text: /*
  * Copyright (c) 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 "b2PulleyJoint.h"
  #include "../b2Body.h"
  #include "../b2TimeStep.h"
  
  // Pulley:
  // length1 = norm(p1 - s1)
  // length2 = norm(p2 - s2)
  // C0 = (length1 + ratio * length2)_initial
  // C = C0 - (length1 + ratio * length2)
  // u1 = (p1 - s1) / norm(p1 - s1)
  // u2 = (p2 - s2) / norm(p2 - s2)
  // Cdot = -dot(u1, v1 + cross(w1, r1)) - ratio * dot(u2, v2 + cross(w2, r2))
  // J = -[u1 cross(r1, u1) ratio * u2  ratio * cross(r2, u2)]
  // K = J * invM * JT
  //   = invMass1 + invI1 * cross(r1, u1)^2 + ratio^2 * (invMass2 + invI2 * cross(r2, u2)^2)
  
  void b2PulleyJointDef::Initialize(b2Body* bA, b2Body* bB,
  				const b2Vec2& groundA, const b2Vec2& groundB,
  				const b2Vec2& anchorA, const b2Vec2& anchorB,
  				float32 r)
  {
  	bodyA = bA;
  	bodyB = bB;
  	groundAnchorA = groundA;
  	groundAnchorB = groundB;
  	localAnchorA = bodyA->GetLocalPoint(anchorA);
  	localAnchorB = bodyB->GetLocalPoint(anchorB);
  	b2Vec2 dA = anchorA - groundA;
  	lengthA = dA.Length();
  	b2Vec2 dB = anchorB - groundB;
  	lengthB = dB.Length();
  	ratio = r;
  	b2Assert(ratio > b2_epsilon);
  }
  
  b2PulleyJoint::b2PulleyJoint(const b2PulleyJointDef* def)
  : b2Joint(def)
  {
  	m_groundAnchorA = def->groundAnchorA;
  	m_groundAnchorB = def->groundAnchorB;
  	m_localAnchorA = def->localAnchorA;
  	m_localAnchorB = def->localAnchorB;
  
  	m_lengthA = def->lengthA;
  	m_lengthB = def->lengthB;
  
  	b2Assert(def->ratio != 0.0f);
  	m_ratio = def->ratio;
  
  	m_constant = def->lengthA + m_ratio * def->lengthB;
  
  	m_impulse = 0.0f;
  }
  
  void b2PulleyJoint::InitVelocityConstraints(const b2SolverData& data)
  {
  	m_indexA = m_bodyA->m_islandIndex;
  	m_indexB = m_bodyB->m_islandIndex;
  	m_localCenterA = m_bodyA->m_sweep.localCenter;
  	m_localCenterB = m_bodyB->m_sweep.localCenter;
  	m_invMassA = m_bodyA->m_invMass;
  	m_invMassB = m_bodyB->m_invMass;
  	m_invIA = m_bodyA->m_invI;
  	m_invIB = m_bodyB->m_invI;
  
  	b2Vec2 cA = data.positions[m_indexA].c;
  	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);
  
  	m_rA = b2Mul(qA, m_localAnchorA - m_localCenterA);
  	m_rB = b2Mul(qB, m_localAnchorB - m_localCenterB);
  
  	// Get the pulley axes.
  	m_uA = cA + m_rA - m_groundAnchorA;
  	m_uB = cB + m_rB - m_groundAnchorB;
  
  	float32 lengthA = m_uA.Length();
  	float32 lengthB = m_uB.Length();
  
  	if (lengthA > 10.0f * b2_linearSlop)
  	{
  		m_uA *= 1.0f / lengthA;
  	}
  	else
  	{
  		m_uA.SetZero();
  	}
  
  	if (lengthB > 10.0f * b2_linearSlop)
  	{
  		m_uB *= 1.0f / lengthB;
  	}
  	else
  	{
  		m_uB.SetZero();
  	}
  
  	// Compute effective mass.
  	float32 ruA = b2Cross(m_rA, m_uA);
  	float32 ruB = b2Cross(m_rB, m_uB);
  
  	float32 mA = m_invMassA + m_invIA * ruA * ruA;
  	float32 mB = m_invMassB + m_invIB * ruB * ruB;
  
  	m_mass = mA + m_ratio * m_ratio * mB;
  
  	if (m_mass > 0.0f)
  	{
  		m_mass = 1.0f / m_mass;
  	}
  
  	if (data.step.warmStarting)
  	{
  		// Scale impulses to support variable time steps.
  		m_impulse *= data.step.dtRatio;
  
  		// Warm starting.
  		b2Vec2 PA = -(m_impulse) * m_uA;
  		b2Vec2 PB = (-m_ratio * m_impulse) * m_uB;
  
  		vA += m_invMassA * PA;
  		wA += m_invIA * b2Cross(m_rA, PA);
  		vB += m_invMassB * PB;
  		wB += m_invIB * b2Cross(m_rB, PB);
  	}
  	else
  	{
  		m_impulse = 0.0f;
  	}
  
  	data.velocities[m_indexA].v = vA;
  	data.velocities[m_indexA].w = wA;
  	data.velocities[m_indexB].v = vB;
  	data.velocities[m_indexB].w = wB;
  }
  
  void b2PulleyJoint::SolveVelocityConstraints(const b2SolverData& data)
  {
  	b2Vec2 vA = data.velocities[m_indexA].v;
  	float32 wA = data.velocities[m_indexA].w;
  	b2Vec2 vB = data.velocities[m_indexB].v;
  	float32 wB = data.velocities[m_indexB].w;
  
