Add initial prototype.

3-mid/physics/implement/box2d/contrib/include/box2d/b2_api.h

@@ -0,0 +1,52 @@
+// 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

3-mid/physics/implement/box2d/contrib/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

3-mid/physics/implement/box2d/contrib/include/box2d/b2_body.h

@@ -0,0 +1,881 @@
+// 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.
+	void GetMassData(b2MassData* data) 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();
+
+	/// Set the user data. Use this to store your application specific data.
+	void SetUserData(void* data);
+
+	/// 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 b2RopeJoint;
+	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 void b2Body::GetMassData(b2MassData* data) const
+{
+	data->mass = m_mass;
+	data->I = m_I + m_mass * b2Dot(m_sweep.localCenter, m_sweep.localCenter);
+	data->center = m_sweep.localCenter;
+}
+
+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 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

3-mid/physics/implement/box2d/contrib/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

3-mid/physics/implement/box2d/contrib/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

3-mid/physics/implement/box2d/contrib/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

3-mid/physics/implement/box2d/contrib/include/box2d/b2_collision.h

@@ -0,0 +1,283 @@
+// 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* circleB, 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);
+
+// ---------------- 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

3-mid/physics/implement/box2d/contrib/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

3-mid/physics/implement/box2d/contrib/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

3-mid/physics/implement/box2d/contrib/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

3-mid/physics/implement/box2d/contrib/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

3-mid/physics/implement/box2d/contrib/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

3-mid/physics/implement/box2d/contrib/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

3-mid/physics/implement/box2d/contrib/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

3-mid/physics/implement/box2d/contrib/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

3-mid/physics/implement/box2d/contrib/include/box2d/b2_fixture.h

@@ -0,0 +1,365 @@
+// 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();
+
+	/// 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 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

3-mid/physics/implement/box2d/contrib/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

3-mid/physics/implement/box2d/contrib/include/box2d/b2_gear_joint.h

@@ -0,0 +1,130 @@
+// 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_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

3-mid/physics/implement/box2d/contrib/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

3-mid/physics/implement/box2d/contrib/include/box2d/b2_joint.h

@@ -0,0 +1,228 @@
+// 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_ropeJoint,
+	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();
+
+	/// 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 bool b2Joint::GetCollideConnected() const
+{
+	return m_collideConnected;
+}
+
+#endif

3-mid/physics/implement/box2d/contrib/include/box2d/b2_math.h

@@ -0,0 +1,715 @@
+// 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() {}
+
+	/// 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() {}
+
+	/// 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() {}
+
+	/// 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() {}
+
+	/// 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() {}
+
+	/// 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() {}
+
+	/// 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
+{
+	/// 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

3-mid/physics/implement/box2d/contrib/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

3-mid/physics/implement/box2d/contrib/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

3-mid/physics/implement/box2d/contrib/include/box2d/b2_polygon_shape.h

@@ -0,0 +1,95 @@
+// 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"
+
+/// 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 collinear points are handled but not removed. Collinear points
+	/// may lead to poor stacking behavior.
+	void Set(const b2Vec2* points, int32 count);
+
+	/// 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;
+};
+
+inline b2PolygonShape::b2PolygonShape()
+{
+	m_type = e_polygon;
+	m_radius = b2_polygonRadius;
+	m_count = 0;
+	m_centroid.SetZero();
+}
+
+#endif

3-mid/physics/implement/box2d/contrib/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

3-mid/physics/implement/box2d/contrib/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

3-mid/physics/implement/box2d/contrib/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

3-mid/physics/implement/box2d/contrib/include/box2d/b2_rope.h

@@ -0,0 +1,153 @@
+// 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;
+		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

3-mid/physics/implement/box2d/contrib/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

3-mid/physics/implement/box2d/contrib/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

3-mid/physics/implement/box2d/contrib/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

3-mid/physics/implement/box2d/contrib/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

3-mid/physics/implement/box2d/contrib/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

3-mid/physics/implement/box2d/contrib/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

3-mid/physics/implement/box2d/contrib/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

3-mid/physics/implement/box2d/contrib/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 hz) { m_stiffness = hz; }
+	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

3-mid/physics/implement/box2d/contrib/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

3-mid/physics/implement/box2d/contrib/include/box2d/b2_world.h

@@ -0,0 +1,345 @@
+// 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;
+
+	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

3-mid/physics/implement/box2d/contrib/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

3-mid/physics/implement/box2d/contrib/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