boxdd-sys 0.4.0

// SPDX-FileCopyrightText: 2023 Erin Catto
// SPDX-License-Identifier: MIT

#include "body.h"
#include "core.h"
#include "joint.h"
#include "physics_world.h"
#include "solver.h"
#include "solver_set.h"

// needed for dll export
#include "box2d/box2d.h"

#include <stdio.h>

void b2PrismaticJoint_EnableSpring( b2JointId jointId, bool enableSpring )
{
	b2JointSim* joint = b2GetJointSimCheckType( jointId, b2_prismaticJoint );
	if ( enableSpring != joint->prismaticJoint.enableSpring )
	{
		joint->prismaticJoint.enableSpring = enableSpring;
		joint->prismaticJoint.springImpulse = 0.0f;
	}
}

bool b2PrismaticJoint_IsSpringEnabled( b2JointId jointId )
{
	b2JointSim* joint = b2GetJointSimCheckType( jointId, b2_prismaticJoint );
	return joint->prismaticJoint.enableSpring;
}

void b2PrismaticJoint_SetSpringHertz( b2JointId jointId, float hertz )
{
	b2JointSim* joint = b2GetJointSimCheckType( jointId, b2_prismaticJoint );
	joint->prismaticJoint.hertz = hertz;
}

float b2PrismaticJoint_GetSpringHertz( b2JointId jointId )
{
	b2JointSim* joint = b2GetJointSimCheckType( jointId, b2_prismaticJoint );
	return joint->prismaticJoint.hertz;
}

void b2PrismaticJoint_SetSpringDampingRatio( b2JointId jointId, float dampingRatio )
{
	b2JointSim* joint = b2GetJointSimCheckType( jointId, b2_prismaticJoint );
	joint->prismaticJoint.dampingRatio = dampingRatio;
}

float b2PrismaticJoint_GetSpringDampingRatio( b2JointId jointId )
{
	b2JointSim* joint = b2GetJointSimCheckType( jointId, b2_prismaticJoint );
	return joint->prismaticJoint.dampingRatio;
}

void b2PrismaticJoint_SetTargetTranslation( b2JointId jointId, float translation )
{
	b2JointSim* joint = b2GetJointSimCheckType( jointId, b2_prismaticJoint );
	joint->prismaticJoint.targetTranslation = translation;
}

float b2PrismaticJoint_GetTargetTranslation( b2JointId jointId )
{
	b2JointSim* joint = b2GetJointSimCheckType( jointId, b2_prismaticJoint );
	return joint->prismaticJoint.targetTranslation;
}

void b2PrismaticJoint_EnableLimit( b2JointId jointId, bool enableLimit )
{
	b2JointSim* joint = b2GetJointSimCheckType( jointId, b2_prismaticJoint );
	if ( enableLimit != joint->prismaticJoint.enableLimit )
	{
		joint->prismaticJoint.enableLimit = enableLimit;
		joint->prismaticJoint.lowerImpulse = 0.0f;
		joint->prismaticJoint.upperImpulse = 0.0f;
	}
}

bool b2PrismaticJoint_IsLimitEnabled( b2JointId jointId )
{
	b2JointSim* joint = b2GetJointSimCheckType( jointId, b2_prismaticJoint );
	return joint->prismaticJoint.enableLimit;
}

float b2PrismaticJoint_GetLowerLimit( b2JointId jointId )
{
	b2JointSim* joint = b2GetJointSimCheckType( jointId, b2_prismaticJoint );
	return joint->prismaticJoint.lowerTranslation;
}

float b2PrismaticJoint_GetUpperLimit( b2JointId jointId )
{
	b2JointSim* joint = b2GetJointSimCheckType( jointId, b2_prismaticJoint );
	return joint->prismaticJoint.upperTranslation;
}

void b2PrismaticJoint_SetLimits( b2JointId jointId, float lower, float upper )
{
	B2_ASSERT( lower <= upper );

