text: /*
  * Copyright (c) 2006-2011 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 "b2WeldJoint.h"
  #include "../b2Body.h"
  #include "../b2TimeStep.h"
  
  // Point-to-point constraint
  // C = p2 - p1
  // Cdot = v2 - v1
  //      = v2 + cross(w2, r2) - v1 - cross(w1, r1)
  // J = [-I -r1_skew I r2_skew ]
  // Identity used:
  // w k % (rx i + ry j) = w * (-ry i + rx j)
  
  // Angle constraint
  // C = angle2 - angle1 - referenceAngle
  // Cdot = w2 - w1
  // J = [0 0 -1 0 0 1]
  // K = invI1 + invI2
  
  void b2WeldJointDef::Initialize(b2Body* bA, b2Body* bB, const b2Vec2& anchor)
  {
  	bodyA = bA;
  	bodyB = bB;
  	localAnchorA = bodyA->GetLocalPoint(anchor);
  	localAnchorB = bodyB->GetLocalPoint(anchor);
  	referenceAngle = bodyB->GetAngle() - bodyA->GetAngle();
  }
  
  b2WeldJoint::b2WeldJoint(const b2WeldJointDef* def)
  : b2Joint(def)
  {
  	m_localAnchorA = def->localAnchorA;
  	m_localAnchorB = def->localAnchorB;
  	m_referenceAngle = def->referenceAngle;
  	m_frequencyHz = def->frequencyHz;
  	m_dampingRatio = def->dampingRatio;
  
  	m_impulse.SetZero();
  }
  
  void b2WeldJoint::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 aA = data.positions[m_indexA].a;
  	b2Vec2 vA = data.velocities[m_indexA].v;
  	float32 wA = data.velocities[m_indexA].w;
  
  	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);
  
  	// J = [-I -r1_skew I r2_skew]
  	//     [ 0       -1 0       1]
  	// r_skew = [-ry; rx]
  
  	// Matlab
  	// K = [ mA+r1y^2*iA+mB+r2y^2*iB,  -r1y*iA*r1x-r2y*iB*r2x,          -r1y*iA-r2y*iB]
  	//     [  -r1y*iA*r1x-r2y*iB*r2x, mA+r1x^2*iA+mB+r2x^2*iB,           r1x*iA+r2x*iB]
  	//     [          -r1y*iA-r2y*iB,           r1x*iA+r2x*iB,                   iA+iB]
  
  	float32 mA = m_invMassA, mB = m_invMassB;
  	float32 iA = m_invIA, iB = m_invIB;
  
  	b2Mat33 K;
  	K.ex.x = mA + mB + m_rA.y * m_rA.y * iA + m_rB.y * m_rB.y * iB;
  	K.ey.x = -m_rA.y * m_rA.x * iA - m_rB.y * m_rB.x * iB;
  	K.ez.x = -m_rA.y * iA - m_rB.y * iB;
  	K.ex.y = K.ey.x;
  	K.ey.y = mA + mB + m_rA.x * m_rA.x * iA + m_rB.x * m_rB.x * iB;
  	K.ez.y = m_rA.x * iA + m_rB.x * iB;
  	K.ex.z = K.ez.x;
  	K.ey.z = K.ez.y;
  	K.ez.z = iA + iB;
  
  	if (m_frequencyHz > 0.0f)
  	{
  		K.GetInverse22(&m_mass);
  
  		float32 invM = iA + iB;
  		float32 m = invM > 0.0f ? 1.0f / invM : 0.0f;
  
  		float32 C = aB - aA - m_referenceAngle;
  
  		// Frequency
  		float32 omega = 2.0f * b2_pi * m_frequencyHz;
  
  		// Damping coefficient
  		float32 d = 2.0f * m * m_dampingRatio * omega;
  
  		// Spring stiffness
  		float32 k = m * omega * omega;
  
  		// magic formulas
  		float32 h = data.step.dt;
  		m_gamma = h * (d + h * k);
  		m_gamma = m_gamma != 0.0f ? 1.0f / m_gamma : 0.0f;
  		m_bias = C * h * k * m_gamma;
  
  		invM += m_gamma;
  		m_mass.ez.z = invM != 0.0f ? 1.0f / invM : 0.0f;
  	}
  	else
  	{
  		K.GetSymInverse33(&m_mass);
  		m_gamma = 0.0f;
  		m_bias = 0.0f;
  	}
  
  	if (data.step.warmStarting)
  	{
  		// Scale impulses to support a variable time step.
  		m_impulse *= data.step.dtRatio;
  
  		b2Vec2 P(m_impulse.x, m_impulse.y);
  
  		vA -= mA * P;
  		wA -= iA * (b2Cross(m_rA, P) + m_impulse.z);
  
  		vB += mB * P;
  		wB += iB * (b2Cross(m_rB, P) + m_impulse.z);
  	}
  	else
  	{
  		m_impulse.SetZero();
  	}
  
