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;
}
void b2MotorJoint::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);
// Compute the effective mass matrix.
m_rA = b2Mul(qA, -m_localCenterA);
m_rB = b2Mul(qB, -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;
b2Mat22 K;
K.ex.x = mA + mB + iA * m_rA.y * m_rA.y + iB * m_rB.y * m_rB.y;
K.ex.y = -iA * m_rA.x * m_rA.y - iB * m_rB.x * m_rB.y;
K.ey.x = K.ex.y;
K.ey.y = mA + mB + iA * m_rA.x * m_rA.x + iB * m_rB.x * m_rB.x;
m_linearMass = K.GetInverse();
m_angularMass = iA + iB;
if (m_angularMass > 0.0f)
{
m_angularMass = 1.0f / m_angularMass;
}
m_linearError = cB + m_rB - cA - m_rA - b2Mul(qA, m_linearOffset);
m_angularError = aB - aA - m_angularOffset;
if (data.step.warmStarting)
{
// Scale impulses to support a variable time step.
m_linearImpulse *= data.step.dtRatio;
m_angularImpulse *= data.step.dtRatio;
b2Vec2 P(m_linearImpulse.x, m_linearImpulse.y);
vA -= mA * P;
wA -= iA * (b2Cross(m_rA, P) + m_angularImpulse);
vB += mB * P;
wB += iB * (b2Cross(m_rB, P) + m_angularImpulse);
}
else
{
m_linearImpulse.SetZero();
m_angularImpulse = 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 b2GearJoint::InitVelocityConstraints(const b2SolverData& data)
{
m_indexA = m_bodyA->m_islandIndex;
m_indexB = m_bodyB->m_islandIndex;
m_indexC = m_bodyC->m_islandIndex;
m_indexD = m_bodyD->m_islandIndex;
m_lcA = m_bodyA->m_sweep.localCenter;
m_lcB = m_bodyB->m_sweep.localCenter;
m_lcC = m_bodyC->m_sweep.localCenter;
m_lcD = m_bodyD->m_sweep.localCenter;
m_mA = m_bodyA->m_invMass;
m_mB = m_bodyB->m_invMass;
m_mC = m_bodyC->m_invMass;
m_mD = m_bodyD->m_invMass;
m_iA = m_bodyA->m_invI;
m_iB = m_bodyB->m_invI;
m_iC = m_bodyC->m_invI;
m_iD = m_bodyD->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;
float32 aC = data.positions[m_indexC].a;
b2Vec2 vC = data.velocities[m_indexC].v;
float32 wC = data.velocities[m_indexC].w;
float32 aD = data.positions[m_indexD].a;
b2Vec2 vD = data.velocities[m_indexD].v;
float32 wD = data.velocities[m_indexD].w;
b2Rot qA(aA), qB(aB), qC(aC), qD(aD);
m_mass = 0.0f;
if (m_typeA == e_revoluteJoint)
{
m_JvAC.SetZero();
m_JwA = 1.0f;
m_JwC = 1.0f;
m_mass += m_iA + m_iC;
}
else
{
b2Vec2 u = b2Mul(qC, m_localAxisC);
b2Vec2 rC = b2Mul(qC, m_localAnchorC - m_lcC);
b2Vec2 rA = b2Mul(qA, m_localAnchorA - m_lcA);
m_JvAC = u;
m_JwC = b2Cross(rC, u);
m_JwA = b2Cross(rA, u);
m_mass += m_mC + m_mA + m_iC * m_JwC * m_JwC + m_iA * m_JwA * m_JwA;
}
if (m_typeB == e_revoluteJoint)
{
m_JvBD.SetZero();
m_JwB = m_ratio;
m_JwD = m_ratio;
m_mass += m_ratio * m_ratio * (m_iB + m_iD);
}
else
{
b2Vec2 u = b2Mul(qD, m_localAxisD);
b2Vec2 rD = b2Mul(qD, m_localAnchorD - m_lcD);
b2Vec2 rB = b2Mul(qB, m_localAnchorB - m_lcB);
m_JvBD = m_ratio * u;
m_JwD = m_ratio * b2Cross(rD, u);
m_JwB = m_ratio * b2Cross(rB, u);
m_mass += m_ratio * m_ratio * (m_mD + m_mB) + m_iD * m_JwD * m_JwD + m_iB * m_JwB * m_JwB;
}
// Compute effective mass.
m_mass = m_mass > 0.0f ? 1.0f / m_mass : 0.0f;
if (data.step.warmStarting)
{
vA += (m_mA * m_impulse) * m_JvAC;
wA += m_iA * m_impulse * m_JwA;
vB += (m_mB * m_impulse) * m_JvBD;
wB += m_iB * m_impulse * m_JwB;
vC -= (m_mC * m_impulse) * m_JvAC;
wC -= m_iC * m_impulse * m_JwC;
vD -= (m_mD * m_impulse) * m_JvBD;
wD -= m_iD * m_impulse * m_JwD;
}
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;
data.velocities[m_indexC].v = vC;
data.velocities[m_indexC].w = wC;
data.velocities[m_indexD].v = vD;
data.velocities[m_indexD].w = wD;
}
float32 Initialize(const b2SimplexCache* cache,
const b2DistanceProxy* proxyA, const b2Sweep& sweepA,
const b2DistanceProxy* proxyB, const b2Sweep& sweepB,
float32 t1)
{
m_proxyA = proxyA;
m_proxyB = proxyB;
int32 count = cache->count;
b2Assert(0 < count && count < 3);
m_sweepA = sweepA;
m_sweepB = sweepB;
b2Transform xfA, xfB;
m_sweepA.GetTransform(&xfA, t1);
m_sweepB.GetTransform(&xfB, t1);
if (count == 1)
{
m_type = e_points;
b2Vec2 localPointA = m_proxyA->GetVertex(cache->indexA[0]);
b2Vec2 localPointB = m_proxyB->GetVertex(cache->indexB[0]);
b2Vec2 pointA = b2Mul(xfA, localPointA);
b2Vec2 pointB = b2Mul(xfB, localPointB);
m_axis = pointB - pointA;
float32 s = m_axis.Normalize();
return s;
}
else if (cache->indexA[0] == cache->indexA[1])
{
// Two points on B and one on A.
m_type = e_faceB;
b2Vec2 localPointB1 = proxyB->GetVertex(cache->indexB[0]);
b2Vec2 localPointB2 = proxyB->GetVertex(cache->indexB[1]);
m_axis = b2Cross(localPointB2 - localPointB1, 1.0f);
m_axis.Normalize();
b2Vec2 normal = b2Mul(xfB.q, m_axis);
m_localPoint = 0.5f * (localPointB1 + localPointB2);
b2Vec2 pointB = b2Mul(xfB, m_localPoint);
b2Vec2 localPointA = proxyA->GetVertex(cache->indexA[0]);
b2Vec2 pointA = b2Mul(xfA, localPointA);
float32 s = b2Dot(pointA - pointB, normal);
if (s < 0.0f)
{
m_axis = -m_axis;
s = -s;
}
return s;
}
else
{
// Two points on A and one or two points on B.
m_type = e_faceA;
b2Vec2 localPointA1 = m_proxyA->GetVertex(cache->indexA[0]);
b2Vec2 localPointA2 = m_proxyA->GetVertex(cache->indexA[1]);
m_axis = b2Cross(localPointA2 - localPointA1, 1.0f);
m_axis.Normalize();
b2Vec2 normal = b2Mul(xfA.q, m_axis);
m_localPoint = 0.5f * (localPointA1 + localPointA2);
b2Vec2 pointA = b2Mul(xfA, m_localPoint);
b2Vec2 localPointB = m_proxyB->GetVertex(cache->indexB[0]);
b2Vec2 pointB = b2Mul(xfB, localPointB);
float32 s = b2Dot(pointB - pointA, normal);
if (s < 0.0f)
{
m_axis = -m_axis;
s = -s;
}
return s;
}
}
bool b2RevoluteJoint::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 angularError = 0.0f;
float32 positionError = 0.0f;
bool fixedRotation = (m_invIA + m_invIB == 0.0f);
// Solve angular limit constraint.
if (m_enableLimit && m_limitState != e_inactiveLimit && fixedRotation == false)
{
float32 angle = aB - aA - m_referenceAngle;
float32 limitImpulse = 0.0f;
if (m_limitState == e_equalLimits)
{
// Prevent large angular corrections
float32 C = b2Clamp(angle - m_lowerAngle, -b2_maxAngularCorrection, b2_maxAngularCorrection);
limitImpulse = -m_motorMass * C;
angularError = b2Abs(C);
}
else if (m_limitState == e_atLowerLimit)
{
float32 C = angle - m_lowerAngle;
angularError = -C;
// Prevent large angular corrections and allow some slop.
C = b2Clamp(C + b2_angularSlop, -b2_maxAngularCorrection, 0.0f);
limitImpulse = -m_motorMass * C;
}
else if (m_limitState == e_atUpperLimit)
{
float32 C = angle - m_upperAngle;
angularError = C;
// Prevent large angular corrections and allow some slop.
C = b2Clamp(C - b2_angularSlop, 0.0f, b2_maxAngularCorrection);
limitImpulse = -m_motorMass * C;
}
aA -= m_invIA * limitImpulse;
aB += m_invIB * limitImpulse;
}
// Solve point-to-point constraint.
{
qA.Set(aA);
qB.Set(aB);
b2Vec2 rA = b2Mul(qA, m_localAnchorA - m_localCenterA);
b2Vec2 rB = b2Mul(qB, m_localAnchorB - m_localCenterB);
b2Vec2 C = cB + rB - cA - rA;
positionError = C.Length();
float32 mA = m_invMassA, mB = m_invMassB;
float32 iA = m_invIA, iB = m_invIB;
b2Mat22 K;
K.ex.x = mA + mB + iA * rA.y * rA.y + iB * rB.y * rB.y;
K.ex.y = -iA * rA.x * rA.y - iB * rB.x * rB.y;
K.ey.x = K.ex.y;
K.ey.y = mA + mB + iA * rA.x * rA.x + iB * rB.x * rB.x;
b2Vec2 impulse = -K.Solve(C);
cA -= mA * impulse;
aA -= iA * b2Cross(rA, impulse);
cB += mB * impulse;
aB += iB * b2Cross(rB, impulse);
}
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;
}
bool b2RevoluteJoint::SolvePositionConstraints(float32 baumgarte)
{
// TODO_ERIN block solve with limit.
B2_NOT_USED(baumgarte);
b2Body* b1 = m_bodyA;
b2Body* b2 = m_bodyB;
float32 angularError = 0.0f;
float32 positionError = 0.0f;
// Solve angular limit constraint.
if (m_enableLimit && m_limitState != e_inactiveLimit)
{
float32 angle = b2->m_sweep.a - b1->m_sweep.a - m_referenceAngle;
float32 limitImpulse = 0.0f;
if (m_limitState == e_equalLimits)
{
// Prevent large angular corrections
float32 C = b2Clamp(angle - m_lowerAngle, -b2_maxAngularCorrection, b2_maxAngularCorrection);
limitImpulse = -m_motorMass * C;
angularError = b2Abs(C);
}
else if (m_limitState == e_atLowerLimit)
{
float32 C = angle - m_lowerAngle;
angularError = -C;
// Prevent large angular corrections and allow some slop.