	b2JointSim* joint = b2GetJointSimCheckType( jointId, b2_prismaticJoint );
	if ( lower != joint->prismaticJoint.lowerTranslation || upper != joint->prismaticJoint.upperTranslation )
	{
		joint->prismaticJoint.lowerTranslation = b2MinFloat( lower, upper );
		joint->prismaticJoint.upperTranslation = b2MaxFloat( lower, upper );
		joint->prismaticJoint.lowerImpulse = 0.0f;
		joint->prismaticJoint.upperImpulse = 0.0f;
	}
}

void b2PrismaticJoint_EnableMotor( b2JointId jointId, bool enableMotor )
{
	b2JointSim* joint = b2GetJointSimCheckType( jointId, b2_prismaticJoint );
	if ( enableMotor != joint->prismaticJoint.enableMotor )
	{
		joint->prismaticJoint.enableMotor = enableMotor;
		joint->prismaticJoint.motorImpulse = 0.0f;
	}
}

bool b2PrismaticJoint_IsMotorEnabled( b2JointId jointId )
{
	b2JointSim* joint = b2GetJointSimCheckType( jointId, b2_prismaticJoint );
	return joint->prismaticJoint.enableMotor;
}

void b2PrismaticJoint_SetMotorSpeed( b2JointId jointId, float motorSpeed )
{
	b2JointSim* joint = b2GetJointSimCheckType( jointId, b2_prismaticJoint );
	joint->prismaticJoint.motorSpeed = motorSpeed;
}

float b2PrismaticJoint_GetMotorSpeed( b2JointId jointId )
{
	b2JointSim* joint = b2GetJointSimCheckType( jointId, b2_prismaticJoint );
	return joint->prismaticJoint.motorSpeed;
}

float b2PrismaticJoint_GetMotorForce( b2JointId jointId )
{
	b2World* world = b2GetWorld( jointId.world0 );
	b2JointSim* base = b2GetJointSimCheckType( jointId, b2_prismaticJoint );
	return world->inv_h * base->prismaticJoint.motorImpulse;
}

void b2PrismaticJoint_SetMaxMotorForce( b2JointId jointId, float force )
{
	b2JointSim* joint = b2GetJointSimCheckType( jointId, b2_prismaticJoint );
	joint->prismaticJoint.maxMotorForce = force;
}

float b2PrismaticJoint_GetMaxMotorForce( b2JointId jointId )
{
	b2JointSim* joint = b2GetJointSimCheckType( jointId, b2_prismaticJoint );
	return joint->prismaticJoint.maxMotorForce;
}

float b2PrismaticJoint_GetTranslation( b2JointId jointId )
{
	b2World* world = b2GetWorld( jointId.world0 );
	b2JointSim* jointSim = b2GetJointSimCheckType( jointId, b2_prismaticJoint );
	b2Transform transformA = b2GetBodyTransform( world, jointSim->bodyIdA );
	b2Transform transformB = b2GetBodyTransform( world, jointSim->bodyIdB );

	b2Vec2 localAxisA = b2RotateVector( jointSim->localFrameA.q, (b2Vec2){ 1.0f, 0.0f } );
	b2Vec2 axisA = b2RotateVector( transformA.q, localAxisA );
	b2Vec2 pA = b2TransformPoint( transformA, jointSim->localFrameA.p );
	b2Vec2 pB = b2TransformPoint( transformB, jointSim->localFrameB.p );
	b2Vec2 d = b2Sub( pB, pA );
	float translation = b2Dot( d, axisA );
	return translation;
}

float b2PrismaticJoint_GetSpeed( b2JointId jointId )
{
	b2World* world = b2GetWorld( jointId.world0 );
	b2Joint* joint = b2GetJointFullId( world, jointId );
	B2_ASSERT( joint->type == b2_prismaticJoint );
	b2JointSim* base = b2GetJointSim( world, joint );
	B2_ASSERT( base->type == b2_prismaticJoint );

