text: /*
  * Copyright (c) 2006-2007 Erin Catto http://www.box2d.org
  *
  * This software is provided 'as-is', without any express or implied
  * warranty.  In no event will the authors be held liable for any damages
  * arising from the use of this software.
  * Permission is granted to anyone to use this software for any purpose,
  * including commercial applications, and to alter it and redistribute it
  * freely, subject to the following restrictions:
  * 1. The origin of this software must not be misrepresented; you must not
  * claim that you wrote the original software. If you use this software
  * in a product, an acknowledgment in the product documentation would be
  * appreciated but is not required.
  * 2. Altered source versions must be plainly marked as such, and must not be
  * misrepresented as being the original software.
  * 3. This notice may not be removed or altered from any source distribution.
  */
  
  #include <XMBox2D/Dynamics/Joints/b2WheelJoint.h>
  #include <XMBox2D/Dynamics/b2Body.h>
  #include <XMBox2D/Dynamics/b2TimeStep.h>
  
  // Linear constraint (point-to-line)
  // d = pB - pA = xB + rB - xA - rA
  // C = dot(ay, d)
  // Cdot = dot(d, cross(wA, ay)) + dot(ay, vB + cross(wB, rB) - vA - cross(wA, rA))
  //      = -dot(ay, vA) - dot(cross(d + rA, ay), wA) + dot(ay, vB) + dot(cross(rB, ay), vB)
  // J = [-ay, -cross(d + rA, ay), ay, cross(rB, ay)]
  
  // Spring linear constraint
  // C = dot(ax, d)
  // Cdot = = -dot(ax, vA) - dot(cross(d + rA, ax), wA) + dot(ax, vB) + dot(cross(rB, ax), vB)
  // J = [-ax -cross(d+rA, ax) ax cross(rB, ax)]
  
  // Motor rotational constraint
  // Cdot = wB - wA
  // J = [0 0 -1 0 0 1]
  
  void b2WheelJointDef::Initialize(b2Body* bA, b2Body* bB, const b2Vec2& anchor, const b2Vec2& axis)
  {
  	bodyA = bA;
  	bodyB = bB;
  	localAnchorA = bodyA->GetLocalPoint(anchor);
  	localAnchorB = bodyB->GetLocalPoint(anchor);
  	localAxisA = bodyA->GetLocalVector(axis);
  }
  
  b2WheelJoint::b2WheelJoint(const b2WheelJointDef* def)
  : b2Joint(def)
  {
  	m_localAnchorA = def->localAnchorA;
  	m_localAnchorB = def->localAnchorB;
  	m_localXAxisA = def->localAxisA;
  	m_localYAxisA = b2Cross(1.0f, m_localXAxisA);
  
  	m_mass = 0.0f;
  	m_impulse = 0.0f;
  	m_motorMass = 0.0;
  	m_motorImpulse = 0.0f;
  	m_springMass = 0.0f;
  	m_springImpulse = 0.0f;
  
  	m_maxMotorTorque = def->maxMotorTorque;
  	m_motorSpeed = def->motorSpeed;
  	m_enableMotor = def->enableMotor;
  
  	m_frequencyHz = def->frequencyHz;
  	m_dampingRatio = def->dampingRatio;
  
  	m_bias = 0.0f;
  	m_gamma = 0.0f;
  
  	m_ax.SetZero();
  	m_ay.SetZero();
  }
  
  void b2WheelJoint::InitVelocityConstraints(const b2SolverData& data)
  {
  	m_indexA = m_bodyA->m_islandIndex;
  	m_indexB = m_bodyB->m_islandIndex;
  	m_localCenterA = m_bodyA->m_sweep.localCenter;
  	m_localCenterB = m_bodyB->m_sweep.localCenter;
  	m_invMassA = m_bodyA->m_invMass;
  	m_invMassB = m_bodyB->m_invMass;
  	m_invIA = m_bodyA->m_invI;
  	m_invIB = m_bodyB->m_invI;
  
  	float32 mA = m_invMassA, mB = m_invMassB;
  	float32 iA = m_invIA, iB = m_invIB;
  
  	b2Vec2 cA = data.positions[m_indexA].c;
  	float32 aA = data.positions[m_indexA].a;
  	b2Vec2 vA = data.velocities[m_indexA].v;
  	float32 wA = data.velocities[m_indexA].w;
  
  	b2Vec2 cB = data.positions[m_indexB].c;
  	float32 aB = data.positions[m_indexB].a;
  	b2Vec2 vB = data.velocities[m_indexB].v;
  	float32 wB = data.velocities[m_indexB].w;
  
  	b2Rot qA(aA), qB(aB);
  