C = b2Clamp(C + b2_angularSlop, -b2_maxAngularCorrection, 0.0f);
limitImpulse = -m_motorMass * C;
}
else if (m_limitState == e_atUpperLimit)
{
float32 C = angle - m_upperAngle;
angularError = C;
// Prevent large angular corrections and allow some slop.
C = b2Clamp(C - b2_angularSlop, 0.0f, b2_maxAngularCorrection);
limitImpulse = -m_motorMass * C;
}
b1->m_sweep.a -= b1->m_invI * limitImpulse;
b2->m_sweep.a += b2->m_invI * limitImpulse;
b1->SynchronizeTransform();
b2->SynchronizeTransform();
}
// Solve point-to-point constraint.
{
b2Vec2 r1 = b2Mul(b1->GetTransform().R, m_localAnchor1 - b1->GetLocalCenter());
b2Vec2 r2 = b2Mul(b2->GetTransform().R, m_localAnchor2 - b2->GetLocalCenter());
b2Vec2 C = b2->m_sweep.c + r2 - b1->m_sweep.c - r1;
positionError = C.Length();
float32 invMass1 = b1->m_invMass, invMass2 = b2->m_invMass;
float32 invI1 = b1->m_invI, invI2 = b2->m_invI;
// Handle large detachment.
const float32 k_allowedStretch = 10.0f * b2_linearSlop;
if (C.LengthSquared() > k_allowedStretch * k_allowedStretch)
{
// Use a particle solution (no rotation).
b2Vec2 u = C; u.Normalize();
float32 m = invMass1 + invMass2;
if (m > 0.0f)
{
m = 1.0f / m;
}
b2Vec2 impulse = m * (-C);
const float32 k_beta = 0.5f;
b1->m_sweep.c -= k_beta * invMass1 * impulse;
b2->m_sweep.c += k_beta * invMass2 * impulse;
C = b2->m_sweep.c + r2 - b1->m_sweep.c - r1;
}
b2Mat22 K1;
K1.col1.x = invMass1 + invMass2; K1.col2.x = 0.0f;
K1.col1.y = 0.0f; K1.col2.y = invMass1 + invMass2;
b2Mat22 K2;
K2.col1.x = invI1 * r1.y * r1.y; K2.col2.x = -invI1 * r1.x * r1.y;
K2.col1.y = -invI1 * r1.x * r1.y; K2.col2.y = invI1 * r1.x * r1.x;
b2Mat22 K3;
K3.col1.x = invI2 * r2.y * r2.y; K3.col2.x = -invI2 * r2.x * r2.y;
K3.col1.y = -invI2 * r2.x * r2.y; K3.col2.y = invI2 * r2.x * r2.x;
b2Mat22 K = K1 + K2 + K3;
b2Vec2 impulse = K.Solve(-C);
b1->m_sweep.c -= b1->m_invMass * impulse;
b1->m_sweep.a -= b1->m_invI * b2Cross(r1, impulse);
b2->m_sweep.c += b2->m_invMass * impulse;
b2->m_sweep.a += b2->m_invI * b2Cross(r2, impulse);
b1->SynchronizeTransform();
b2->SynchronizeTransform();
}
return positionError <= b2_linearSlop && angularError <= b2_angularSlop;
}
void b2PrismaticJoint::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);
// Compute the effective masses.
b2Vec2 rA = b2Mul(qA, m_localAnchorA - m_localCenterA);
b2Vec2 rB = b2Mul(qB, m_localAnchorB - m_localCenterB);
b2Vec2 d = (cB - cA) + rB - rA;
float32 mA = m_invMassA, mB = m_invMassB;
float32 iA = m_invIA, iB = m_invIB;
// Compute motor Jacobian and effective mass.
{
m_axis = b2Mul(qA, m_localXAxisA);
m_a1 = b2Cross(d + rA, m_axis);
m_a2 = b2Cross(rB, m_axis);
m_motorMass = mA + mB + iA * m_a1 * m_a1 + iB * m_a2 * m_a2;
if (m_motorMass > 0.0f)
{
m_motorMass = 1.0f / m_motorMass;
}
}
// Prismatic constraint.
{
m_perp = b2Mul(qA, m_localYAxisA);
m_s1 = b2Cross(d + rA, m_perp);
m_s2 = b2Cross(rB, m_perp);
float32 k11 = mA + mB + iA * m_s1 * m_s1 + iB * m_s2 * m_s2;
float32 k12 = iA * m_s1 + iB * m_s2;
float32 k13 = iA * m_s1 * m_a1 + iB * m_s2 * m_a2;
float32 k22 = iA + iB;
if (k22 == 0.0f)
{
// For bodies with fixed rotation.
k22 = 1.0f;
}
float32 k23 = iA * m_a1 + iB * m_a2;
float32 k33 = mA + mB + iA * m_a1 * m_a1 + iB * m_a2 * m_a2;
m_K.ex.Set(k11, k12, k13);
m_K.ey.Set(k12, k22, k23);
m_K.ez.Set(k13, k23, k33);
}
// Compute motor and limit terms.
if (m_enableLimit)
{
float32 jointTranslation = b2Dot(m_axis, d);
if (b2Abs(m_upperTranslation - m_lowerTranslation) < 2.0f * b2_linearSlop)
{
m_limitState = e_equalLimits;
}
else if (jointTranslation <= m_lowerTranslation)
{
if (m_limitState != e_atLowerLimit)
{
m_limitState = e_atLowerLimit;
m_impulse.z = 0.0f;
}
}
else if (jointTranslation >= m_upperTranslation)
{
if (m_limitState != e_atUpperLimit)
{
m_limitState = e_atUpperLimit;
m_impulse.z = 0.0f;
}
}
else
{
m_limitState = e_inactiveLimit;
m_impulse.z = 0.0f;
}
}
else
{
m_limitState = e_inactiveLimit;
m_impulse.z = 0.0f;
}
if (m_enableMotor == false)
{
m_motorImpulse = 0.0f;
}
if (data.step.warmStarting)
{
// Account for variable time step.
m_impulse *= data.step.dtRatio;
m_motorImpulse *= data.step.dtRatio;
b2Vec2 P = m_impulse.x * m_perp + (m_motorImpulse + m_impulse.z) * m_axis;
float32 LA = m_impulse.x * m_s1 + m_impulse.y + (m_motorImpulse + m_impulse.z) * m_a1;
float32 LB = m_impulse.x * m_s2 + m_impulse.y + (m_motorImpulse + m_impulse.z) * m_a2;
vA -= mA * P;
wA -= iA * LA;
vB += mB * P;
wB += iB * LB;
}
else
{
m_impulse.SetZero();
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 b2PolygonShape::ComputeMass(b2MassData* massData, float32 density) const
{
// Polygon mass, centroid, and inertia.
// Let rho be the polygon density in mass per unit area.
// Then:
// mass = rho * int(dA)
// centroid.x = (1/mass) * rho * int(x * dA)
// centroid.y = (1/mass) * rho * int(y * dA)
// I = rho * int((x*x + y*y) * dA)
//
// We can compute these integrals by summing all the integrals
// for each triangle of the polygon. To evaluate the integral
// for a single triangle, we make a change of variables to
// the (u,v) coordinates of the triangle:
// x = x0 + e1x * u + e2x * v
// y = y0 + e1y * u + e2y * v
// where 0 <= u && 0 <= v && u + v <= 1.
//
// We integrate u from [0,1-v] and then v from [0,1].
// We also need to use the Jacobian of the transformation:
// D = cross(e1, e2)
//
// Simplification: triangle centroid = (1/3) * (p1 + p2 + p3)
//
// The rest of the derivation is handled by computer algebra.
b2Assert(m_count >= 3);
b2Vec2 center; center.Set(0.0f, 0.0f);
float32 area = 0.0f;
float32 I = 0.0f;
// s is the reference point for forming triangles.
// It's location doesn't change the result (except for rounding error).
b2Vec2 s(0.0f, 0.0f);
// This code would put the reference point inside the polygon.
for (int32 i = 0; i < m_count; ++i)
{
s += m_vertices[i];
}
s *= 1.0f / m_count;
const float32 k_inv3 = 1.0f / 3.0f;
for (int32 i = 0; i < m_count; ++i)
{
// Triangle vertices.
b2Vec2 e1 = m_vertices[i] - s;
b2Vec2 e2 = i + 1 < m_count ? m_vertices[i+1] - s : m_vertices[0] - s;
float32 D = b2Cross(e1, e2);
float32 triangleArea = 0.5f * D;
area += triangleArea;
// Area weighted centroid
center += triangleArea * k_inv3 * (e1 + e2);
float32 ex1 = e1.x, ey1 = e1.y;
float32 ex2 = e2.x, ey2 = e2.y;
float32 intx2 = ex1*ex1 + ex2*ex1 + ex2*ex2;
float32 inty2 = ey1*ey1 + ey2*ey1 + ey2*ey2;
I += (0.25f * k_inv3 * D) * (intx2 + inty2);
}
// Total mass
massData->mass = density * area;
// Center of mass
b2Assert(area > b2_epsilon);
center *= 1.0f / area;
massData->center = center + s;
// Inertia tensor relative to the local origin (point s).
massData->I = density * I;
// Shift to center of mass then to original body origin.
massData->I += massData->mass * (b2Dot(massData->center, massData->center) - b2Dot(center, center));
}
void b2PrismaticJoint::InitVelocityConstraints(const b2TimeStep& step)
{
b2Body* b1 = m_bodyA;
b2Body* b2 = m_bodyB;
m_localCenterA = b1->GetLocalCenter();
m_localCenterB = b2->GetLocalCenter();
b2Transform xf1 = b1->GetTransform();
b2Transform xf2 = b2->GetTransform();
// Compute the effective masses.
b2Vec2 r1 = b2Mul(xf1.R, m_localAnchor1 - m_localCenterA);
b2Vec2 r2 = b2Mul(xf2.R, m_localAnchor2 - m_localCenterB);
b2Vec2 d = b2->m_sweep.c + r2 - b1->m_sweep.c - r1;
m_invMassA = b1->m_invMass;
m_invIA = b1->m_invI;
m_invMassB = b2->m_invMass;
m_invIB = b2->m_invI;
// Compute motor Jacobian and effective mass.
{
m_axis = b2Mul(xf1.R, m_localXAxis1);
m_a1 = b2Cross(d + r1, m_axis);
m_a2 = b2Cross(r2, m_axis);
m_motorMass = m_invMassA + m_invMassB + m_invIA * m_a1 * m_a1 + m_invIB * m_a2 * m_a2;
if (m_motorMass > b2_epsilon)
{
m_motorMass = 1.0f / m_motorMass;
}
}
// Prismatic constraint.