	b2Body* bodyA = b2BodyArray_Get( &world->bodies, base->bodyIdA );
	b2Body* bodyB = b2BodyArray_Get( &world->bodies, base->bodyIdB );
	b2BodySim* bodySimA = b2GetBodySim( world, bodyA );
	b2BodySim* bodySimB = b2GetBodySim( world, bodyB );
	b2BodyState* bodyStateA = b2GetBodyState( world, bodyA );
	b2BodyState* bodyStateB = b2GetBodyState( world, bodyB );

	b2Transform transformA = bodySimA->transform;
	b2Transform transformB = bodySimB->transform;

	b2Vec2 localAxisA = b2RotateVector( base->localFrameA.q, (b2Vec2){ 1.0f, 0.0f } );
	b2Vec2 axisA = b2RotateVector( transformA.q, localAxisA );
	b2Vec2 cA = bodySimA->center;
	b2Vec2 cB = bodySimB->center;
	b2Vec2 rA = b2RotateVector( transformA.q, b2Sub( base->localFrameA.p, bodySimA->localCenter ) );
	b2Vec2 rB = b2RotateVector( transformB.q, b2Sub( base->localFrameB.p, bodySimB->localCenter ) );

	b2Vec2 d = b2Add( b2Sub( cB, cA ), b2Sub( rB, rA ) );

	b2Vec2 vA = bodyStateA ? bodyStateA->linearVelocity : b2Vec2_zero;
	b2Vec2 vB = bodyStateB ? bodyStateB->linearVelocity : b2Vec2_zero;
	float wA = bodyStateA ? bodyStateA->angularVelocity : 0.0f;
	float wB = bodyStateB ? bodyStateB->angularVelocity : 0.0f;

	b2Vec2 vRel = b2Sub( b2Add( vB, b2CrossSV( wB, rB ) ), b2Add( vA, b2CrossSV( wA, rA ) ) );
	float speed = b2Dot( d, b2CrossSV( wA, axisA ) ) + b2Dot( axisA, vRel );
	return speed;
}

b2Vec2 b2GetPrismaticJointForce( b2World* world, b2JointSim* base )
{
	int idA = base->bodyIdA;
	b2Transform transformA = b2GetBodyTransform( world, idA );

	b2PrismaticJoint* joint = &base->prismaticJoint;

	b2Vec2 localAxisA = b2RotateVector( base->localFrameA.q, (b2Vec2){ 1.0f, 0.0f } );
	b2Vec2 axisA = b2RotateVector( transformA.q, localAxisA );
	b2Vec2 perpA = b2LeftPerp( axisA );

	float inv_h = world->inv_h;
	float perpForce = inv_h * joint->impulse.x;
	float axialForce = inv_h * ( joint->motorImpulse + joint->lowerImpulse - joint->upperImpulse );

	b2Vec2 force = b2Add( b2MulSV( perpForce, perpA ), b2MulSV( axialForce, axisA ) );
	return force;
}

float b2GetPrismaticJointTorque( b2World* world, b2JointSim* base )
{
	return world->inv_h * base->prismaticJoint.impulse.y;
}

// Linear constraint (point-to-line)
// d = pB - pA = xB + rB - xA - rA
// C = dot(perp, d)
// Cdot = dot(d, cross(wA, perp)) + dot(perp, vB + cross(wB, rB) - vA - cross(wA, rA))
//      = -dot(perp, vA) - dot(cross(rA + d, perp), wA) + dot(perp, vB) + dot(cross(rB, perp), vB)
// J = [-perp, -cross(rA + d, perp), perp, cross(rB, perp)]
//
// Angular constraint
// C = aB - aA + a_initial
// Cdot = wB - wA
// J = [0 0 -1 0 0 1]
//
// K = J * invM * JT
//
// J = [-a -sA a sB]
//     [0  -1  0  1]
// a = perp
// sA = cross(rA + d, a) = cross(pB - xA, a)
// sB = cross(rB, a) = cross(pB - xB, a)

