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 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; }
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; }
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; 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; b2Vec2 cC = data.positions[m_indexC].c; float32 aC = data.positions[m_indexC].a; b2Vec2 vC = data.velocities[m_indexC].v; float32 wC = data.velocities[m_indexC].w; b2Vec2 cD = data.positions[m_indexD].c; 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; }
void b2DistanceJoint::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; // Handle singularity. float32 length = m_u.Length(); if (length > b2_linearSlop) { m_u *= 1.0f / length; } else { m_u.Set(0.0f, 0.0f); } float32 crAu = b2Cross(m_rA, m_u); float32 crBu = b2Cross(m_rB, m_u); float32 invMass = m_invMassA + m_invIA * crAu * crAu + m_invMassB + m_invIB * crBu * crBu; // Compute the effective mass matrix. m_mass = invMass != 0.0f ? 1.0f / invMass : 0.0f; if (m_frequencyHz > 0.0f) { float32 C = length - m_length; // Frequency float32 omega = 2.0f * b2_pi * m_frequencyHz; // Damping coefficient float32 d = 2.0f * m_mass * m_dampingRatio * omega; // Spring stiffness float32 k = m_mass * 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; invMass += m_gamma; m_mass = invMass != 0.0f ? 1.0f / invMass : 0.0f; } else { m_gamma = 0.0f; m_bias = 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 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; }
bool b2WeldJoint::SolvePositionConstraints(const b2SolverData& data) { b2Vec2 cA = data.positions[m_indexA].c; float aA = data.positions[m_indexA].a; b2Vec2 cB = data.positions[m_indexB].c; float aB = data.positions[m_indexB].a; b2Rot qA(aA), qB(aB); float mA = m_invMassA, mB = m_invMassB; float iA = m_invIA, iB = m_invIB; b2Vec2 rA = b2Mul(qA, m_localAnchorA - m_localCenterA); b2Vec2 rB = b2Mul(qB, m_localAnchorB - m_localCenterB); float 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; float 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 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; //b2Vec2 cA = data.positions[m_indexA].c; float aA = data.positions[m_indexA].a; b2Vec2 vA = data.velocities[m_indexA].v; float wA = data.velocities[m_indexA].w; //b2Vec2 cB = data.positions[m_indexB].c; float aB = data.positions[m_indexB].a; b2Vec2 vB = data.velocities[m_indexB].v; float 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] float mA = m_invMassA, mB = m_invMassB; float 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); float invM = iA + iB; float m = invM > 0.0f ? 1.0f / invM : 0.0f; float C = aB - aA - m_referenceAngle; // Frequency float omega = 2.0f * b2_pi * m_frequencyHz; // Damping coefficient float d = 2.0f * m * m_dampingRatio * omega; // Spring stiffness float k = m * omega * omega; // magic formulas float 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 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 b2WheelJoint::InitVelocityConstraints(const b2SolverData& data) { m_indexA = m_bodyA->m_islandIndex; m_indexB = m_bodyB->m_islandIndex; m_localCenterA = m_bodyA->m_sweep.localCenter; m_localCenterB = m_bodyB->m_sweep.localCenter; m_invMassA = m_bodyA->m_invMass; m_invMassB = m_bodyB->m_invMass; m_invIA = m_bodyA->m_invI; m_invIB = m_bodyB->m_invI; float32 mA = m_invMassA, mB = m_invMassB; float32 iA = m_invIA, iB = m_invIB; b2Vec2 cA = data.positions[m_indexA].c; float32 aA = data.positions[m_indexA].a; b2Vec2 vA = data.velocities[m_indexA].v; float32 wA = data.velocities[m_indexA].w; b2Vec2 cB = data.positions[m_indexB].c; float32 aB = data.positions[m_indexB].a; b2Vec2 vB = data.velocities[m_indexB].v; float32 wB = data.velocities[m_indexB].w; b2Rot qA(aA), qB(aB); // Compute the effective masses. b2Vec2 rA = b2Mul(qA, m_localAnchorA - m_localCenterA); b2Vec2 