{
m_perp = b2Mul(xf1.R, m_localYAxis1);
m_s1 = b2Cross(d + r1, m_perp);
m_s2 = b2Cross(r2, m_perp);
float32 m1 = m_invMassA, m2 = m_invMassB;
float32 i1 = m_invIA, i2 = m_invIB;
float32 k11 = m1 + m2 + i1 * m_s1 * m_s1 + i2 * m_s2 * m_s2;
float32 k12 = i1 * m_s1 + i2 * m_s2;
float32 k13 = i1 * m_s1 * m_a1 + i2 * m_s2 * m_a2;
float32 k22 = i1 + i2;
float32 k23 = i1 * m_a1 + i2 * m_a2;
float32 k33 = m1 + m2 + i1 * m_a1 * m_a1 + i2 * m_a2 * m_a2;
m_K.col1.Set(k11, k12, k13);
m_K.col2.Set(k12, k22, k23);
m_K.col3.Set(k13, k23, k33);
}
// Compute motor and limit terms.
if (m_enableLimit)
{
float32 jointTranslation = b2Dot(m_axis, d);
if (b2Abs(m_upperTranslation - m_lowerTranslation) < 2.0f * b2_linearSlop)
{
m_limitState = e_equalLimits;
}
else if (jointTranslation <= m_lowerTranslation)
{
if (m_limitState != e_atLowerLimit)
{
m_limitState = e_atLowerLimit;
m_impulse.z = 0.0f;
}
}
else if (jointTranslation >= m_upperTranslation)
{
if (m_limitState != e_atUpperLimit)
{
m_limitState = e_atUpperLimit;
m_impulse.z = 0.0f;
}
}
else
{
m_limitState = e_inactiveLimit;
m_impulse.z = 0.0f;
}
}
else
{
m_limitState = e_inactiveLimit;
m_impulse.z = 0.0f;
}
if (m_enableMotor == false)
{
m_motorImpulse = 0.0f;
}
if (step.warmStarting)
{
// Account for variable time step.
m_impulse *= step.dtRatio;
m_motorImpulse *= step.dtRatio;
b2Vec2 P = m_impulse.x * m_perp + (m_motorImpulse + m_impulse.z) * m_axis;
float32 L1 = m_impulse.x * m_s1 + m_impulse.y + (m_motorImpulse + m_impulse.z) * m_a1;
float32 L2 = m_impulse.x * m_s2 + m_impulse.y + (m_motorImpulse + m_impulse.z) * m_a2;
b1->m_linearVelocity -= m_invMassA * P;
b1->m_angularVelocity -= m_invIA * L1;
b2->m_linearVelocity += m_invMassB * P;
b2->m_angularVelocity += m_invIB * L2;
}
else
{
m_impulse.SetZero();
m_motorImpulse = 0.0f;
}
}
void b2Body::ResetMass()
{
// Compute mass data from shapes. Each shape has its own density.
m_mass = 0.0f;
m_invMass = 0.0f;
m_I = 0.0f;
m_invI = 0.0f;
b2Vec2 center = b2Vec2_zero;
for (b2Fixture* f = m_fixtureList; f; f = f->m_next)
{
const b2MassData& massData = f->GetMassData();
m_mass += massData.mass;
center += massData.mass * massData.center;
m_I += massData.I;
}
// Compute center of mass.
if (m_mass > 0.0f)
{
m_invMass = 1.0f / m_mass;
center *= m_invMass;
}
if (m_I > 0.0f && (m_flags & e_fixedRotationFlag) == 0)
{
// Center the inertia about the center of mass.
m_I -= m_mass * b2Dot(center, center);
b2Assert(m_I > 0.0f);
m_invI = 1.0f / m_I;
}
else
{
m_I = 0.0f;
m_invI = 0.0f;
}
// Move center of mass.
b2Vec2 oldCenter = m_sweep.c;
m_sweep.localCenter = center;
m_sweep.c0 = m_sweep.c = b2Mul(m_xf, m_sweep.localCenter);
// Update center of mass velocity.
m_linearVelocity += b2Cross(m_angularVelocity, m_sweep.c - oldCenter);
// Determine the new body type.
int16 oldType = m_type;
if (m_invMass == 0.0f && m_invI == 0.0f)
{
m_type = e_staticType;
}
else
{
m_type = e_dynamicType;
}
// If the body type changed, we need to flag contacts for filtering.
if (oldType != m_type)
{
for (b2ContactEdge* ce = m_contactList; ce; ce = ce->next)
{
ce->contact->FlagForFiltering();
}
}
}
void b2PolygonShape::Set(const b2Vec2* vertices, int32 count)
{
b2Assert(3 <= count && count <= b2_maxPolygonVertices);
if (count < 3)
{
SetAsBox(1.0f, 1.0f);
return;
}
int32 n = b2Min(count, b2_maxPolygonVertices);
// Perform welding and copy vertices into local buffer.
b2Vec2 ps[b2_maxPolygonVertices];
int32 tempCount = 0;
for (int32 i = 0; i < n; ++i)
{
b2Vec2 v = vertices[i];
bool unique = true;
for (int32 j = 0; j < tempCount; ++j)
{
if (b2DistanceSquared(v, ps[j]) < 0.5f * b2_linearSlop)
{
unique = false;
break;
}
}
if (unique)
{
ps[tempCount++] = v;
}
}
n = tempCount;
if (n < 3)
{
// Polygon is degenerate.
b2Assert(false);
SetAsBox(1.0f, 1.0f);
return;
}
// Create the convex hull using the Gift wrapping algorithm
// http://en.wikipedia.org/wiki/Gift_wrapping_algorithm
// Find the right most point on the hull
int32 i0 = 0;
float32 x0 = ps[0].x;
for (int32 i = 1; i < n; ++i)
{
float32 x = ps[i].x;
if (x > x0 || (x == x0 && ps[i].y < ps[i0].y))
{
i0 = i;
x0 = x;
}
}
int32 hull[b2_maxPolygonVertices];
int32 m = 0;
int32 ih = i0;
for (;;)
{
hull[m] = ih;
int32 ie = 0;
for (int32 j = 1; j < n; ++j)
{
if (ie == ih)
{
ie = j;
continue;
}
b2Vec2 r = ps[ie] - ps[hull[m]];
b2Vec2 v = ps[j] - ps[hull[m]];
float32 c = b2Cross(r, v);
if (c < 0.0f)
{
ie = j;
}
// Collinearity check
if (c == 0.0f && v.LengthSquared() > r.LengthSquared())
{
ie = j;
}
}
++m;
ih = ie;
if (ie == i0)
{
break;
}
}
m_count = m;
// Copy vertices.
for (int32 i = 0; i < m; ++i)
{
m_vertices[i] = ps[hull[i]];
}
// Compute normals. Ensure the edges have non-zero length.
for (int32 i = 0; i < m; ++i)
{
int32 i1 = i;
int32 i2 = i + 1 < m ? i + 1 : 0;
b2Vec2 edge = m_vertices[i2] - m_vertices[i1];
b2Assert(edge.LengthSquared() > b2_epsilon * b2_epsilon);
m_normals[i] = b2Cross(edge, 1.0f);
m_normals[i].Normalize();
}
// Compute the polygon centroid.
m_centroid = ComputeCentroid(m_vertices, m);
}
float32 LH_b2BuoyancyController::ComputeSubmergedArea(b2Shape* shape,
const b2Vec2& normal,
float32 offset,
const b2Transform& xf,
b2Vec2* c,
float32 density) const
{
if(shape->GetType() == b2Shape::e_edge)
{
//Note that v0 is independant of any details of the specific edge
//We are relying on v0 being consistent between multiple edges of the same body
b2Vec2 v0 = offset * normal;
//b2Vec2 v0 = xf.position + (offset - b2Dot(normal, xf.position)) * normal;
b2Vec2 v1 = b2Mul(xf, ((b2EdgeShape*)shape)->m_vertex1);
b2Vec2 v2 = b2Mul(xf, ((b2EdgeShape*)shape)->m_vertex2);
float32 d1 = b2Dot(normal, v1) - offset;
float32 d2 = b2Dot(normal, v2) - offset;
if(d1>0)
{
if(d2>0)
{
return 0;
}
else
{
v1 = -d2 / (d1 - d2) * v1 + d1 / (d1 - d2) * v2;
}
}
else
{
if(d2>0)
{
v2 = -d2 / (d1 - d2) * v1 + d1 / (d1 - d2) * v2;
}
else
{
//Nothing
}
}
// v0,v1,v2 represents a fully submerged triangle
float32 k_inv3 = 1.0f / 3.0f;
// Area weighted centroid
*c = k_inv3 * (v0 + v1 + v2);
b2Vec2 e1 = v1 - v0;
b2Vec2 e2 = v2 - v0;
return 0.5f * b2Cross(e1, e2);
}
else if(shape->GetType() == b2Shape::e_polygon)
{
//Transform plane into shape co-ordinates
b2Vec2 normalL = b2MulT(xf.q,normal);
float32 offsetL = offset - b2Dot(normal,xf.p);
float32 depths[b2_maxPolygonVertices];
int32 diveCount = 0;
int32 intoIndex = -1;
int32 outoIndex = -1;
bool lastSubmerged = false;
int32 i;
for(i=0;i<((b2PolygonShape*)shape)->m_vertexCount;i++){
depths[i] = b2Dot(normalL,((b2PolygonShape*)shape)->m_vertices[i]) - offsetL;
bool isSubmerged = depths[i]<-FLT_EPSILON;
if(i>0){
if(isSubmerged){
if(!lastSubmerged){
intoIndex = i-1;
diveCount++;
}
}else{
if(lastSubmerged){
outoIndex = i-1;
diveCount++;
}
}
}
lastSubmerged = isSubmerged;
}
switch(diveCount){
case 0:
if(lastSubmerged){
//Completely submerged
b2MassData md;
((b2PolygonShape*)shape)->ComputeMass(&md, density);
*c = b2Mul(xf,md.center);
return md.mass/density;
}else{
//Completely dry
return 0;
}
break;
case 1:
if(intoIndex==-1){
intoIndex = ((b2PolygonShape*)shape)->m_vertexCount-1;
}else{
outoIndex = ((b2PolygonShape*)shape)->m_vertexCount-1;
}
break;
}
int32 intoIndex2 = (intoIndex+1)%((b2PolygonShape*)shape)->m_vertexCount;
int32 outoIndex2 = (outoIndex+1)%((b2PolygonShape*)shape)->m_vertexCount;
float32 intoLambda = (0 - depths[intoIndex]) / (depths[intoIndex2] - depths[intoIndex]);
float32 outoLambda = (0 - depths[outoIndex]) / (depths[outoIndex2] - depths[outoIndex]);
b2Vec2 intoVec( ((b2PolygonShape*)shape)->m_vertices[intoIndex].x*(1-intoLambda)+((b2PolygonShape*)shape)->m_vertices[intoIndex2].x*intoLambda,
((b2PolygonShape*)shape)->m_vertices[intoIndex].y*(1-intoLambda)+((b2PolygonShape*)shape)->m_vertices[intoIndex2].y*intoLambda);
b2Vec2 outoVec( ((b2PolygonShape*)shape)->m_vertices[outoIndex].x*(1-outoLambda)+((b2PolygonShape*)shape)->m_vertices[outoIndex2].x*outoLambda,
((b2PolygonShape*)shape)->m_vertices[outoIndex].y*(1-outoLambda)+((b2PolygonShape*)shape)->m_vertices[outoIndex2].y*outoLambda);
//Initialize accumulator
float32 area = 0;
b2Vec2 center(0,0);
b2Vec2 p2 = ((b2PolygonShape*)shape)->m_vertices[intoIndex2];
b2Vec2 p3;
float32 k_inv3 = 1.0f / 3.0f;
//An awkward loop from intoIndex2+1 to outIndex2
i = intoIndex2;
while(i!=outoIndex2){
i=(i+1)%((b2PolygonShape*)shape)->m_vertexCount;
if(i==outoIndex2)
p3 = outoVec;
else
p3 = ((b2PolygonShape*)shape)->m_vertices[i];
//Add the triangle formed by intoVec,p2,p3
{
b2Vec2 e1 = p2 - intoVec;
b2Vec2 e2 = p3 - intoVec;
float32 D = b2Cross(e1, e2);
float32 triangleArea = 0.5f * D;
area += triangleArea;
// Area weighted centroid
center += triangleArea * k_inv3 * (intoVec + p2 + p3);
}
//
p2=p3;
}
//Normalize and transform centroid
center *= 1.0f/area;
*c = b2Mul(xf,center);
return area;
}
else if(shape->GetType() == b2Shape::e_circle)
{
b2Vec2 p = b2Mul(xf,((b2CircleShape*)shape)->m_p);
float32 l = -(b2Dot(normal,p) - offset);
if(l<-((b2CircleShape*)shape)->m_radius+FLT_EPSILON){
//Completely dry
return 0;
}
if(l > ((b2CircleShape*)shape)->m_radius){
//Completely wet
*c = p;
return b2_pi*((b2CircleShape*)shape)->m_radius*((b2CircleShape*)shape)->m_radius;
}
//Magic
float32 r2 = ((b2CircleShape*)shape)->m_radius*((b2CircleShape*)shape)->m_radius;
float32 l2 = l*l;
//TODO: write b2Sqrt to handle fixed point case.
