RopeBend& c = m_bendConstraints[i];
+
+		b2Vec2 p1 = m_ps[c.i1];
+		b2Vec2 p2 = m_ps[c.i2];
+		b2Vec2 p3 = m_ps[c.i3];
+
+		b2Vec2 v1 = m_vs[c.i1];
+		b2Vec2 v2 = m_vs[c.i2];
+		b2Vec2 v3 = m_vs[c.i3];
+
+		b2Vec2 d1 = p2 - p1;
+		b2Vec2 d2 = p3 - p2;
+
+		float L1sqr, L2sqr;
+
+		if (m_tuning.isometric)
+		{
+			L1sqr = c.L1 * c.L1;
+			L2sqr = c.L2 * c.L2;
+		}
+		else
+		{
+			L1sqr = d1.LengthSquared();
+			L2sqr = d2.LengthSquared();
+		}
+
+		if (L1sqr * L2sqr == 0.0f)
+		{
+			continue;
+		}
+
+		float a = b2Cross(d1, d2);
+		float b = b2Dot(d1, d2);
+
+		float angle = b2Atan2(a, b);
+
+		b2Vec2 Jd1 = (-1.0f / L1sqr) * d1.Skew();
+		b2Vec2 Jd2 = (1.0f / L2sqr) * d2.Skew();
+
+		b2Vec2 J1 = -Jd1;
+		b2Vec2 J2 = Jd1 - Jd2;
+		b2Vec2 J3 = Jd2;
+
+		float sum;
+		if (m_tuning.fixedEffectiveMass)
+		{
+			sum = c.invEffectiveMass;
+		}
+		else
+		{
+			sum = c.invMass1 * b2Dot(J1, J1) + c.invMass2 * b2Dot(J2, J2) + c.invMass3 * b2Dot(J3, J3);
+		}
+
+		if (sum == 0.0f)
+		{
+			continue;
+		}
+
+		float mass = 1.0f / sum;
+
+		const float spring = mass * omega * omega;
+		const float damper = 2.0f * mass * m_tuning.bendDamping * omega;
+
+		float C = angle;
+		float Cdot = b2Dot(J1, v1) + b2Dot(J2, v2) + b2Dot(J3, v3);
+
+		float impulse = -dt * (spring * C + damper * Cdot);
+
+		m_vs[c.i1] += (c.invMass1 * impulse) * J1;
+		m_vs[c.i2] += (c.invMass2 * impulse) * J2;
+		m_vs[c.i3] += (c.invMass3 * impulse) * J3;
+	}
+}
+
+void b2Rope::SolveBend_PBD_Distance()
+{
+	const float stiffness = m_tuning.bendStiffness;
+
+	for (int32 i = 0; i < m_bendCount; ++i)
+	{
+		const b2RopeBend& c = m_bendConstraints[i];
+
+		int32 i1 = c.i1;
+		int32 i2 = c.i3;
+
+		b2Vec2 p1 = m_ps[i1];
+		b2Vec2 p2 = m_ps[i2];
+
+		b2Vec2 d = p2 - p1;
+		float L = d.Normalize();
+
+		float sum = c.invMass1 + c.invMass3;
+		if (sum == 0.0f)
+		{
+			continue;
+		}
+
+		float s1 = c.invMass1 / sum;
+		float s2 = c.invMass3 / sum;
+
+		p1 -= stiffness * s1 * (c.L1 + c.L2 - L) * d;
+		p2 += stiffness * s2 * (c.L1 + c.L2 - L) * d;
+
+		m_ps[i1] = p1;
+		m_ps[i2] = p2;
+	}
+}
+
+// Constraint based implementation of:
+// P. Volino: Simple Linear Bending Stiffness in Particle Systems
+void b2Rope::SolveBend_PBD_Height()
+{
+	const float stiffness = m_tuning.bendStiffness;
+
+	for (int32 i = 0; i < m_bendCount; ++i)
+	{
+		const b2RopeBend& c = m_bendConstraints[i];
+
+		b2Vec2 p1 = m_ps[c.i1];
+		b2Vec2 p2 = m_ps[c.i2];
+		b2Vec2 p3 = m_ps[c.i3];
+
+		// Barycentric coordinates are held constant
+		b2Vec2 d = c.alpha1 * p1 + c.alpha2 * p3 - p2;
+		float dLen = d.Length();
+
+		if (dLen == 0.0f)
+		{
+			continue;
+		}
+
+		b2Vec2 dHat = (1.0f / dLen) * d;
+
+		b2Vec2 J1 = c.alpha1 * dHat;
+		b2Vec2 J2 = -dHat;
+		b2Vec2 J3 = c.alpha2 * dHat;
+
+		float sum = c.invMass1 * c.alpha1 * c.alpha1 + c.invMass2 + c.invMass3 * c.alpha2 * c.alpha2;
+
+		if (sum == 0.0f)
+		{
+			continue;
+		}
+
+		float C = dLen;
+		float mass = 1.0f / sum;
+		float impulse = -stiffness * mass * C;
+
+		p1 += (c.invMass1 * impulse) * J1;
+		p2 += (c.invMass2 * impulse) * J2;
+		p3 += (c.invMass3 * impulse) * J3;
+
+		m_ps[c.i1] = p1;
+		m_ps[c.i2] = p2;
+		m_ps[c.i3] = p3;
+	}
+}
+
+// M. Kelager: A Triangle Bending Constraint Model for PBD
+void b2Rope::SolveBend_PBD_Triangle()
+{
+	const float stiffness = m_tuning.bendStiffness;
+
+	for (int32 i = 0; i < m_bendCount; ++i)
+	{
+		const b2RopeBend& c = m_bendConstraints[i];
+
+		b2Vec2 b0 = m_ps[c.i1];
+		b2Vec2 v = m_ps[c.i2];
+		b2Vec2 b1 = m_ps[c.i3];
+
+		float wb0 = c.invMass1;
+		float wv = c.invMass2;
+		float wb1 = c.invMass3;
+
+		float W = wb0 + wb1 + 2.0f * wv;
+		float invW = stiffness / W;
+
+		b2Vec2 d = v - (1.0f / 3.0f) * (b0 + v + b1);
+
+		b2Vec2 db0 = 2.0f * wb0 * invW * d;
+		b2Vec2 dv = -4.0f * wv * invW * d;
+		b2Vec2 db1 = 2.0f * wb1 * invW * d;
+
+		b0 += db0;
+		v += dv;
+		b1 += db1;
+
+		m_ps[c.i1] = b0;
+		m_ps[c.i2] = v;
+		m_ps[c.i3] = b1;
+	}
+}
+
+void b2Rope::Draw(b2Draw* draw) const
+{
+	b2Color c(0.4f, 0.5f, 0.7f);
+	b2Color pg(0.1f, 0.8f, 0.1f);
+	b2Color pd(0.7f, 0.2f, 0.4f);
+
+	for (int32 i = 0; i < m_count - 1; ++i)
+	{
+		draw->DrawSegment(m_ps[i], m_ps[i+1], c);
+
+		const b2Color& pc = m_invMasses[i] > 0.0f ? pd : pg;
+		draw->DrawPoint(m_ps[i], 5.0f, pc);
+	}
+
+	const b2Color& pc = m_invMasses[m_count - 1] > 0.0f ? pd : pg;
+	draw->DrawPoint(m_ps[m_count - 1], 5.0f, pc);
+}