// Motor/Limit linear constraint
// C = dot(axA, d)
// Cdot = -dot(axA, vA) - dot(cross(rA + d, axA), wA) + dot(axA, vB) + dot(cross(rB, axA), vB)
// J = [-axA -cross(rA + d, axA) axA cross(rB, ax1)]

// Predictive limit is applied even when the limit is not active.
// Prevents a constraint speed that can lead to a constraint error in one time step.
// Want C2 = C1 + h * Cdot >= 0
// Or:
// Cdot + C1/h >= 0
// I do not apply a negative constraint error because that is handled in position correction.
// So:
// Cdot + max(C1, 0)/h >= 0

// Block Solver
// We develop a block solver that includes the angular and linear constraints. This makes the limit stiffer.
//
// The Jacobian has 2 rows:
// J = [-uT -s1 uT s2] // linear
//     [0   -1   0  1] // angular
//
// u = perp
// s1 = cross(d + r1, u), s2 = cross(r2, u)
// a1 = cross(d + r1, v), a2 = cross(r2, v)

void b2PreparePrismaticJoint( b2JointSim* base, b2StepContext* context )
{
	B2_ASSERT( base->type == b2_prismaticJoint );

	// chase body id to the solver set where the body lives
	int idA = base->bodyIdA;
	int idB = base->bodyIdB;

	b2World* world = context->world;

	b2Body* bodyA = b2BodyArray_Get( &world->bodies, idA );
	b2Body* bodyB = b2BodyArray_Get( &world->bodies, idB );

	B2_ASSERT( bodyA->setIndex == b2_awakeSet || bodyB->setIndex == b2_awakeSet );
	b2SolverSet* setA = b2SolverSetArray_Get( &world->solverSets, bodyA->setIndex );
	b2SolverSet* setB = b2SolverSetArray_Get( &world->solverSets, bodyB->setIndex );

	int localIndexA = bodyA->localIndex;
	int localIndexB = bodyB->localIndex;

	b2BodySim* bodySimA = b2BodySimArray_Get( &setA->bodySims, localIndexA );
	b2BodySim* bodySimB = b2BodySimArray_Get( &setB->bodySims, localIndexB );

	float mA = bodySimA->invMass;
	float iA = bodySimA->invInertia;
	float mB = bodySimB->invMass;
	float iB = bodySimB->invInertia;

	base->invMassA = mA;
	base->invMassB = mB;
	base->invIA = iA;
	base->invIB = iB;

	b2PrismaticJoint* joint = &base->prismaticJoint;
	joint->indexA = bodyA->setIndex == b2_awakeSet ? localIndexA : B2_NULL_INDEX;
	joint->indexB = bodyB->setIndex == b2_awakeSet ? localIndexB : B2_NULL_INDEX;

	// Compute joint anchor frames with world space rotation, relative to center of mass
	joint->frameA.q = b2MulRot( bodySimA->transform.q, base->localFrameA.q );
	joint->frameA.p = b2RotateVector( bodySimA->transform.q, b2Sub( base->localFrameA.p, bodySimA->localCenter ) );
	joint->frameB.q = b2MulRot( bodySimB->transform.q, base->localFrameB.q );
	joint->frameB.p = b2RotateVector( bodySimB->transform.q, b2Sub( base->localFrameB.p, bodySimB->localCenter ) );

	// Compute the initial center delta. Incremental position updates are relative to this.
	joint->deltaCenter = b2Sub( bodySimB->center, bodySimA->center );

	joint->springSoftness = b2MakeSoft( joint->hertz, joint->dampingRatio, context->h );

	if ( context->enableWarmStarting == false )
	{
		joint->impulse = b2Vec2_zero;
		joint->springImpulse = 0.0f;
		joint->motorImpulse = 0.0f;
		joint->lowerImpulse = 0.0f;
		joint->upperImpulse = 0.0f;
	}
}

void b2WarmStartPrismaticJoint( b2JointSim* base, b2StepContext* context )
{
	B2_ASSERT( base->type == b2_prismaticJoint );

	float mA = base->invMassA;
	float mB = base->invMassB;
	float iA = base->invIA;
	float iB = base->invIB;