float32 area = r2 * (asin(l/((b2CircleShape*)shape)->m_radius) + b2_pi/2.0f)+ l * b2Sqrt(r2 - l2);
float32 com = -2.0f/3.0f*pow(r2-l2,1.5f)/area;
c->x = p.x + normal.x * com;
c->y = p.y + normal.y * com;
return area;
}
return 0;
}
b2ContactSolver::b2ContactSolver(b2Contact * *contacts, int32
contactCount,
b2StackAllocator *allocator, float32
impulseRatio)
{
m_allocator = allocator;
m_constraintCount = contactCount;
m_constraints = (b2ContactConstraint *) m_allocator->Allocate(
m_constraintCount * sizeof(b2ContactConstraint));
for (
int32 i = 0;
i<m_constraintCount;
++i)
{
b2Contact *contact = contacts[i];
b2Fixture *fixtureA = contact->m_fixtureA;
b2Fixture *fixtureB = contact->m_fixtureB;
b2Shape *shapeA = fixtureA->GetShape();
b2Shape *shapeB = fixtureB->GetShape();
float32 radiusA = shapeA->m_radius;
float32 radiusB = shapeB->m_radius;
b2Body *bodyA = fixtureA->GetBody();
b2Body *bodyB = fixtureB->GetBody();
b2Manifold *manifold = contact->GetManifold();
float32 friction = b2MixFriction(fixtureA->GetFriction(), fixtureB->GetFriction());
float32 restitution = b2MixRestitution(fixtureA->GetRestitution(), fixtureB->GetRestitution());
b2Vec2 vA = bodyA->m_linearVelocity;
b2Vec2 vB = bodyB->m_linearVelocity;
float32 wA = bodyA->m_angularVelocity;
float32 wB = bodyB->m_angularVelocity;
b2Assert(manifold
->pointCount > 0);
b2WorldManifold worldManifold;
worldManifold.
Initialize(manifold, bodyA
->m_xf, radiusA, bodyB->m_xf, radiusB);
b2ContactConstraint *cc = m_constraints + i;
cc->
bodyA = bodyA;
cc->
bodyB = bodyB;
cc->
manifold = manifold;
cc->
normal = worldManifold.normal;
cc->
pointCount = manifold->pointCount;
cc->
friction = friction;
cc->
localNormal = manifold->localNormal;
cc->
localPoint = manifold->localPoint;
cc->
radius = radiusA + radiusB;
cc->
type = manifold->type;
for (
int32 j = 0;
j<cc->
pointCount;
++j)
{
b2ManifoldPoint *cp = manifold->points + j;
b2ContactConstraintPoint *ccp = cc->points + j;
ccp->
normalImpulse = impulseRatio * cp->normalImpulse;
ccp->
tangentImpulse = impulseRatio * cp->tangentImpulse;
ccp->
localPoint = cp->localPoint;
ccp->
rA = worldManifold.points[j] - bodyA->m_sweep.c;
ccp->
rB = worldManifold.points[j] - bodyB->m_sweep.c;
float32 rnA = b2Cross(ccp->rA, cc->normal);
float32 rnB = b2Cross(ccp->rB, cc->normal);
rnA *=
rnA;
rnB *=
rnB;
float32 kNormal = bodyA->m_invMass + bodyB->m_invMass + bodyA->m_invI * rnA + bodyB->m_invI * rnB;
b2Assert(kNormal
> b2_epsilon);
ccp->
normalMass = 1.0f / kNormal;
b2Vec2 tangent = b2Cross(cc->normal, 1.0f);
float32 rtA = b2Cross(ccp->rA, tangent);
float32 rtB = b2Cross(ccp->rB, tangent);
rtA *=
rtA;
rtB *=
rtB;
float32 kTangent = bodyA->m_invMass + bodyB->m_invMass + bodyA->m_invI * rtA + bodyB->m_invI * rtB;
b2Assert(kTangent
> b2_epsilon);
ccp->
tangentMass = 1.0f / kTangent;
// Setup a velocity bias for restitution.
ccp->
velocityBias = 0.0f;
float32 vRel = b2Dot(cc->normal, vB + b2Cross(wB, ccp->rB) - vA - b2Cross(wA, ccp->rA));
if (vRel < -b2_velocityThreshold)
{
ccp->
velocityBias = -restitution * vRel;
}
}
// If we have two points, then prepare the block solver.
if (cc->pointCount == 2)
{
b2ContactConstraintPoint *ccp1 = cc->points + 0;
b2ContactConstraintPoint *ccp2 = cc->points + 1;
float32 invMassA = bodyA->m_invMass;
float32 invIA = bodyA->m_invI;
float32 invMassB = bodyB->m_invMass;
float32 invIB = bodyB->m_invI;
float32 rn1A = b2Cross(ccp1->rA, cc->normal);
float32 rn1B = b2Cross(ccp1->rB, cc->normal);
float32 rn2A = b2Cross(ccp2->rA, cc->normal);
float32 rn2B = b2Cross(ccp2->rB, cc->normal);
float32 k11 = invMassA + invMassB + invIA * rn1A * rn1A + invIB * rn1B * rn1B;
float32 k22 = invMassA + invMassB + invIA * rn2A * rn2A + invIB * rn2B * rn2B;
float32 k12 = invMassA + invMassB + invIA * rn1A * rn2A + invIB * rn1B * rn2B;
// Ensure a reasonable condition number.
const float32 k_maxConditionNumber = 100.0f;
if (
k11 *k11<k_maxConditionNumber *(k11 *k22
-
k12 *k12
))
{
// K is safe to invert.
cc->K.col1.
Set(k11, k12
);
cc->K.col2.
Set(k12, k22
);
cc->
normalMass = cc->K.GetInverse();
}
else
{
// The constraints are redundant, just use one.
// TODO_ERIN use deepest?
cc->
pointCount = 1;
}
}
}
}
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;
}
// Possible regions:
// - points[2]
// - edge points[0]-points[2]
// - edge points[1]-points[2]
// - inside the triangle
void b2Simplex::Solve3()
{
b2Vec2 w1 = m_v1.w;
b2Vec2 w2 = m_v2.w;
b2Vec2 w3 = m_v3.w;
// Edge12
// [1 1 ][a1] = [1]
// [w1.e12 w2.e12][a2] = [0]
// a3 = 0
b2Vec2 e12 = w2 - w1;
float32 w1e12 = b2Dot(w1, e12);
float32 w2e12 = b2Dot(w2, e12);
float32 d12_1 = w2e12;
float32 d12_2 = -w1e12;
// Edge13
// [1 1 ][a1] = [1]
// [w1.e13 w3.e13][a3] = [0]
// a2 = 0
b2Vec2 e13 = w3 - w1;
float32 w1e13 = b2Dot(w1, e13);
float32 w3e13 = b2Dot(w3, e13);
float32 d13_1 = w3e13;
float32 d13_2 = -w1e13;
// Edge23
// [1 1 ][a2] = [1]
// [w2.e23 w3.e23][a3] = [0]
// a1 = 0
b2Vec2 e23 = w3 - w2;
float32 w2e23 = b2Dot(w2, e23);
float32 w3e23 = b2Dot(w3, e23);
float32 d23_1 = w3e23;
float32 d23_2 = -w2e23;
// Triangle123
float32 n123 = b2Cross(e12, e13);
float32 d123_1 = n123 * b2Cross(w2, w3);
float32 d123_2 = n123 * b2Cross(w3, w1);
float32 d123_3 = n123 * b2Cross(w1, w2);
// w1 region
if (d12_2 <= 0.0f && d13_2 <= 0.0f)
{
m_v1.a = 1.0f;
m_count = 1;
return;
}
// e12
if (d12_1 > 0.0f && d12_2 > 0.0f && d123_3 <= 0.0f)
{
float32 inv_d12 = 1.0f / (d12_1 + d12_2);
m_v1.a = d12_1 * inv_d12;
m_v2.a = d12_2 * inv_d12;
m_count = 2;
return;
}
// e13
if (d13_1 > 0.0f && d13_2 > 0.0f && d123_2 <= 0.0f)
{
float32 inv_d13 = 1.0f / (d13_1 + d13_2);
m_v1.a = d13_1 * inv_d13;
m_v3.a = d13_2 * inv_d13;
m_count = 2;
m_v2 = m_v3;
return;
}
// w2 region
if (d12_1 <= 0.0f && d23_2 <= 0.0f)
{
m_v2.a = 1.0f;
m_count = 1;
m_v1 = m_v2;
return;
}
// w3 region
if (d13_1 <= 0.0f && d23_1 <= 0.0f)
{
m_v3.a = 1.0f;
m_count = 1;
m_v1 = m_v3;
return;
}
// e23
if (d23_1 > 0.0f && d23_2 > 0.0f && d123_1 <= 0.0f)
{
float32 inv_d23 = 1.0f / (d23_1 + d23_2);
m_v2.a = d23_1 * inv_d23;
m_v3.a = d23_2 * inv_d23;
m_count = 2;
m_v1 = m_v3;
return;
}
// Must be in triangle123
float32 inv_d123 = 1.0f / (d123_1 + d123_2 + d123_3);
m_v1.a = d123_1 * inv_d123;
m_v2.a = d123_2 * inv_d123;
m_v3.a = d123_3 * inv_d123;
m_count = 3;
}
bool b2PrismaticJoint::SolvePositionConstraints(float32 baumgarte)
{
B2_NOT_USED(baumgarte);
b2Body* b1 = m_bodyA;
b2Body* b2 = m_bodyB;
b2Vec2 c1 = b1->m_sweep.c;
float32 a1 = b1->m_sweep.a;
b2Vec2 c2 = b2->m_sweep.c;
float32 a2 = b2->m_sweep.a;
// Solve linear limit constraint.