  	// Compute the effective masses.
  	b2Vec2 rA = b2Mul(qA, m_localAnchorA - m_localCenterA);
  	b2Vec2 rB = b2Mul(qB, m_localAnchorB - m_localCenterB);
  	b2Vec2 d = cB + rB - cA - rA;
  
  	// Point to line constraint
  	{
  		m_ay = b2Mul(qA, m_localYAxisA);
  		m_sAy = b2Cross(d + rA, m_ay);
  		m_sBy = b2Cross(rB, m_ay);
  
  		m_mass = mA + mB + iA * m_sAy * m_sAy + iB * m_sBy * m_sBy;
  
  		if (m_mass > 0.0f)
  		{
  			m_mass = 1.0f / m_mass;
  		}
  	}
  
  	// Spring constraint
  	m_springMass = 0.0f;
  	m_bias = 0.0f;
  	m_gamma = 0.0f;
  	if (m_frequencyHz > 0.0f)
  	{
  		m_ax = b2Mul(qA, m_localXAxisA);
  		m_sAx = b2Cross(d + rA, m_ax);
  		m_sBx = b2Cross(rB, m_ax);
  
  		float32 invMass = mA + mB + iA * m_sAx * m_sAx + iB * m_sBx * m_sBx;
  
  		if (invMass > 0.0f)
  		{
  			m_springMass = 1.0f / invMass;
  
  			float32 C = b2Dot(d, m_ax);
  
  			// Frequency
  			float32 omega = 2.0f * b2_pi * m_frequencyHz;
  
  			// Damping coefficient
  			float32 d = 2.0f * m_springMass * m_dampingRatio * omega;
  
  			// Spring stiffness
  			float32 k = m_springMass * omega * omega;
  
  			// magic formulas
  			float32 h = data.step.dt;
  			m_gamma = h * (d + h * k);
  			if (m_gamma > 0.0f)
  			{
  				m_gamma = 1.0f / m_gamma;
  			}
  
  			m_bias = C * h * k * m_gamma;
  
  			m_springMass = invMass + m_gamma;
  			if (m_springMass > 0.0f)
  			{
  				m_springMass = 1.0f / m_springMass;
  			}
  		}
  	}
  	else
  	{
  		m_springImpulse = 0.0f;
  	}
  
  	// Rotational motor
  	if (m_enableMotor)
  	{
  		m_motorMass = iA + iB;
  		if (m_motorMass > 0.0f)
  		{
  			m_motorMass = 1.0f / m_motorMass;
  		}
  	}
  	else
  	{
  		m_motorMass = 0.0f;
  		m_motorImpulse = 0.0f;
  	}
  
  	if (data.step.warmStarting)
  	{
  		// Account for variable time step.
  		m_impulse *= data.step.dtRatio;
  		m_springImpulse *= data.step.dtRatio;
  		m_motorImpulse *= data.step.dtRatio;
  
  		b2Vec2 P = m_impulse * m_ay + m_springImpulse * m_ax;
  		float32 LA = m_impulse * m_sAy + m_springImpulse * m_sAx + m_motorImpulse;
  		float32 LB = m_impulse * m_sBy + m_springImpulse * m_sBx + m_motorImpulse;
  
  		vA -= m_invMassA * P;
  		wA -= m_invIA * LA;
  
  		vB += m_invMassB * P;
  		wB += m_invIB * LB;
  	}
  	else
  	{
  		m_impulse = 0.0f;
  		m_springImpulse = 0.0f;
  		m_motorImpulse = 0.0f;
  	}
  