	// dummy state for static bodies
	b2BodyState dummyState = b2_identityBodyState;

	b2PrismaticJoint* joint = &base->prismaticJoint;

	b2BodyState* stateA = joint->indexA == B2_NULL_INDEX ? &dummyState : context->states + joint->indexA;
	b2BodyState* stateB = joint->indexB == B2_NULL_INDEX ? &dummyState : context->states + joint->indexB;

	b2Vec2 rA = b2RotateVector( stateA->deltaRotation, joint->frameA.p );
	b2Vec2 rB = b2RotateVector( stateB->deltaRotation, joint->frameB.p );

	b2Vec2 d = b2Add( b2Add( b2Sub( stateB->deltaPosition, stateA->deltaPosition ), joint->deltaCenter ), b2Sub( rB, rA ) );

	b2Vec2 axisA = b2RotateVector( joint->frameA.q, (b2Vec2){ 1.0f, 0.0f } );
	axisA = b2RotateVector( stateA->deltaRotation, axisA );

	// impulse is applied at anchor point on body B
	float a1 = b2Cross( b2Add( rA, d ), axisA );
	float a2 = b2Cross( rB, axisA );
	float axialImpulse = joint->springImpulse + joint->motorImpulse + joint->lowerImpulse - joint->upperImpulse;

	// perpendicular constraint
	b2Vec2 perpA = b2LeftPerp( axisA );
	float s1 = b2Cross( b2Add( rA, d ), perpA );
	float s2 = b2Cross( rB, perpA );
	float perpImpulse = joint->impulse.x;
	float angleImpulse = joint->impulse.y;

	b2Vec2 P = b2Add( b2MulSV( axialImpulse, axisA ), b2MulSV( perpImpulse, perpA ) );
	float LA = axialImpulse * a1 + perpImpulse * s1 + angleImpulse;
	float LB = axialImpulse * a2 + perpImpulse * s2 + angleImpulse;

	if ( stateA->flags & b2_dynamicFlag )
	{
		stateA->linearVelocity = b2MulSub( stateA->linearVelocity, mA, P );
		stateA->angularVelocity -= iA * LA;
	}

	if ( stateB->flags & b2_dynamicFlag )
	{
		stateB->linearVelocity = b2MulAdd( stateB->linearVelocity, mB, P );
		stateB->angularVelocity += iB * LB;
	}
}

void b2SolvePrismaticJoint( b2JointSim* base, b2StepContext* context, bool useBias )
{
	B2_ASSERT( base->type == b2_prismaticJoint );

	float mA = base->invMassA;
	float mB = base->invMassB;
	float iA = base->invIA;
	float iB = base->invIB;

	// dummy state for static bodies
	b2BodyState dummyState = b2_identityBodyState;

	b2PrismaticJoint* joint = &base->prismaticJoint;

	b2BodyState* stateA = joint->indexA == B2_NULL_INDEX ? &dummyState : context->states + joint->indexA;
	b2BodyState* stateB = joint->indexB == B2_NULL_INDEX ? &dummyState : context->states + joint->indexB;

	b2Vec2 vA = stateA->linearVelocity;
	float wA = stateA->angularVelocity;
	b2Vec2 vB = stateB->linearVelocity;
	float wB = stateB->angularVelocity;

	b2Rot qA = b2MulRot( stateA->deltaRotation, joint->frameA.q );
	b2Rot qB = b2MulRot( stateB->deltaRotation, joint->frameB.q );
	b2Rot relQ = b2InvMulRot( qA, qB );

	// current anchors
	b2Vec2 rA = b2RotateVector( stateA->deltaRotation, joint->frameA.p );
	b2Vec2 rB = b2RotateVector( stateB->deltaRotation, joint->frameB.p );

	b2Vec2 d = b2Add( b2Add( b2Sub( stateB->deltaPosition, stateA->deltaPosition ), joint->deltaCenter ), b2Sub( rB, rA ) );

	b2Vec2 axisA = b2RotateVector( joint->frameA.q, (b2Vec2){ 1.0f, 0.0f } );
	axisA = b2RotateVector( stateA->deltaRotation, axisA );
	float translation = b2Dot( axisA, d );