float32 linearError = 0.0f, angularError = 0.0f;
bool active = false;
float32 C2 = 0.0f;
b2Mat22 R1(a1), R2(a2);
b2Vec2 r1 = b2Mul(R1, m_localAnchor1 - m_localCenterA);
b2Vec2 r2 = b2Mul(R2, m_localAnchor2 - m_localCenterB);
b2Vec2 d = c2 + r2 - c1 - r1;
if (m_enableLimit)
{
m_axis = b2Mul(R1, m_localXAxis1);
m_a1 = b2Cross(d + r1, m_axis);
m_a2 = b2Cross(r2, m_axis);
float32 translation = b2Dot(m_axis, d);
if (b2Abs(m_upperTranslation - m_lowerTranslation) < 2.0f * b2_linearSlop)
{
// Prevent large angular corrections
C2 = b2Clamp(translation, -b2_maxLinearCorrection, b2_maxLinearCorrection);
linearError = b2Abs(translation);
active = true;
}
else if (translation <= m_lowerTranslation)
{
// Prevent large linear corrections and allow some slop.
C2 = b2Clamp(translation - m_lowerTranslation + b2_linearSlop, -b2_maxLinearCorrection, 0.0f);
linearError = m_lowerTranslation - translation;
active = true;
}
else if (translation >= m_upperTranslation)
{
// Prevent large linear corrections and allow some slop.
C2 = b2Clamp(translation - m_upperTranslation - b2_linearSlop, 0.0f, b2_maxLinearCorrection);
linearError = translation - m_upperTranslation;
active = true;
}
}
m_perp = b2Mul(R1, m_localYAxis1);
m_s1 = b2Cross(d + r1, m_perp);
m_s2 = b2Cross(r2, m_perp);
b2Vec3 impulse;
b2Vec2 C1;
C1.x = b2Dot(m_perp, d);
C1.y = a2 - a1 - m_refAngle;
linearError = b2Max(linearError, b2Abs(C1.x));
angularError = b2Abs(C1.y);
if (active)
{
float32 m1 = m_invMassA, m2 = m_invMassB;
float32 i1 = m_invIA, i2 = m_invIB;
float32 k11 = m1 + m2 + i1 * m_s1 * m_s1 + i2 * m_s2 * m_s2;
float32 k12 = i1 * m_s1 + i2 * m_s2;
float32 k13 = i1 * m_s1 * m_a1 + i2 * m_s2 * m_a2;
float32 k22 = i1 + i2;
float32 k23 = i1 * m_a1 + i2 * m_a2;
float32 k33 = m1 + m2 + i1 * m_a1 * m_a1 + i2 * m_a2 * m_a2;
m_K.col1.Set(k11, k12, k13);
m_K.col2.Set(k12, k22, k23);
m_K.col3.Set(k13, k23, k33);
b2Vec3 C;
C.x = C1.x;
C.y = C1.y;
C.z = C2;
impulse = m_K.Solve33(-C);
}
else
{
float32 m1 = m_invMassA, m2 = m_invMassB;
float32 i1 = m_invIA, i2 = m_invIB;
float32 k11 = m1 + m2 + i1 * m_s1 * m_s1 + i2 * m_s2 * m_s2;
float32 k12 = i1 * m_s1 + i2 * m_s2;
float32 k22 = i1 + i2;
m_K.col1.Set(k11, k12, 0.0f);
m_K.col2.Set(k12, k22, 0.0f);
b2Vec2 impulse1 = m_K.Solve22(-C1);
impulse.x = impulse1.x;
impulse.y = impulse1.y;
impulse.z = 0.0f;
}
b2Vec2 P = impulse.x * m_perp + impulse.z * m_axis;
float32 L1 = impulse.x * m_s1 + impulse.y + impulse.z * m_a1;
float32 L2 = impulse.x * m_s2 + impulse.y + impulse.z * m_a2;
c1 -= m_invMassA * P;
a1 -= m_invIA * L1;
c2 += m_invMassB * P;
a2 += m_invIB * L2;
// TODO_ERIN remove need for this.
b1->m_sweep.c = c1;
b1->m_sweep.a = a1;
b2->m_sweep.c = c2;
b2->m_sweep.a = a2;
b1->SynchronizeTransform();
b2->SynchronizeTransform();
return linearError <= b2_linearSlop && angularError <= b2_angularSlop;
}
void b2RevoluteJoint::SolveVelocityConstraints(const b2TimeStep& step)
{
b2Body* b1 = m_bodyA;
b2Body* b2 = m_bodyB;
b2Vec2 v1 = b1->m_linearVelocity;
float32 w1 = b1->m_angularVelocity;
b2Vec2 v2 = b2->m_linearVelocity;
float32 w2 = b2->m_angularVelocity;
float32 m1 = b1->m_invMass, m2 = b2->m_invMass;
float32 i1 = b1->m_invI, i2 = b2->m_invI;
// Solve motor constraint.
if (m_enableMotor && m_limitState != e_equalLimits)
{
float32 Cdot = w2 - w1 - m_motorSpeed;
float32 impulse = m_motorMass * (-Cdot);
float32 oldImpulse = m_motorImpulse;
float32 maxImpulse = step.dt * m_maxMotorTorque;
m_motorImpulse = b2Clamp(m_motorImpulse + impulse, -maxImpulse, maxImpulse);
impulse = m_motorImpulse - oldImpulse;
w1 -= i1 * impulse;
w2 += i2 * impulse;
}
// Solve limit constraint.
if (m_enableLimit && m_limitState != e_inactiveLimit)
{
b2Vec2 r1 = b2Mul(b1->GetTransform().R, m_localAnchor1 - b1->GetLocalCenter());
b2Vec2 r2 = b2Mul(b2->GetTransform().R, m_localAnchor2 - b2->GetLocalCenter());
// Solve point-to-point constraint
b2Vec2 Cdot1 = v2 + b2Cross(w2, r2) - v1 - b2Cross(w1, r1);
float32 Cdot2 = w2 - w1;
b2Vec3 Cdot(Cdot1.x, Cdot1.y, Cdot2);
b2Vec3 impulse = m_mass.Solve33(-Cdot);
if (m_limitState == e_equalLimits)
{
m_impulse += impulse;
}
else if (m_limitState == e_atLowerLimit)
{
float32 newImpulse = m_impulse.z + impulse.z;
if (newImpulse < 0.0f)
{
b2Vec2 reduced = m_mass.Solve22(-Cdot1);
impulse.x = reduced.x;
impulse.y = reduced.y;
impulse.z = -m_impulse.z;
m_impulse.x += reduced.x;
m_impulse.y += reduced.y;
m_impulse.z = 0.0f;
}
}
else if (m_limitState == e_atUpperLimit)
{
float32 newImpulse = m_impulse.z + impulse.z;
if (newImpulse > 0.0f)
{
b2Vec2 reduced = m_mass.Solve22(-Cdot1);
impulse.x = reduced.x;
impulse.y = reduced.y;
impulse.z = -m_impulse.z;
m_impulse.x += reduced.x;
m_impulse.y += reduced.y;
m_impulse.z = 0.0f;
}
}
b2Vec2 P(impulse.x, impulse.y);
v1 -= m1 * P;
w1 -= i1 * (b2Cross(r1, P) + impulse.z);
v2 += m2 * P;
w2 += i2 * (b2Cross(r2, P) + impulse.z);
}
else
{
b2Vec2 r1 = b2Mul(b1->GetTransform().R, m_localAnchor1 - b1->GetLocalCenter());
b2Vec2 r2 = b2Mul(b2->GetTransform().R, m_localAnchor2 - b2->GetLocalCenter());
// Solve point-to-point constraint
b2Vec2 Cdot = v2 + b2Cross(w2, r2) - v1 - b2Cross(w1, r1);
b2Vec2 impulse = m_mass.Solve22(-Cdot);
m_impulse.x += impulse.x;
m_impulse.y += impulse.y;
v1 -= m1 * impulse;
w1 -= i1 * b2Cross(r1, impulse);
v2 += m2 * impulse;
w2 += i2 * b2Cross(r2, impulse);
}
b1->m_linearVelocity = v1;
b1->m_angularVelocity = w1;
b2->m_linearVelocity = v2;
b2->m_angularVelocity = w2;
}
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;
}
void b2RevoluteJoint::InitVelocityConstraints(const b2TimeStep& step)
{
b2Body* b1 = m_bodyA;
b2Body* b2 = m_bodyB;
if (m_enableMotor || m_enableLimit)
{
// You cannot create a rotation limit between bodies that
// both have fixed rotation.
b2Assert(b1->m_invI > 0.0f || b2->m_invI > 0.0f);
}
// Compute the effective mass matrix.
b2Vec2 r1 = b2Mul(b1->GetTransform().R, m_localAnchor1 - b1->GetLocalCenter());
b2Vec2 r2 = b2Mul(b2->GetTransform().R, m_localAnchor2 - b2->GetLocalCenter());
// J = [-I -r1_skew I r2_skew]
// [ 0 -1 0 1]
// r_skew = [-ry; rx]
// Matlab
// K = [ m1+r1y^2*i1+m2+r2y^2*i2, -r1y*i1*r1x-r2y*i2*r2x, -r1y*i1-r2y*i2]
// [ -r1y*i1*r1x-r2y*i2*r2x, m1+r1x^2*i1+m2+r2x^2*i2, r1x*i1+r2x*i2]
// [ -r1y*i1-r2y*i2, r1x*i1+r2x*i2, i1+i2]
float32 m1 = b1->m_invMass, m2 = b2->m_invMass;
float32 i1 = b1->m_invI, i2 = b2->m_invI;
m_mass.col1.x = m1 + m2 + r1.y * r1.y * i1 + r2.y * r2.y * i2;
m_mass.col2.x = -r1.y * r1.x * i1 - r2.y * r2.x * i2;
m_mass.col3.x = -r1.y * i1 - r2.y * i2;
m_mass.col1.y = m_mass.col2.x;
m_mass.col2.y = m1 + m2 + r1.x * r1.x * i1 + r2.x * r2.x * i2;
m_mass.col3.y = r1.x * i1 + r2.x * i2;
m_mass.col1.z = m_mass.col3.x;
m_mass.col2.z = m_mass.col3.y;
m_mass.col3.z = i1 + i2;
m_motorMass = i1 + i2;
if (m_motorMass > 0.0f)
{
m_motorMass = 1.0f / m_motorMass;
}
if (m_enableMotor == false)
{
m_motorImpulse = 0.0f;
}
if (m_enableLimit)
{
float32 jointAngle = b2->m_sweep.a - b1->m_sweep.a - m_referenceAngle;
if (b2Abs(m_upperAngle - m_lowerAngle) < 2.0f * b2_angularSlop)
{
m_limitState = e_equalLimits;
}
else if (jointAngle <= m_lowerAngle)
{
if (m_limitState != e_atLowerLimit)
{
m_impulse.z = 0.0f;
}
m_limitState = e_atLowerLimit;
}
else if (jointAngle >= m_upperAngle)
{
if (m_limitState != e_atUpperLimit)
{
m_impulse.z = 0.0f;
}
m_limitState = e_atUpperLimit;
}
else
{
m_limitState = e_inactiveLimit;
m_impulse.z = 0.0f;
}
}
else
{
m_limitState = e_inactiveLimit;
}
if (step.warmStarting)
{
// Scale impulses to support a variable time step.