  	b2Vec2 vpA = vA + b2Cross(wA, m_rA);
  	b2Vec2 vpB = vB + b2Cross(wB, m_rB);
  
  	float32 Cdot = -b2Dot(m_uA, vpA) - m_ratio * b2Dot(m_uB, vpB);
  	float32 impulse = -m_mass * Cdot;
  	m_impulse += impulse;
  
  	b2Vec2 PA = -impulse * m_uA;
  	b2Vec2 PB = -m_ratio * impulse * m_uB;
  	vA += m_invMassA * PA;
  	wA += m_invIA * b2Cross(m_rA, PA);
  	vB += m_invMassB * PB;
  	wB += m_invIB * b2Cross(m_rB, PB);
  
  	data.velocities[m_indexA].v = vA;
  	data.velocities[m_indexA].w = wA;
  	data.velocities[m_indexB].v = vB;
  	data.velocities[m_indexB].w = wB;
  }
  
  bool b2PulleyJoint::SolvePositionConstraints(const b2SolverData& data)
  {
  	b2Vec2 cA = data.positions[m_indexA].c;
  	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);
  
  	// Get the pulley axes.
  	b2Vec2 uA = cA + rA - m_groundAnchorA;
  	b2Vec2 uB = cB + rB - m_groundAnchorB;
  
  	float32 lengthA = uA.Length();
  	float32 lengthB = uB.Length();
  
  	if (lengthA > 10.0f * b2_linearSlop)
  	{
  		uA *= 1.0f / lengthA;
  	}
  	else
  	{
  		uA.SetZero();
  	}
  
  	if (lengthB > 10.0f * b2_linearSlop)
  	{
  		uB *= 1.0f / lengthB;
  	}
  	else
  	{
  		uB.SetZero();
  	}
  
  	// Compute effective mass.
  	float32 ruA = b2Cross(rA, uA);
  	float32 ruB = b2Cross(rB, uB);
  
  	float32 mA = m_invMassA + m_invIA * ruA * ruA;
  	float32 mB = m_invMassB + m_invIB * ruB * ruB;
  
  	float32 mass = mA + m_ratio * m_ratio * mB;
  
  	if (mass > 0.0f)
  	{
  		mass = 1.0f / mass;
  	}
  
  	float32 C = m_constant - lengthA - m_ratio * lengthB;
  	float32 linearError = b2Abs(C);
  
  	float32 impulse = -mass * C;
  
  	b2Vec2 PA = -impulse * uA;
  	b2Vec2 PB = -m_ratio * impulse * uB;
  
  	cA += m_invMassA * PA;
  	aA += m_invIA * b2Cross(rA, PA);
  	cB += m_invMassB * PB;
  	aB += m_invIB * b2Cross(rB, PB);
  
  	data.positions[m_indexA].c = cA;
  	data.positions[m_indexA].a = aA;
  	data.positions[m_indexB].c = cB;
  	data.positions[m_indexB].a = aB;
  
  	return linearError < b2_linearSlop;
  }
  
  b2Vec2 b2PulleyJoint::GetAnchorA() const
  {
  	return m_bodyA->GetWorldPoint(m_localAnchorA);
  }
  
  b2Vec2 b2PulleyJoint::GetAnchorB() const
  {
  	return m_bodyB->GetWorldPoint(m_localAnchorB);
  }
  
  b2Vec2 b2PulleyJoint::GetReactionForce(float32 inv_dt) const
  {
  	b2Vec2 P = m_impulse * m_uB;
  	return inv_dt * P;
  }
  
  float32 b2PulleyJoint::GetReactionTorque(float32 inv_dt) const
  {
  	B2_NOT_USED(inv_dt);
  	return 0.0f;
  }
  
  b2Vec2 b2PulleyJoint::GetGroundAnchorA() const
  {
  	return m_groundAnchorA;
  }
  
  b2Vec2 b2PulleyJoint::GetGroundAnchorB() const
  {
  	return m_groundAnchorB;
  }
  
  float32 b2PulleyJoint::GetLengthA() const
  {
  	b2Vec2 p = m_bodyA->GetWorldPoint(m_localAnchorA);
  	b2Vec2 s = m_groundAnchorA;
  	b2Vec2 d = p - s;
  	return d.Length();
  }
  
  float32 b2PulleyJoint::GetLengthB() const
  {
  	b2Vec2 p = m_bodyB->GetWorldPoint(m_localAnchorB);
  	b2Vec2 s = m_groundAnchorB;
  	b2Vec2 d = p - s;
  	return d.Length();
  }
  
  float32 b2PulleyJoint::GetRatio() const
  {
  	return m_ratio;
  }
  
  void b2PulleyJoint::Dump()
  {
  	int32 indexA = m_bodyA->m_islandIndex;
  	int32 indexB = m_bodyB->m_islandIndex;
  
  	b2Log("  b2PulleyJointDef 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.groundAnchorA.Set(%.15lef, %.15lef);\n", m_groundAnchorA.x, m_groundAnchorA.y);
  	b2Log("  jd.groundAnchorB.Set(%.15lef, %.15lef);\n", m_groundAnchorB.x, m_groundAnchorB.y);
  	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.lengthA = %.15lef;\n", m_lengthA);
  	b2Log("  jd.lengthB = %.15lef;\n", m_lengthB);
  	b2Log("  jd.ratio = %.15lef;\n", m_ratio);
  	b2Log("  joints[%d] = m_world->CreateJoint(&jd);\n", m_index);
  }
  