	// These scalars are for torques generated by axial forces
	float a1 = b2Cross( b2Add( rA, d ), axisA );
	float a2 = b2Cross( rB, axisA );

	float k = mA + mB + iA * a1 * a1 + iB * a2 * a2;
	float axialMass = k > 0.0f ? 1.0f / k : 0.0f;

	b2Softness softness = base->constraintSoftness;

	// spring constraint
	if ( joint->enableSpring )
	{
		// This is a real spring and should be applied even during relax
		float C = translation - joint->targetTranslation;
		float bias = joint->springSoftness.biasRate * C;
		float massScale = joint->springSoftness.massScale;
		float impulseScale = joint->springSoftness.impulseScale;

		float Cdot = b2Dot( axisA, b2Sub( vB, vA ) ) + a2 * wB - a1 * wA;
		float deltaImpulse = -massScale * axialMass * ( Cdot + bias ) - impulseScale * joint->springImpulse;
		joint->springImpulse += deltaImpulse;

		b2Vec2 P = b2MulSV( deltaImpulse, axisA );
		float LA = deltaImpulse * a1;
		float LB = deltaImpulse * a2;

		vA = b2MulSub( vA, mA, P );
		wA -= iA * LA;
		vB = b2MulAdd( vB, mB, P );
		wB += iB * LB;
	}

	// Solve motor constraint
	if ( joint->enableMotor )
	{
		float Cdot = b2Dot( axisA, b2Sub( vB, vA ) ) + a2 * wB - a1 * wA;
		float impulse = axialMass * ( joint->motorSpeed - Cdot );
		float oldImpulse = joint->motorImpulse;
		float maxImpulse = context->h * joint->maxMotorForce;
		joint->motorImpulse = b2ClampFloat( joint->motorImpulse + impulse, -maxImpulse, maxImpulse );
		impulse = joint->motorImpulse - oldImpulse;

		b2Vec2 P = b2MulSV( impulse, axisA );
		float LA = impulse * a1;
		float LB = impulse * a2;

		vA = b2MulSub( vA, mA, P );
		wA -= iA * LA;
		vB = b2MulAdd( vB, mB, P );
		wB += iB * LB;
	}

	if ( joint->enableLimit )
	{
		// Clamp the speculative distance to a reasonable value
		float speculativeDistance = 0.25f * ( joint->upperTranslation - joint->lowerTranslation );

		// Lower limit
		{
			float C = translation - joint->lowerTranslation;

			if ( C < speculativeDistance )
			{
				float bias = 0.0f;
				float massScale = 1.0f;
				float impulseScale = 0.0f;

				if ( C > 0.0f )
				{
					// speculation
					float safe = b2_lengthUnitsPerMeter;
					bias = b2MinFloat( C, safe ) * context->inv_h;
				}
				else if ( useBias )
				{
					bias = softness.biasRate * C;
					massScale = softness.massScale;
					impulseScale = softness.impulseScale;
				}

				float oldImpulse = joint->lowerImpulse;
				float Cdot = b2Dot( axisA, b2Sub( vB, vA ) ) + a2 * wB - a1 * wA;
				float deltaImpulse = -axialMass * massScale * ( Cdot + bias ) - impulseScale * oldImpulse;
				joint->lowerImpulse = b2MaxFloat( oldImpulse + deltaImpulse, 0.0f );
				deltaImpulse = joint->lowerImpulse - oldImpulse;

				b2Vec2 P = b2MulSV( deltaImpulse, axisA );
				float LA = deltaImpulse * a1;
				float LB = deltaImpulse * a2;

				vA = b2MulSub( vA, mA, P );
				wA -= iA * LA;
				vB = b2MulAdd( vB, mB, P );
				wB += iB * LB;
			}
			else
			{
				joint->lowerImpulse = 0.0f;
			}
		}