m_impulse *= step.dtRatio;
m_motorImpulse *= step.dtRatio;
b2Vec2 P(m_impulse.x, m_impulse.y);
b1->m_linearVelocity -= m1 * P;
b1->m_angularVelocity -= i1 * (b2Cross(r1, P) + m_motorImpulse + m_impulse.z);
b2->m_linearVelocity += m2 * P;
b2->m_angularVelocity += i2 * (b2Cross(r2, P) + m_motorImpulse + m_impulse.z);
}
else
{
m_impulse.SetZero();
m_motorImpulse = 0.0f;
}
}
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;
}
bool b2PrismaticJoint::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;
// Compute fresh Jacobians
b2Vec2 rA = b2Mul(qA, m_localAnchorA - m_localCenterA);
b2Vec2 rB = b2Mul(qB, m_localAnchorB - m_localCenterB);
b2Vec2 d = cB + rB - cA - rA;
b2Vec2 axis = b2Mul(qA, m_localXAxisA);
float32 a1 = b2Cross(d + rA, axis);
float32 a2 = b2Cross(rB, axis);
b2Vec2 perp = b2Mul(qA, m_localYAxisA);
float32 s1 = b2Cross(d + rA, perp);
float32 s2 = b2Cross(rB, perp);
b2Vec3 impulse;
b2Vec2 C1;
C1.x = b2Dot(perp, d);
C1.y = aB - aA - m_referenceAngle;
float32 linearError = b2Abs(C1.x);
float32 angularError = b2Abs(C1.y);
bool active = false;
float32 C2 = 0.0f;
if (m_enableLimit)
{
float32 translation = b2Dot(axis, d);
if (b2Abs(m_upperTranslation - m_lowerTranslation) < 2.0f * b2_linearSlop)
{
// Prevent large angular corrections
C2 = b2Clamp(translation, -b2_maxLinearCorrection, b2_maxLinearCorrection);
linearError = b2Max(linearError, b2Abs(translation));
active = true;
}
else if (translation <= m_lowerTranslation)
{
// Prevent large linear corrections and allow some slop.
C2 = b2Clamp(translation - m_lowerTranslation + b2_linearSlop, -b2_maxLinearCorrection, 0.0f);
linearError = b2Max(linearError, m_lowerTranslation - translation);
active = true;
}
else if (translation >= m_upperTranslation)
{
// Prevent large linear corrections and allow some slop.
C2 = b2Clamp(translation - m_upperTranslation - b2_linearSlop, 0.0f, b2_maxLinearCorrection);
linearError = b2Max(linearError, translation - m_upperTranslation);
active = true;
}
}
if (active)
{
float32 k11 = mA + mB + iA * s1 * s1 + iB * s2 * s2;
float32 k12 = iA * s1 + iB * s2;
float32 k13 = iA * s1 * a1 + iB * s2 * a2;
float32 k22 = iA + iB;
if (k22 == 0.0f)
{
// For fixed rotation
k22 = 1.0f;
}
float32 k23 = iA * a1 + iB * a2;
float32 k33 = mA + mB + iA * a1 * a1 + iB * a2 * a2;
b2Mat33 K;
K.ex.Set(k11, k12, k13);
K.ey.Set(k12, k22, k23);
K.ez.Set(k13, k23, k33);
b2Vec3 C;
C.x = C1.x;
C.y = C1.y;
C.z = C2;
impulse = K.Solve33(-C);
}
else
{
float32 k11 = mA + mB + iA * s1 * s1 + iB * s2 * s2;
float32 k12 = iA * s1 + iB * s2;
float32 k22 = iA + iB;
if (k22 == 0.0f)
{
k22 = 1.0f;
}
b2Mat22 K;
K.ex.Set(k11, k12);
K.ey.Set(k12, k22);
b2Vec2 impulse1 = K.Solve(-C1);
impulse.x = impulse1.x;
impulse.y = impulse1.y;
impulse.z = 0.0f;
}
b2Vec2 P = impulse.x * perp + impulse.z * axis;
float32 LA = impulse.x * s1 + impulse.y + impulse.z * a1;
float32 LB = impulse.x * s2 + impulse.y + impulse.z * a2;
cA -= mA * P;
aA -= iA * LA;
cB += mB * P;
aB += iB * 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 linearError <= b2_linearSlop && angularError <= b2_angularSlop;
}
// Initialize position dependent portions of the velocity constraints.
void b2ContactSolver::InitializeVelocityConstraints()
{
for (int32 i = 0; i < m_count; ++i)
{
b2ContactConstraint* cc = m_constraints + i;
float32 radiusA = cc->radiusA;
float32 radiusB = cc->radiusB;
b2Body* bodyA = cc->bodyA;
b2Body* bodyB = cc->bodyB;
b2Manifold* manifold = cc->manifold;
b2Vec2 vA = bodyA->m_linearVelocity;
b2Vec2 vB = bodyB->m_linearVelocity;
float32 wA = bodyA->m_angularVelocity;
float32 wB = bodyB->m_angularVelocity;
b2Assert(manifold->pointCount > 0);
b2WorldManifold worldManifold;
worldManifold.Initialize(manifold, bodyA->m_xf, radiusA, bodyB->m_xf, radiusB);
cc->normal = worldManifold.normal;
for (int32 j = 0; j < cc->pointCount; ++j)
{
b2ContactConstraintPoint* ccp = cc->points + j;
ccp->rA = worldManifold.points[j] - bodyA->m_sweep.c;
ccp->rB = worldManifold.points[j] - bodyB->m_sweep.c;
float32 rnA = b2Cross(ccp->rA, cc->normal);
float32 rnB = b2Cross(ccp->rB, cc->normal);
rnA *= rnA;
rnB *= rnB;
float32 kNormal = bodyA->m_invMass + bodyB->m_invMass + bodyA->m_invI * rnA + bodyB->m_invI * rnB;
b2Assert(kNormal > b2_epsilon);
ccp->normalMass = 1.0f / kNormal;
b2Vec2 tangent = b2Cross(cc->normal, 1.0f);
float32 rtA = b2Cross(ccp->rA, tangent);
float32 rtB = b2Cross(ccp->rB, tangent);
rtA *= rtA;
rtB *= rtB;
float32 kTangent = bodyA->m_invMass + bodyB->m_invMass + bodyA->m_invI * rtA + bodyB->m_invI * rtB;
b2Assert(kTangent > b2_epsilon);
ccp->tangentMass = 1.0f / kTangent;
// Setup a velocity bias for restitution.
ccp->velocityBias = 0.0f;
float32 vRel = b2Dot(cc->normal, vB + b2Cross(wB, ccp->rB) - vA - b2Cross(wA, ccp->rA));
if (vRel < -b2_velocityThreshold)
{
ccp->velocityBias = -cc->restitution * vRel;
}
}
// If we have two points, then prepare the block solver.
if (cc->pointCount == 2)
{
b2ContactConstraintPoint* ccp1 = cc->points + 0;
b2ContactConstraintPoint* ccp2 = cc->points + 1;
float32 invMassA = bodyA->m_invMass;
float32 invIA = bodyA->m_invI;
float32 invMassB = bodyB->m_invMass;
float32 invIB = bodyB->m_invI;
float32 rn1A = b2Cross(ccp1->rA, cc->normal);
float32 rn1B = b2Cross(ccp1->rB, cc->normal);
float32 rn2A = b2Cross(ccp2->rA, cc->normal);
float32 rn2B = b2Cross(ccp2->rB, cc->normal);
float32 k11 = invMassA + invMassB + invIA * rn1A * rn1A + invIB * rn1B * rn1B;
float32 k22 = invMassA + invMassB + invIA * rn2A * rn2A + invIB * rn2B * rn2B;
float32 k12 = invMassA + invMassB + invIA * rn1A * rn2A + invIB * rn1B * rn2B;
// Ensure a reasonable condition number.
const float32 k_maxConditionNumber = 1000.0f;
if (k11 * k11 < k_maxConditionNumber * (k11 * k22 - k12 * k12))
{
// K is safe to invert.
cc->K.col1.Set(k11, k12);
cc->K.col2.Set(k12, k22);
cc->normalMass = cc->K.GetInverse();
}
else
{
// The constraints are redundant, just use one.
// TODO_ERIN use deepest?
cc->pointCount = 1;
}
}
}
}
void b2RevoluteJoint::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;
bool fixedRotation = (iA + iB == 0.0f);
// Solve motor constraint.
if (m_enableMotor && m_limitState != e_equalLimits && fixedRotation == false)
{
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 limit constraint.
