text: /*
  * Copyright (c) 2007-2011 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 <Dynamics/Joints/b2RopeJoint.h>
  #include <Dynamics/b2Body.h>
  #include <Dynamics/b2TimeStep.h>
  
  
  // Limit:
  // C = norm(pB - pA) - L
  // u = (pB - pA) / norm(pB - pA)
  // Cdot = dot(u, vB + cross(wB, rB) - vA - cross(wA, rA))
  // J = [-u -cross(rA, u) u cross(rB, u)]
  // K = J * invM * JT
  //   = invMassA + invIA * cross(rA, u)^2 + invMassB + invIB * cross(rB, u)^2
  
  b2RopeJoint::b2RopeJoint(const b2RopeJointDef* def)
  : b2Joint(def)
  {
  	m_localAnchorA = def->localAnchorA;
  	m_localAnchorB = def->localAnchorB;
  
  	m_maxLength = def->maxLength;
  
  	m_mass = 0.0f;
  	m_impulse = 0.0f;
  	m_state = e_inactiveLimit;
  	m_length = 0.0f;
  }
  
  void b2RopeJoint::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);
  	m_u = cB + m_rB - cA - m_rA;
  
  	m_length = m_u.Length();
  
  	float32 C = m_length - m_maxLength;
  	if (C > 0.0f)
  	{
  		m_state = e_atUpperLimit;
  	}
  	else
  	{
  		m_state = e_inactiveLimit;
  	}
  
  	if (m_length > b2_linearSlop)
  	{
  		m_u *= 1.0f / m_length;
  	}
  	else
  	{
  		m_u.SetZero();
  		m_mass = 0.0f;
  		m_impulse = 0.0f;
  		return;
  	}
  
  	// Compute effective mass.
  	float32 crA = b2Cross(m_rA, m_u);
  	float32 crB = b2Cross(m_rB, m_u);
  	float32 invMass = m_invMassA + m_invIA * crA * crA + m_invMassB + m_invIB * crB * crB;
  
  	m_mass = invMass != 0.0f ? 1.0f / invMass : 0.0f;
  
  	if (data.step.warmStarting)
  	{
  		// Scale the impulse to support a variable time step.
  		m_impulse *= data.step.dtRatio;
  
  		b2Vec2 P = m_impulse * m_u;
  		vA -= m_invMassA * P;
  		wA -= m_invIA * b2Cross(m_rA, P);
  		vB += m_invMassB * P;
  		wB += m_invIB * b2Cross(m_rB, P);
  	}
  	else
  	{
  		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 b2RopeJoint::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;
  
  	// Cdot = dot(u, v + cross(w, r))
  	b2Vec2 vpA = vA + b2Cross(wA, m_rA);
  	b2Vec2 vpB = vB + b2Cross(wB, m_rB);
  	float32 C = m_length - m_maxLength;
  	float32 Cdot = b2Dot(m_u, vpB - vpA);
  
  	// Predictive constraint.
  	if (C < 0.0f)
  	{
  		Cdot += data.step.inv_dt * C;
  	}
  
  	float32 impulse = -m_mass * Cdot;
  	float32 oldImpulse = m_impulse;
  	m_impulse = b2Min(0.0f, m_impulse + impulse);
  	impulse = m_impulse - oldImpulse;
  
  	b2Vec2 P = impulse * m_u;
  	vA -= m_invMassA * P;
  	wA -= m_invIA * b2Cross(m_rA, P);
  	vB += m_invMassB * P;
  	wB += m_invIB * b2Cross(m_rB, P);
  
  	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 b2RopeJoint::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 u = cB + rB - cA - rA;
  
  	float32 length = u.Normalize();
  	float32 C = length - m_maxLength;
  
  	C = b2Clamp(C, 0.0f, b2_maxLinearCorrection);
  
  	float32 impulse = -m_mass * C;
  	b2Vec2 P = impulse * u;
  
  	cA -= m_invMassA * P;
  	aA -= m_invIA * b2Cross(rA, P);
  	cB += m_invMassB * P;
  	aB += m_invIB * b2Cross(rB, P);
  
  	data.positions[m_indexA].c = cA;
  	data.positions[m_indexA].a = aA;
  	data.positions[m_indexB].c = cB;
  	data.positions[m_indexB].a = aB;
  
  	return length - m_maxLength < b2_linearSlop;
  }
  
  b2Vec2 b2RopeJoint::GetAnchorA() const
  {
  	return m_bodyA->GetWorldPoint(m_localAnchorA);
  }
  
  b2Vec2 b2RopeJoint::GetAnchorB() const
  {
  	return m_bodyB->GetWorldPoint(m_localAnchorB);
  }
  
  b2Vec2 b2RopeJoint::GetReactionForce(float32 inv_dt) const
  {
  	b2Vec2 F = (inv_dt * m_impulse) * m_u;
  	return F;
  }
  
  float32 b2RopeJoint::GetReactionTorque(float32 inv_dt) const
  {
  	B2_NOT_USED(inv_dt);
  	return 0.0f;
  }
  
  float32 b2RopeJoint::GetMaxLength() const
  {
  	return m_maxLength;
  }
  
  b2LimitState b2RopeJoint::GetLimitState() const
  {
  	return m_state;
  }
  
  void b2RopeJoint::Dump()
  {
  	int32 indexA = m_bodyA->m_islandIndex;
  	int32 indexB = m_bodyB->m_islandIndex;
  
  	b2Log("  b2RopeJointDef 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.maxLength = %.15lef;\n", m_maxLength);
  	b2Log("  joints[%d] = m_world->CreateJoint(&jd);\n", m_index);
  }
  