		// Upper limit
		// Note: signs are flipped to keep C positive when the constraint is satisfied.
		// This also keeps the impulse positive when the limit is active.
		{
			// sign flipped
			float C = joint->upperTranslation - translation;

			if ( C < speculativeDistance )
			{
				float bias = 0.0f;
				float massScale = 1.0f;
				float impulseScale = 0.0f;

				if ( C > 0.0f )
				{
					// speculation
					float safe = b2_lengthUnitsPerMeter;
					bias = b2MinFloat( C, safe ) * context->inv_h;
				}
				else if ( useBias )
				{
					bias = softness.biasRate * C;
					massScale = softness.massScale;
					impulseScale = softness.impulseScale;
				}

				float oldImpulse = joint->upperImpulse;

				// sign flipped
				float Cdot = b2Dot( axisA, b2Sub( vA, vB ) ) + a1 * wA - a2 * wB;
				float deltaImpulse = -axialMass * massScale * ( Cdot + bias ) - impulseScale * oldImpulse;
				joint->upperImpulse = b2MaxFloat( oldImpulse + deltaImpulse, 0.0f );
				deltaImpulse = joint->upperImpulse - oldImpulse;

				b2Vec2 P = b2MulSV( deltaImpulse, axisA );
				float LA = deltaImpulse * a1;
				float LB = deltaImpulse * a2;

				// sign flipped
				vA = b2MulAdd( vA, mA, P );
				wA += iA * LA;
				vB = b2MulSub( vB, mB, P );
				wB -= iB * LB;
			}
			else
			{
				joint->upperImpulse = 0.0f;
			}
		}
	}

	// Solve the prismatic constraint in block form
	{
		b2Vec2 perpA = b2LeftPerp( axisA );

		// These scalars are for torques generated by the perpendicular constraint force
		float s1 = b2Cross( b2Add( d, rA ), perpA );
		float s2 = b2Cross( rB, perpA );

		b2Vec2 Cdot;
		Cdot.x = b2Dot( perpA, b2Sub( vB, vA ) ) + s2 * wB - s1 * wA;
		Cdot.y = wB - wA;

		b2Vec2 bias = b2Vec2_zero;
		float massScale = 1.0f;
		float impulseScale = 0.0f;
		if ( useBias )
		{
			b2Vec2 C;
			C.x = b2Dot( perpA, d );
			C.y = b2Rot_GetAngle( relQ );

			bias = b2MulSV( softness.biasRate, C );
			massScale = softness.massScale;
			impulseScale = softness.impulseScale;
		}

		float k11 = mA + mB + iA * s1 * s1 + iB * s2 * s2;
		float k12 = iA * s1 + iB * s2;
		float k22 = iA + iB;
		if ( k22 == 0.0f )
		{
			// For bodies with fixed rotation.
			k22 = 1.0f;
		}

		b2Mat22 K = { { k11, k12 }, { k12, k22 } };

		b2Vec2 b = b2Solve22( K, b2Add( Cdot, bias ) );
		b2Vec2 deltaImpulse;
		deltaImpulse.x = -massScale * b.x - impulseScale * joint->impulse.x;
		deltaImpulse.y = -massScale * b.y - impulseScale * joint->impulse.y;

		joint->impulse.x += deltaImpulse.x;
		joint->impulse.y += deltaImpulse.y;

		b2Vec2 P = b2MulSV( deltaImpulse.x, perpA );
		float LA = deltaImpulse.x * s1 + deltaImpulse.y;
		float LB = deltaImpulse.x * s2 + deltaImpulse.y;

		vA = b2MulSub( vA, mA, P );
		wA -= iA * LA;
		vB = b2MulAdd( vB, mB, P );
		wB += iB * LB;
	}