if (m_enableLimit && m_limitState != e_inactiveLimit && fixedRotation == false)
{
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 = -m_mass.Solve33(Cdot);
if (m_limitState == e_equalLimits)
{
m_impulse += impulse;
}
else if (m_limitState == e_atLowerLimit)
{
float32 newImpulse = m_impulse.z + impulse.z;
if (newImpulse < 0.0f)
{
b2Vec2 rhs = -Cdot1 + m_impulse.z * b2Vec2(m_mass.ez.x, m_mass.ez.y);
b2Vec2 reduced = m_mass.Solve22(rhs);
impulse.x = reduced.x;
impulse.y = reduced.y;
impulse.z = -m_impulse.z;
m_impulse.x += reduced.x;
m_impulse.y += reduced.y;
m_impulse.z = 0.0f;
}
else
{
m_impulse += impulse;
}
}
else if (m_limitState == e_atUpperLimit)
{
float32 newImpulse = m_impulse.z + impulse.z;
if (newImpulse > 0.0f)
{
b2Vec2 rhs = -Cdot1 + m_impulse.z * b2Vec2(m_mass.ez.x, m_mass.ez.y);
b2Vec2 reduced = m_mass.Solve22(rhs);
impulse.x = reduced.x;
impulse.y = reduced.y;
impulse.z = -m_impulse.z;
m_impulse.x += reduced.x;
m_impulse.y += reduced.y;
m_impulse.z = 0.0f;
}
else
{
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);
}
else
{
// Solve point-to-point constraint
b2Vec2 Cdot = vB + b2Cross(wB, m_rB) - vA - b2Cross(wA, m_rA);
b2Vec2 impulse = m_mass.Solve22(-Cdot);
m_impulse.x += impulse.x;
m_impulse.y += impulse.y;
vA -= mA * impulse;
wA -= iA * b2Cross(m_rA, impulse);
vB += mB * impulse;
wB += iB * b2Cross(m_rB, impulse);
}
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 b2ContactSolver::SolveVelocityConstraints()
{
for (int32 i = 0; i < m_count; ++i)
{
b2ContactConstraint* c = m_constraints + i;
b2Body* bodyA = c->bodyA;
b2Body* bodyB = c->bodyB;
float32 wA = bodyA->m_angularVelocity;
float32 wB = bodyB->m_angularVelocity;
b2Vec2 vA = bodyA->m_linearVelocity;
b2Vec2 vB = bodyB->m_linearVelocity;
float32 invMassA = bodyA->m_invMass;
float32 invIA = bodyA->m_invI;
float32 invMassB = bodyB->m_invMass;
float32 invIB = bodyB->m_invI;
b2Vec2 normal = c->normal;
b2Vec2 tangent = b2Cross(normal, 1.0f);
float32 friction = c->friction;
b2Assert(c->pointCount == 1 || c->pointCount == 2);
// Solve tangent constraints
for (int32 j = 0; j < c->pointCount; ++j)
{
b2ContactConstraintPoint* ccp = c->points + j;
// Relative velocity at contact
b2Vec2 dv = vB + b2Cross(wB, ccp->rB) - vA - b2Cross(wA, ccp->rA);
// Compute tangent force
float32 vt = b2Dot(dv, tangent);
float32 lambda = ccp->tangentMass * (-vt);
// b2Clamp the accumulated force
float32 maxFriction = friction * ccp->normalImpulse;
float32 newImpulse = b2Clamp(ccp->tangentImpulse + lambda, -maxFriction, maxFriction);
lambda = newImpulse - ccp->tangentImpulse;
// Apply contact impulse
b2Vec2 P = lambda * tangent;
vA -= invMassA * P;
wA -= invIA * b2Cross(ccp->rA, P);
vB += invMassB * P;
wB += invIB * b2Cross(ccp->rB, P);
ccp->tangentImpulse = newImpulse;
}
// Solve normal constraints
if (c->pointCount == 1)
{
b2ContactConstraintPoint* ccp = c->points + 0;
// Relative velocity at contact
b2Vec2 dv = vB + b2Cross(wB, ccp->rB) - vA - b2Cross(wA, ccp->rA);
// Compute normal impulse
float32 vn = b2Dot(dv, normal);
float32 lambda = -ccp->normalMass * (vn - ccp->velocityBias);
// b2Clamp the accumulated impulse
float32 newImpulse = b2Max(ccp->normalImpulse + lambda, 0.0f);
lambda = newImpulse - ccp->normalImpulse;
// Apply contact impulse
b2Vec2 P = lambda * normal;
vA -= invMassA * P;
wA -= invIA * b2Cross(ccp->rA, P);
vB += invMassB * P;
wB += invIB * b2Cross(ccp->rB, P);
ccp->normalImpulse = newImpulse;
}
else
{
// Block solver developed in collaboration with Dirk Gregorius (back in 01/07 on Box2D_Lite).
// Build the mini LCP for this contact patch
//
// vn = A * x + b, vn >= 0, , vn >= 0, x >= 0 and vn_i * x_i = 0 with i = 1..2
//
// A = J * W * JT and J = ( -n, -r1 x n, n, r2 x n )
// b = vn_0 - velocityBias
//
// The system is solved using the "Total enumeration method" (s. Murty). The complementary constraint vn_i * x_i
// implies that we must have in any solution either vn_i = 0 or x_i = 0. So for the 2D contact problem the cases
// vn1 = 0 and vn2 = 0, x1 = 0 and x2 = 0, x1 = 0 and vn2 = 0, x2 = 0 and vn1 = 0 need to be tested. The first valid
// solution that satisfies the problem is chosen.
//
// In order to account of the accumulated impulse 'a' (because of the iterative nature of the solver which only requires
// that the accumulated impulse is clamped and not the incremental impulse) we change the impulse variable (x_i).
//
// Substitute:
//
// x = x' - a
//
// Plug into above equation:
//
// vn = A * x + b
// = A * (x' - a) + b
// = A * x' + b - A * a
// = A * x' + b'
// b' = b - A * a;
b2ContactConstraintPoint* cp1 = c->points + 0;
b2ContactConstraintPoint* cp2 = c->points + 1;
b2Vec2 a(cp1->normalImpulse, cp2->normalImpulse);
b2Assert(a.x >= 0.0f && a.y >= 0.0f);
// Relative velocity at contact
b2Vec2 dv1 = vB + b2Cross(wB, cp1->rB) - vA - b2Cross(wA, cp1->rA);
b2Vec2 dv2 = vB + b2Cross(wB, cp2->rB) - vA - b2Cross(wA, cp2->rA);
// Compute normal velocity
float32 vn1 = b2Dot(dv1, normal);
float32 vn2 = b2Dot(dv2, normal);
b2Vec2 b;
b.x = vn1 - cp1->velocityBias;
b.y = vn2 - cp2->velocityBias;
b -= b2Mul(c->K, a);
const float32 k_errorTol = 1e-3f;
B2_NOT_USED(k_errorTol);
for (;;)
{
//
// Case 1: vn = 0
//
// 0 = A * x' + b'
//
// Solve for x':
//
// x' = - inv(A) * b'
//
b2Vec2 x = - b2Mul(c->normalMass, b);
if (x.x >= 0.0f && x.y >= 0.0f)
{
// Resubstitute for the incremental impulse
b2Vec2 d = x - a;
// Apply incremental impulse
b2Vec2 P1 = d.x * normal;
b2Vec2 P2 = d.y * normal;
vA -= invMassA * (P1 + P2);
wA -= invIA * (b2Cross(cp1->rA, P1) + b2Cross(cp2->rA, P2));
vB += invMassB * (P1 + P2);
wB += invIB * (b2Cross(cp1->rB, P1) + b2Cross(cp2->rB, P2));
// Accumulate
cp1->normalImpulse = x.x;
cp2->normalImpulse = x.y;
#if B2_DEBUG_SOLVER == 1
// Postconditions
dv1 = vB + b2Cross(wB, cp1->rB) - vA - b2Cross(wA, cp1->rA);
dv2 = vB + b2Cross(wB, cp2->rB) - vA - b2Cross(wA, cp2->rA);
// Compute normal velocity
vn1 = b2Dot(dv1, normal);
vn2 = b2Dot(dv2, normal);
b2Assert(b2Abs(vn1 - cp1->velocityBias) < k_errorTol);
b2Assert(b2Abs(vn2 - cp2->velocityBias) < k_errorTol);
#endif
break;
}
//
// Case 2: vn1 = 0 and x2 = 0
//
// 0 = a11 * x1' + a12 * 0 + b1'
// vn2 = a21 * x1' + a22 * 0 + b2'
//
x.x = - cp1->normalMass * b.x;
x.y = 0.0f;
vn1 = 0.0f;
vn2 = c->K.col1.y * x.x + b.y;
if (x.x >= 0.0f && vn2 >= 0.0f)
{
// Resubstitute for the incremental impulse
b2Vec2 d = x - a;
// Apply incremental impulse
b2Vec2 P1 = d.x * normal;
b2Vec2 P2 = d.y * normal;
vA -= invMassA * (P1 + P2);
wA -= invIA * (b2Cross(cp1->rA, P1) + b2Cross(cp2->rA, P2));
vB += invMassB * (P1 + P2);
wB += invIB * (b2Cross(cp1->rB, P1) + b2Cross(cp2->rB, P2));
// Accumulate
cp1->normalImpulse = x.x;
cp2->normalImpulse = x.y;
#if B2_DEBUG_SOLVER == 1
// Postconditions
dv1 = vB + b2Cross(wB, cp1->rB) - vA - b2Cross(wA, cp1->rA);
// Compute normal velocity
vn1 = b2Dot(dv1, normal);
b2Assert(b2Abs(vn1 - cp1->velocityBias) < k_errorTol);
#endif
break;
}
//
// Case 3: vn2 = 0 and x1 = 0
//
// vn1 = a11 * 0 + a12 * x2' + b1'
// 0 = a21 * 0 + a22 * x2' + b2'
//
x.x = 0.0f;
x.y = - cp2->normalMass * b.y;
vn1 = c->K.col2.x * x.y + b.x;
vn2 = 0.0f;
if (x.y >= 0.0f && vn1 >= 0.0f)
{
// Resubstitute for the incremental impulse
b2Vec2 d = x - a;
// Apply incremental impulse
b2Vec2 P1 = d.x * normal;
b2Vec2 P2 = d.y * normal;
vA -= invMassA * (P1 + P2);
wA -= invIA * (b2Cross(cp1->rA, P1) + b2Cross(cp2->rA, P2));
vB += invMassB * (P1 + P2);
wB += invIB * (b2Cross(cp1->rB, P1) + b2Cross(cp2->rB, P2));
// Accumulate
cp1->normalImpulse = x.x;
cp2->normalImpulse = x.y;
#if B2_DEBUG_SOLVER == 1
// Postconditions
dv2 = vB + b2Cross(wB, cp2->rB) - vA - b2Cross(wA, cp2->rA);
// Compute normal velocity
vn2 = b2Dot(dv2, normal);
b2Assert(b2Abs(vn2 - cp2->velocityBias) < k_errorTol);
#endif
break;
}
//
// Case 4: x1 = 0 and x2 = 0
//
// vn1 = b1
// vn2 = b2;
x.x = 0.0f;
x.y = 0.0f;
vn1 = b.x;
vn2 = b.y;
if (vn1 >= 0.0f && vn2 >= 0.0f )
{
// Resubstitute for the incremental impulse
b2Vec2 d = x - a;
// Apply incremental impulse
b2Vec2 P1 = d.x * normal;
b2Vec2 P2 = d.y * normal;
vA -= invMassA * (P1 + P2);
wA -= invIA * (b2Cross(cp1->rA, P1) + b2Cross(cp2->rA, P2));
vB += invMassB * (P1 + P2);
wB += invIB * (b2Cross(cp1->rB, P1) + b2Cross(cp2->rB, P2));
// Accumulate
cp1->normalImpulse = x.x;
cp2->normalImpulse = x.y;
break;
}
// No solution, give up. This is hit sometimes, but it doesn't seem to matter.