rB = b2Mul(qB, m_localAnchorB - m_localCenterB); b2Vec2 d = cB + rB - cA - rA; // Point to line constraint { m_ay = b2Mul(qA, m_localYAxisA); m_sAy = b2Cross(d + rA, m_ay); m_sBy = b2Cross(rB, m_ay); m_mass = mA + mB + iA * m_sAy * m_sAy + iB * m_sBy * m_sBy; if (m_mass > 0.0f) { m_mass = 1.0f / m_mass; } } // Spring constraint m_springMass = 0.0f; m_bias = 0.0f; m_gamma = 0.0f; if (m_frequencyHz > 0.0f) { m_ax = b2Mul(qA, m_localXAxisA); m_sAx = b2Cross(d + rA, m_ax); m_sBx = b2Cross(rB, m_ax); float32 invMass = mA + mB + iA * m_sAx * m_sAx + iB * m_sBx * m_sBx; if (invMass > 0.0f) { m_springMass = 1.0f / invMass; float32 C = b2Dot(d, m_ax); // Frequency float32 omega = 2.0f * b2_pi * m_frequencyHz; // Damping coefficient float32 d = 2.0f * m_springMass * m_dampingRatio * omega; // Spring stiffness float32 k = m_springMass * omega * omega; // magic formulas float32 h = data.step.dt; m_gamma = h * (d + h * k); if (m_gamma > 0.0f) { m_gamma = 1.0f / m_gamma; } m_bias = C * h * k * m_gamma; m_springMass = invMass + m_gamma; if (m_springMass > 0.0f) { m_springMass = 1.0f / m_springMass; } } } else { m_springImpulse = 0.0f; } // Rotational motor if (m_enableMotor) { m_motorMass = iA + iB; if (m_motorMass > 0.0f) { m_motorMass = 1.0f / m_motorMass; } } else { m_motorMass = 0.0f; m_motorImpulse = 0.0f; } if (data.step.warmStarting) { // Account for variable time step. m_impulse *= data.step.dtRatio; m_springImpulse *= data.step.dtRatio; m_motorImpulse *= data.step.dtRatio; b2Vec2 P = m_impulse * m_ay + m_springImpulse * m_ax; float32 LA = m_impulse * m_sAy + m_springImpulse * m_sAx + m_motorImpulse; float32 LB = m_impulse * m_sBy + m_springImpulse * m_sBx + m_motorImpulse; vA -= m_invMassA * P; wA -= m_invIA * LA; vB += m_invMassB * P; wB += m_invIB * LB; } else { m_impulse = 0.0f; m_springImpulse = 0.0f; m_motorImpulse = 0.0f; } data.velocities[m_indexA].v = vA; data.velocities[m_indexA].w = wA; data.velocities[m_indexB].v = vB; data.velocities[m_indexB].w = wB; }
void 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; }
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 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; }
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; }
void b2MouseJoint::InitVelocityConstraints(const b2SolverData& data) { m_indexB = m_bodyB->m_islandIndex; m_localCenterB = m_bodyB->m_sweep.localCenter; m_invMassB = m_bodyB->m_invMass; m_invIB = m_bodyB->m_invI; 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 qB(aB); float32 mass = m_bodyB->GetMass(); // Frequency float32 omega = 2.0f * b2_pi * m_frequencyHz; // Damping coefficient float32 d = 2.0f * mass * m_dampingRatio * omega; // Spring stiffness float32 k = mass * (omega * omega); // magic formulas // gamma has units of inverse mass. // beta has units of inverse time. float32 h = data.step.dt; b2Assert(d + h * k > b2_epsilon); m_gamma = h * (d + h * k); if (m_gamma != 0.0f) { m_gamma = 1.0f / m_gamma; } m_beta = h * k * m_gamma; // Compute the effective mass matrix. m_rB = b2Mul(qB, m_localAnchorB - m_localCenterB); // K = [(1/m1 + 1/m2) * eye(2) - skew(r1) * invI1 * skew(r1) - skew(r2) * invI2 * skew(r2)] // = [1/m1+1/m2 0 ] + invI1 * [r1.y*r1.y -r1.x*r1.y] + invI2 * [r1.y*r1.y -r1.x*r1.y] // [ 0 1/m1+1/m2] [-r1.x*r1.y r1.x*r1.x] [-r1.x*r1.y r1.x*r1.x] b2Mat22 K; K.ex.x = m_invMassB + m_invIB * m_rB.y * m_rB.y + m_gamma; K.ex.y = -m_invIB * m_rB.x * m_rB.y; K.ey.x = K.ex.y; K.ey.y = m_invMassB + m_invIB * m_rB.x * m_rB.x + m_gamma; m_mass = K.GetInverse(); m_C = cB + m_rB - m_targetA; m_C *= m_beta; // Cheat with some damping wB *= 0.98f; if (data.step.warmStarting) { m_impulse *= data.step.dtRatio; vB += m_invMassB * m_impulse; wB += m_invIB * b2Cross(m_rB, m_impulse); } else { m_impulse.SetZero(); } data.velocities[m_indexB].v = vB; data.velocities[m_indexB].w = wB; }