	B2_ASSERT( b2IsValidVec2( vA ) );
	B2_ASSERT( b2IsValidFloat( wA ) );
	B2_ASSERT( b2IsValidVec2( vB ) );
	B2_ASSERT( b2IsValidFloat( wB ) );

	if ( stateA->flags & b2_dynamicFlag )
	{
		stateA->linearVelocity = vA;
		stateA->angularVelocity = wA;
	}

	if ( stateB->flags & b2_dynamicFlag )
	{
		stateB->linearVelocity = vB;
		stateB->angularVelocity = wB;
	}
}

#if 0
void b2PrismaticJoint::Dump()
{
	int32 indexA = joint->bodyA->joint->islandIndex;
	int32 indexB = joint->bodyB->joint->islandIndex;

	b2Dump("  b2PrismaticJointDef jd;\n");
	b2Dump("  jd.bodyA = sims[%d];\n", indexA);
	b2Dump("  jd.bodyB = sims[%d];\n", indexB);
	b2Dump("  jd.collideConnected = bool(%d);\n", joint->collideConnected);
	b2Dump("  jd.localAnchorA.Set(%.9g, %.9g);\n", joint->localAnchorA.x, joint->localAnchorA.y);
	b2Dump("  jd.localAnchorB.Set(%.9g, %.9g);\n", joint->localAnchorB.x, joint->localAnchorB.y);
	b2Dump("  jd.referenceAngle = %.9g;\n", joint->referenceAngle);
	b2Dump("  jd.enableLimit = bool(%d);\n", joint->enableLimit);
	b2Dump("  jd.lowerAngle = %.9g;\n", joint->lowerAngle);
	b2Dump("  jd.upperAngle = %.9g;\n", joint->upperAngle);
	b2Dump("  jd.enableMotor = bool(%d);\n", joint->enableMotor);
	b2Dump("  jd.motorSpeed = %.9g;\n", joint->motorSpeed);
	b2Dump("  jd.maxMotorTorque = %.9g;\n", joint->maxMotorTorque);
	b2Dump("  joints[%d] = joint->world->CreateJoint(&jd);\n", joint->index);
}
#endif

void b2DrawPrismaticJoint( b2DebugDraw* draw, b2JointSim* base, b2Transform transformA, b2Transform transformB, float drawScale )
{
	B2_ASSERT( base->type == b2_prismaticJoint );

	b2PrismaticJoint* joint = &base->prismaticJoint;

	b2Transform frameA = b2MulTransforms( transformA, base->localFrameA );
	b2Transform frameB = b2MulTransforms( transformB, base->localFrameB );
	b2Vec2 axisA = b2RotateVector( frameA.q, (b2Vec2){ 1.0f, 0.0f } );

	draw->DrawLineFcn( frameA.p, frameB.p, b2_colorDimGray, draw->context );

	if ( joint->enableLimit )
	{
		float b = 0.25f * drawScale;
		b2Vec2 lower = b2MulAdd( frameA.p, joint->lowerTranslation, axisA );
		b2Vec2 upper = b2MulAdd( frameA.p, joint->upperTranslation, axisA );
		b2Vec2 perp = b2LeftPerp( axisA );
		draw->DrawLineFcn( lower, upper, b2_colorGray, draw->context );
		draw->DrawLineFcn( b2MulSub( lower, b, perp ), b2MulAdd( lower, b, perp ), b2_colorGreen, draw->context );
		draw->DrawLineFcn( b2MulSub( upper, b, perp ), b2MulAdd( upper, b, perp ), b2_colorRed, draw->context );
	}
	else
	{
		draw->DrawLineFcn( b2MulSub( frameA.p, 1.0f, axisA ), b2MulAdd( frameA.p, 1.0f, axisA ), b2_colorGray, draw->context );
	}

	if ( joint->enableSpring )
	{
		b2Vec2 p = b2MulAdd( frameA.p, joint->targetTranslation, axisA );
		draw->DrawPointFcn( p, 8.0f, b2_colorViolet, draw->context );
	}

	draw->DrawPointFcn( frameA.p, 5.0f, b2_colorGray, draw->context );
	draw->DrawPointFcn( frameB.p, 5.0f, b2_colorBlue, draw->context );
}