break;
}
}
bodyA->m_linearVelocity = vA;
bodyA->m_angularVelocity = wA;
bodyB->m_linearVelocity = vB;
bodyB->m_angularVelocity = wB;
}
}
void b2RevoluteJoint::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;
bool fixedRotation = (iA + iB == 0.0f);
m_mass.ex.x = mA + mB + m_rA.y * m_rA.y * iA + m_rB.y * m_rB.y * iB;
m_mass.ey.x = -m_rA.y * m_rA.x * iA - m_rB.y * m_rB.x * iB;
m_mass.ez.x = -m_rA.y * iA - m_rB.y * iB;
m_mass.ex.y = m_mass.ey.x;
m_mass.ey.y = mA + mB + m_rA.x * m_rA.x * iA + m_rB.x * m_rB.x * iB;
m_mass.ez.y = m_rA.x * iA + m_rB.x * iB;
m_mass.ex.z = m_mass.ez.x;
m_mass.ey.z = m_mass.ez.y;
m_mass.ez.z = iA + iB;
m_motorMass = iA + iB;
if (m_motorMass > 0.0f)
{
m_motorMass = 1.0f / m_motorMass;
}
if (m_enableMotor == false || fixedRotation)
{
m_motorImpulse = 0.0f;
}
if (m_enableLimit && fixedRotation == false)
{
float32 jointAngle = aB - aA - m_referenceAngle;
if (b2Abs(m_upperAngle - m_lowerAngle) < 2.0f * b2_angularSlop)
{
m_limitState = e_equalLimits;
}
else if (jointAngle <= m_lowerAngle)
{
if (m_limitState != e_atLowerLimit)
{
m_impulse.z = 0.0f;
}
m_limitState = e_atLowerLimit;
}
else if (jointAngle >= m_upperAngle)
{
if (m_limitState != e_atUpperLimit)
{
m_impulse.z = 0.0f;
}
m_limitState = e_atUpperLimit;
}
else
{
m_limitState = e_inactiveLimit;
m_impulse.z = 0.0f;
}
}
else
{
m_limitState = e_inactiveLimit;
}
if (data.step.warmStarting)
{
// Scale impulses to support a variable time step.
m_impulse *= data.step.dtRatio;
m_motorImpulse *= data.step.dtRatio;
b2Vec2 P(m_impulse.x, m_impulse.y);
vA -= mA * P;
wA -= iA * (b2Cross(m_rA, P) + m_motorImpulse + m_impulse.z);
vB += mB * P;
wB += iB * (b2Cross(m_rB, P) + m_motorImpulse + m_impulse.z);
}
else
{
m_impulse.SetZero();
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;
}
// Sequential position solver for position constraints.
bool b2ContactSolver::SolveTOIPositionConstraints(float32 baumgarte, const b2Body* toiBodyA, const b2Body* toiBodyB)
{
float32 minSeparation = 0.0f;
for (int32 i = 0; i < m_count; ++i)
{
b2ContactConstraint* c = m_constraints + i;
b2Body* bodyA = c->bodyA;
b2Body* bodyB = c->bodyB;
float32 massA = 0.0f;
if (bodyA == toiBodyA || bodyA == toiBodyB)
{
massA = bodyA->m_mass;
}
float32 massB = 0.0f;
if (bodyB == toiBodyA || bodyB == toiBodyB)
{
massB = bodyB->m_mass;
}
float32 invMassA = bodyA->m_mass * bodyA->m_invMass;
float32 invIA = bodyA->m_mass * bodyA->m_invI;
float32 invMassB = bodyB->m_mass * bodyB->m_invMass;
float32 invIB = bodyB->m_mass * bodyB->m_invI;
// Solve normal constraints
for (int32 j = 0; j < c->pointCount; ++j)
{
b2PositionSolverManifold psm(c,j);
//psm.Initialize(c, j);
b2Vec2 normal = psm.normal;
b2Vec2 point = psm.point;
float32 separation = psm.separation;
b2Vec2 rA = point - bodyA->m_sweep.c;
b2Vec2 rB = point - bodyB->m_sweep.c;
// Track max constraint error.
minSeparation = b2Min(minSeparation, separation);
// Prevent large corrections and allow slop.
float32 C = b2Clamp(baumgarte * (separation + b2_linearSlop), -b2_maxLinearCorrection, 0.0f);
// Compute the effective mass.
float32 rnA = b2Cross(rA, normal);
float32 rnB = b2Cross(rB, normal);
float32 K = invMassA + invMassB + invIA * rnA * rnA + invIB * rnB * rnB;
// Compute normal impulse
float32 impulse = K > 0.0f ? - C / K : 0.0f;
b2Vec2 P = impulse * normal;
bodyA->m_sweep.c -= invMassA * P;
bodyA->m_sweep.a -= invIA * b2Cross(rA, P);
bodyA->SynchronizeTransform();
bodyB->m_sweep.c += invMassB * P;
bodyB->m_sweep.a += invIB * b2Cross(rB, P);
bodyB->SynchronizeTransform();
}
}
// We can't expect minSpeparation >= -b2_linearSlop because we don't
// push the separation above -b2_linearSlop.
return minSeparation >= -1.5f * b2_linearSlop;
}
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 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;
}
bool b2GearJoint::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;
b2Vec2 cC = data.positions[m_indexC].c;
float32 aC = data.positions[m_indexC].a;
b2Vec2 cD = data.positions[m_indexD].c;
float32 aD = data.positions[m_indexD].a;
b2Rot qA(aA), qB(aB), qC(aC), qD(aD);
float32 linearError = 0.0f;
float32 coordinateA, coordinateB;
b2Vec2 JvAC, JvBD;
float32 JwA, JwB, JwC, JwD;
float32 mass = 0.0f;
if (m_typeA == e_revoluteJoint)
{
JvAC.SetZero();
JwA = 1.0f;
JwC = 1.0f;
mass += m_iA + m_iC;
coordinateA = aA - aC - m_referenceAngleA;
}
else
{
b2Vec2 u = b2Mul(qC, m_localAxisC);
b2Vec2 rC = b2Mul(qC, m_localAnchorC - m_lcC);
b2Vec2 rA = b2Mul(qA, m_localAnchorA - m_lcA);
JvAC = u;
JwC = b2Cross(rC, u);
JwA = b2Cross(rA, u);
mass += m_mC + m_mA + m_iC * JwC * JwC + m_iA * JwA * JwA;
b2Vec2 pC = m_localAnchorC - m_lcC;
b2Vec2 pA = b2MulT(qC, rA + (cA - cC));
coordinateA = b2Dot(pA - pC, m_localAxisC);
}
if (m_typeB == e_revoluteJoint)
{
JvBD.SetZero();
JwB = m_ratio;
JwD = m_ratio;
mass += m_ratio * m_ratio * (m_iB + m_iD);
coordinateB = aB - aD - m_referenceAngleB;
}
else
{
b2Vec2 u = b2Mul(qD, m_localAxisD);
b2Vec2 rD = b2Mul(qD, m_localAnchorD - m_lcD);
b2Vec2 rB = b2Mul(qB, m_localAnchorB - m_lcB);
JvBD = m_ratio * u;
JwD = m_ratio * b2Cross(rD, u);
JwB = m_ratio * b2Cross(rB, u);
mass += m_ratio * m_ratio * (m_mD + m_mB) + m_iD * JwD * JwD + m_iB * JwB * JwB;
b2Vec2 pD = m_localAnchorD - m_lcD;
b2Vec2 pB = b2MulT(qD, rB + (cB - cD));
coordinateB = b2Dot(pB - pD, m_localAxisD);
}
float32 C = (coordinateA + m_ratio * coordinateB) - m_constant;
float32 impulse = 0.0f;
if (mass > 0.0f)
{
impulse = -C / mass;
}
cA += m_mA * impulse * JvAC;
aA += m_iA * impulse * JwA;
cB += m_mB * impulse * JvBD;
aB += m_iB * impulse * JwB;
cC -= m_mC * impulse * JvAC;
aC -= m_iC * impulse * JwC;
cD -= m_mD * impulse * JvBD;
aD -= m_iD * impulse * JwD;
data.positions[m_indexA].c = cA;
data.positions[m_indexA].a = aA;
data.positions[m_indexB].c = cB;
data.positions[m_indexB].a = aB;
data.positions[m_indexC].c = cC;
data.positions[m_indexC].a = aC;
data.positions[m_indexD].c = cD;
data.positions[m_indexD].a = aD;
// TODO_ERIN not implemented
return linearError < b2_linearSlop;
}
void b2PolygonShape::ComputeMass(b2MassData* massData, qreal density) const
{
// Polygon mass, centroid, and inertia.
// Let rho be the polygon density in mass per unit area.
// Then:
// mass = rho * int(dA)
// centroid.x = (1/mass) * rho * int(x * dA)
// centroid.y = (1/mass) * rho * int(y * dA)
// I = rho * int((x*x + y*y) * dA)
//
// We can compute these integrals by summing all the integrals
// for each triangle of the polygon. To evaluate the integral
// for a single triangle, we make a change of variables to
// the (u,v) coordinates of the triangle:
// x = x0 + e1x * u + e2x * v
// y = y0 + e1y * u + e2y * v
// where 0 <= u && 0 <= v && u + v <= 1.
//
// We integrate u from [0,1-v] and then v from [0,1].
// We also need to use the Jacobian of the transformation:
// D = cross(e1, e2)
//
// Simplification: triangle centroid = (1/3) * (p1 + p2 + p3)
//
// The rest of the derivation is handled by computer algebra.
b2Assert(m_vertexCount >= 3);
b2Vec2 center; center.Set(0.0f, 0.0f);
qreal area = 0.0f;
qreal I = 0.0f;
// pRef is the reference point for forming triangles.
// It's location doesn't change the result (except for rounding error).
b2Vec2 pRef(0.0f, 0.0f);
#if 0
// This code would put the reference point inside the polygon.
for (int32 i = 0; i < m_vertexCount; ++i)
{
pRef += m_vertices[i];
}
pRef *= 1.0f / count;
#endif
const qreal k_inv3 = 1.0f / 3.0f;
for (int32 i = 0; i < m_vertexCount; ++i)
{
// Triangle vertices.
b2Vec2 p1 = pRef;
b2Vec2 p2 = m_vertices[i];
b2Vec2 p3 = i + 1 < m_vertexCount ? m_vertices[i+1] : m_vertices[0];
b2Vec2 e1 = p2 - p1;
b2Vec2 e2 = p3 - p1;
qreal D = b2Cross(e1, e2);
qreal triangleArea = 0.5f * D;
area += triangleArea;
// Area weighted centroid
center += triangleArea * k_inv3 * (p1 + p2 + p3);
qreal px = p1.x, py = p1.y;
qreal ex1 = e1.x, ey1 = e1.y;
qreal ex2 = e2.x, ey2 = e2.y;
qreal intx2 = k_inv3 * (0.25f * (ex1*ex1 + ex2*ex1 + ex2*ex2) + (px*ex1 + px*ex2)) + 0.5f*px*px;
qreal inty2 = k_inv3 * (0.25f * (ey1*ey1 + ey2*ey1 + ey2*ey2) + (py*ey1 + py*ey2)) + 0.5f*py*py;
I += D * (intx2 + inty2);
}
// Total mass
massData->mass = density * area;
// Center of mass
b2Assert(area > b2_epsilon);
center *= 1.0f / area;
massData->center = center;
// Inertia tensor relative to the local origin.
massData->I = density * I;
}