  	data.velocities[m_indexA].v = vA;
  	data.velocities[m_indexA].w = wA;
  	data.velocities[m_indexB].v = vB;
  	data.velocities[m_indexB].w = wB;
  }
  
  void b2WheelJoint::SolveVelocityConstraints(const b2SolverData& data)
  {
  	float32 mA = m_invMassA, mB = m_invMassB;
  	float32 iA = m_invIA, iB = m_invIB;
  
  	b2Vec2 vA = data.velocities[m_indexA].v;
  	float32 wA = data.velocities[m_indexA].w;
  	b2Vec2 vB = data.velocities[m_indexB].v;
  	float32 wB = data.velocities[m_indexB].w;
  
  	// Solve spring constraint
  	{
  		float32 Cdot = b2Dot(m_ax, vB - vA) + m_sBx * wB - m_sAx * wA;
  		float32 impulse = -m_springMass * (Cdot + m_bias + m_gamma * m_springImpulse);
  		m_springImpulse += impulse;
  
  		b2Vec2 P = impulse * m_ax;
  		float32 LA = impulse * m_sAx;
  		float32 LB = impulse * m_sBx;
  
  		vA -= mA * P;
  		wA -= iA * LA;
  
  		vB += mB * P;
  		wB += iB * LB;
  	}
  
  	// Solve rotational motor constraint
  	{
  		float32 Cdot = wB - wA - m_motorSpeed;
  		float32 impulse = -m_motorMass * Cdot;
  
  		float32 oldImpulse = m_motorImpulse;
  		float32 maxImpulse = data.step.dt * m_maxMotorTorque;
  		m_motorImpulse = b2Clamp(m_motorImpulse + impulse, -maxImpulse, maxImpulse);
  		impulse = m_motorImpulse - oldImpulse;
  
  		wA -= iA * impulse;
  		wB += iB * impulse;
  	}
  
  	// Solve point to line constraint
  	{
  		float32 Cdot = b2Dot(m_ay, vB - vA) + m_sBy * wB - m_sAy * wA;
  		float32 impulse = -m_mass * Cdot;
  		m_impulse += impulse;
  
  		b2Vec2 P = impulse * m_ay;
  		float32 LA = impulse * m_sAy;
  		float32 LB = impulse * m_sBy;
  
  		vA -= mA * P;
  		wA -= iA * LA;
  
  		vB += mB * P;
  		wB += iB * LB;
  	}
  
  	data.velocities[m_indexA].v = vA;
  	data.velocities[m_indexA].w = wA;
  	data.velocities[m_indexB].v = vB;
  	data.velocities[m_indexB].w = wB;
  }
  
  bool b2WheelJoint::SolvePositionConstraints(const b2SolverData& data)
  {
  	b2Vec2 cA = data.positions[m_indexA].c;
  	float32 aA = data.positions[m_indexA].a;
  	b2Vec2 cB = data.positions[m_indexB].c;
  	float32 aB = data.positions[m_indexB].a;
  
  	b2Rot qA(aA), qB(aB);
  
  	b2Vec2 rA = b2Mul(qA, m_localAnchorA - m_localCenterA);
  	b2Vec2 rB = b2Mul(qB, m_localAnchorB - m_localCenterB);
  	b2Vec2 d = (cB - cA) + rB - rA;
  
  	b2Vec2 ay = b2Mul(qA, m_localYAxisA);
  
  	float32 sAy = b2Cross(d + rA, ay);
  	float32 sBy = b2Cross(rB, ay);
  
  	float32 C = b2Dot(d, ay);
  
  	float32 k = m_invMassA + m_invMassB + m_invIA * m_sAy * m_sAy + m_invIB * m_sBy * m_sBy;
  
  	float32 impulse;
  	if (k != 0.0f)
  	{
  		impulse = - C / k;
  	}
  	else
  	{
  		impulse = 0.0f;
  	}
  
  	b2Vec2 P = impulse * ay;
  	float32 LA = impulse * sAy;
  	float32 LB = impulse * sBy;
  
  	cA -= m_invMassA * P;
  	aA -= m_invIA * LA;
  	cB += m_invMassB * P;
  	aB += m_invIB * LB;
  