  	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 b2WeldJoint::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;
  
  	float32 mA = m_invMassA, mB = m_invMassB;
  	float32 iA = m_invIA, iB = m_invIB;
  
  	if (m_frequencyHz > 0.0f)
  	{
  		float32 Cdot2 = wB - wA;
  
  		float32 impulse2 = -m_mass.ez.z * (Cdot2 + m_bias + m_gamma * m_impulse.z);
  		m_impulse.z += impulse2;
  
  		wA -= iA * impulse2;
  		wB += iB * impulse2;
  
  		b2Vec2 Cdot1 = vB + b2Cross(wB, m_rB) - vA - b2Cross(wA, m_rA);
  
  		b2Vec2 impulse1 = -b2Mul22(m_mass, Cdot1);
  		m_impulse.x += impulse1.x;
  		m_impulse.y += impulse1.y;
  
  		b2Vec2 P = impulse1;
  
  		vA -= mA * P;
  		wA -= iA * b2Cross(m_rA, P);
  
  		vB += mB * P;
  		wB += iB * b2Cross(m_rB, P);
  	}
  	else
  	{
  		b2Vec2 Cdot1 = vB + b2Cross(wB, m_rB) - vA - b2Cross(wA, m_rA);
  		float32 Cdot2 = wB - wA;
  		b2Vec3 Cdot(Cdot1.x, Cdot1.y, Cdot2);
  
  		b2Vec3 impulse = -b2Mul(m_mass, Cdot);
  		m_impulse += impulse;
  
  		b2Vec2 P(impulse.x, impulse.y);
  
  		vA -= mA * P;
  		wA -= iA * (b2Cross(m_rA, P) + impulse.z);
  
  		vB += mB * P;
  		wB += iB * (b2Cross(m_rB, P) + impulse.z);
  	}
  
  	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 b2WeldJoint::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);
  
  	float32 mA = m_invMassA, mB = m_invMassB;
  	float32 iA = m_invIA, iB = m_invIB;
  
  	b2Vec2 rA = b2Mul(qA, m_localAnchorA - m_localCenterA);
  	b2Vec2 rB = b2Mul(qB, m_localAnchorB - m_localCenterB);
  
  	float32 positionError, angularError;
  
  	b2Mat33 K;
  	K.ex.x = mA + mB + rA.y * rA.y * iA + rB.y * rB.y * iB;
  	K.ey.x = -rA.y * rA.x * iA - rB.y * rB.x * iB;
  	K.ez.x = -rA.y * iA - rB.y * iB;
  	K.ex.y = K.ey.x;
  	K.ey.y = mA + mB + rA.x * rA.x * iA + rB.x * rB.x * iB;
  	K.ez.y = rA.x * iA + rB.x * iB;
  	K.ex.z = K.ez.x;
  	K.ey.z = K.ez.y;
  	K.ez.z = iA + iB;
  
  	if (m_frequencyHz > 0.0f)
  	{
  		b2Vec2 C1 =  cB + rB - cA - rA;
  
  		positionError = C1.Length();
  		angularError = 0.0f;
  
  		b2Vec2 P = -K.Solve22(C1);
  
  		cA -= mA * P;
  		aA -= iA * b2Cross(rA, P);
  
  		cB += mB * P;
  		aB += iB * b2Cross(rB, P);
  	}
  	else
  	{
  		b2Vec2 C1 =  cB + rB - cA - rA;
  		float32 C2 = aB - aA - m_referenceAngle;
  
  		positionError = C1.Length();
  		angularError = b2Abs(C2);
  
  		b2Vec3 C(C1.x, C1.y, C2);
  
  		b2Vec3 impulse = -K.Solve33(C);
  		b2Vec2 P(impulse.x, impulse.y);
  
  		cA -= mA * P;
  		aA -= iA * (b2Cross(rA, P) + impulse.z);
  
  		cB += mB * P;
  		aB += iB * (b2Cross(rB, P) + impulse.z);
  	}
  
  	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 positionError <= b2_linearSlop && angularError <= b2_angularSlop;
  }
  
  b2Vec2 b2WeldJoint::GetAnchorA() const
  {
  	return m_bodyA->GetWorldPoint(m_localAnchorA);
  }
  
  b2Vec2 b2WeldJoint::GetAnchorB() const
  {
  	return m_bodyB->GetWorldPoint(m_localAnchorB);
  }
  
  b2Vec2 b2WeldJoint::GetReactionForce(float32 inv_dt) const
  {
  	b2Vec2 P(m_impulse.x, m_impulse.y);
  	return inv_dt * P;
  }
  
  float32 b2WeldJoint::GetReactionTorque(float32 inv_dt) const
  {
  	return inv_dt * m_impulse.z;
  }
  
  void b2WeldJoint::Dump()
  {
  	int32 indexA = m_bodyA->m_islandIndex;
  	int32 indexB = m_bodyB->m_islandIndex;
  
  	b2Log("  b2WeldJointDef 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.referenceAngle = %.15lef;\n", m_referenceAngle);
  	b2Log("  jd.frequencyHz = %.15lef;\n", m_frequencyHz);
  	b2Log("  jd.dampingRatio = %.15lef;\n", m_dampingRatio);
  	b2Log("  joints[%d] = m_world->CreateJoint(&jd);\n", m_index);
  }
  