  	data.positions[m_indexA].c = cA;
  	data.positions[m_indexA].a = aA;
  	data.positions[m_indexB].c = cB;
  	data.positions[m_indexB].a = aB;
  
  	return b2Abs(C) <= b2_linearSlop;
  }
  
  b2Vec2 b2WheelJoint::GetAnchorA() const
  {
  	return m_bodyA->GetWorldPoint(m_localAnchorA);
  }
  
  b2Vec2 b2WheelJoint::GetAnchorB() const
  {
  	return m_bodyB->GetWorldPoint(m_localAnchorB);
  }
  
  b2Vec2 b2WheelJoint::GetReactionForce(float32 inv_dt) const
  {
  	return inv_dt * (m_impulse * m_ay + m_springImpulse * m_ax);
  }
  
  float32 b2WheelJoint::GetReactionTorque(float32 inv_dt) const
  {
  	return inv_dt * m_motorImpulse;
  }
  
  float32 b2WheelJoint::GetJointTranslation() const
  {
  	b2Body* bA = m_bodyA;
  	b2Body* bB = m_bodyB;
  
  	b2Vec2 pA = bA->GetWorldPoint(m_localAnchorA);
  	b2Vec2 pB = bB->GetWorldPoint(m_localAnchorB);
  	b2Vec2 d = pB - pA;
  	b2Vec2 axis = bA->GetWorldVector(m_localXAxisA);
  
  	float32 translation = b2Dot(d, axis);
  	return translation;
  }
  
  float32 b2WheelJoint::GetJointSpeed() const
  {
  	float32 wA = m_bodyA->m_angularVelocity;
  	float32 wB = m_bodyB->m_angularVelocity;
  	return wB - wA;
  }
  
  bool b2WheelJoint::IsMotorEnabled() const
  {
  	return m_enableMotor;
  }
  
  void b2WheelJoint::EnableMotor(bool flag)
  {
  	m_bodyA->SetAwake(true);
  	m_bodyB->SetAwake(true);
  	m_enableMotor = flag;
  }
  
  void b2WheelJoint::SetMotorSpeed(float32 speed)
  {
  	m_bodyA->SetAwake(true);
  	m_bodyB->SetAwake(true);
  	m_motorSpeed = speed;
  }
  
  void b2WheelJoint::SetMaxMotorTorque(float32 torque)
  {
  	m_bodyA->SetAwake(true);
  	m_bodyB->SetAwake(true);
  	m_maxMotorTorque = torque;
  }
  
  float32 b2WheelJoint::GetMotorTorque(float32 inv_dt) const
  {
  	return inv_dt * m_motorImpulse;
  }
  
  void b2WheelJoint::Dump()
  {
  	int32 indexA = m_bodyA->m_islandIndex;
  	int32 indexB = m_bodyB->m_islandIndex;
  
  	b2Log("  b2WheelJointDef jd;\n");
  	b2Log("  jd.bodyA = bodies[%d];\n", indexA);
  	b2Log("  jd.bodyB = bodies[%d];\n", indexB);
  	b2Log("  jd.collideConnected = bool(%d);\n", m_collideConnected);
  	b2Log("  jd.localAnchorA.Set(%.15lef, %.15lef);\n", m_localAnchorA.x, m_localAnchorA.y);
  	b2Log("  jd.localAnchorB.Set(%.15lef, %.15lef);\n", m_localAnchorB.x, m_localAnchorB.y);
  	b2Log("  jd.localAxisA.Set(%.15lef, %.15lef);\n", m_localXAxisA.x, m_localXAxisA.y);
  	b2Log("  jd.enableMotor = bool(%d);\n", m_enableMotor);
  	b2Log("  jd.motorSpeed = %.15lef;\n", m_motorSpeed);
  	b2Log("  jd.maxMotorTorque = %.15lef;\n", m_maxMotorTorque);
  	b2Log("  jd.frequencyHz = %.15lef;\n", m_frequencyHz);
  	b2Log("  jd.dampingRatio = %.15lef;\n", m_dampingRatio);
  	b2Log("  joints[%d] = m_world->CreateJoint(&jd);\n", m_index);
  }
  