File indexing completed on 2024-12-29 03:29:27

 /*
 * Copyright (c) 2006-2011 Erin Catto http://www.box2d.org
 *
 * This software is provided 'as-is', without any express or implied
 * warranty.  In no event will the authors be held liable for any damages
 * arising from the use of this software.
 * Permission is granted to anyone to use this software for any purpose,
 * including commercial applications, and to alter it and redistribute it
 * freely, subject to the following restrictions:
 * 1. The origin of this software must not be misrepresented; you must not
 * claim that you wrote the original software. If you use this software
 * in a product, an acknowledgment in the product documentation would be
 * appreciated but is not required.
 * 2. Altered source versions must be plainly marked as such, and must not be
 * misrepresented as being the original software.
 * 3. This notice may not be removed or altered from any source distribution.
 */
 
 #include <Box2D/Dynamics/Joints/b2PrismaticJoint.h>
 #include <Box2D/Dynamics/b2Body.h>
 #include <Box2D/Dynamics/b2TimeStep.h>
 
 // Linear constraint (point-to-line)
 // d = p2 - p1 = x2 + r2 - x1 - r1
 // C = dot(perp, d)
 // Cdot = dot(d, cross(w1, perp)) + dot(perp, v2 + cross(w2, r2) - v1 - cross(w1, r1))
 //      = -dot(perp, v1) - dot(cross(d + r1, perp), w1) + dot(perp, v2) + dot(cross(r2, perp), v2)
 // J = [-perp, -cross(d + r1, perp), perp, cross(r2,perp)]
 //
 // Angular constraint
 // C = a2 - a1 + a_initial
 // Cdot = w2 - w1
 // J = [0 0 -1 0 0 1]
 //
 // K = J * invM * JT
 //
 // J = [-a -s1 a s2]
 //     [0  -1  0  1]
 // a = perp
 // s1 = cross(d + r1, a) = cross(p2 - x1, a)
 // s2 = cross(r2, a) = cross(p2 - x2, a)
 
 
 // Motor/Limit linear constraint
 // C = dot(ax1, d)
 // Cdot = = -dot(ax1, v1) - dot(cross(d + r1, ax1), w1) + dot(ax1, v2) + dot(cross(r2, ax1), v2)
 // J = [-ax1 -cross(d+r1,ax1) ax1 cross(r2,ax1)]
 
 // Block Solver
 // We develop a block solver that includes the joint limit. This makes the limit stiff (inelastic) even
 // when the mass has poor distribution (leading to large torques about the joint anchor points).
 //
 // The Jacobian has 3 rows:
 // J = [-uT -s1 uT s2] // linear
 //     [0   -1   0  1] // angular
 //     [-vT -a1 vT a2] // limit
 //
 // u = perp
 // v = axis
 // s1 = cross(d + r1, u), s2 = cross(r2, u)
 // a1 = cross(d + r1, v), a2 = cross(r2, v)
 
 // M * (v2 - v1) = JT * df
 // J * v2 = bias
 //
 // v2 = v1 + invM * JT * df
 // J * (v1 + invM * JT * df) = bias
 // K * df = bias - J * v1 = -Cdot
 // K = J * invM * JT
 // Cdot = J * v1 - bias
 //
 // Now solve for f2.
 // df = f2 - f1
 // K * (f2 - f1) = -Cdot
 // f2 = invK * (-Cdot) + f1
 //
 // Clamp accumulated limit impulse.
 // lower: f2(3) = max(f2(3), 0)
 // upper: f2(3) = min(f2(3), 0)
 //
 // Solve for correct f2(1:2)
 // K(1:2, 1:2) * f2(1:2) = -Cdot(1:2) - K(1:2,3) * f2(3) + K(1:2,1:3) * f1
 //                       = -Cdot(1:2) - K(1:2,3) * f2(3) + K(1:2,1:2) * f1(1:2) + K(1:2,3) * f1(3)
 // K(1:2, 1:2) * f2(1:2) = -Cdot(1:2) - K(1:2,3) * (f2(3) - f1(3)) + K(1:2,1:2) * f1(1:2)
 // f2(1:2) = invK(1:2,1:2) * (-Cdot(1:2) - K(1:2,3) * (f2(3) - f1(3))) + f1(1:2)
 //
 // Now compute impulse to be applied:
 // df = f2 - f1
 
 void b2PrismaticJointDef::Initialize(b2Body* bA, b2Body* bB, const b2Vec2& anchor, const b2Vec2& axis)
 {
     bodyA = bA;
     bodyB = bB;
     localAnchorA = bodyA->GetLocalPoint(anchor);
     localAnchorB = bodyB->GetLocalPoint(anchor);
     localAxisA = bodyA->GetLocalVector(axis);
     referenceAngle = bodyB->GetAngle() - bodyA->GetAngle();
 }
 
 b2PrismaticJoint::b2PrismaticJoint(const b2PrismaticJointDef* def)
 : b2Joint(def)
 {
     m_localAnchorA = def->localAnchorA;
     m_localAnchorB = def->localAnchorB;
     m_localXAxisA = def->localAxisA;
     m_localXAxisA.Normalize();
     m_localYAxisA = b2Cross(1.0f, m_localXAxisA);
     m_referenceAngle = def->referenceAngle;
 
     m_impulse.SetZero();
     m_motorMass = 0.0f;
     m_motorImpulse = 0.0f;
 
     m_lowerTranslation = def->lowerTranslation;
     m_upperTranslation = def->upperTranslation;
     m_maxMotorForce = def->maxMotorForce;
     m_motorSpeed = def->motorSpeed;
     m_enableLimit = def->enableLimit;
     m_enableMotor = def->enableMotor;
     m_limitState = e_inactiveLimit;
 
     m_axis.SetZero();
     m_perp.SetZero();
 }
 
 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 s1test;
         s1test = b2Cross(rA, 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 b2PrismaticJoint::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;
 
     // Solve linear motor constraint.
     if (m_enableMotor && m_limitState != e_equalLimits)
     {
         float32 Cdot = b2Dot(m_axis, vB - vA) + m_a2 * wB - m_a1 * wA;
         float32 impulse = m_motorMass * (m_motorSpeed - Cdot);
         float32 oldImpulse = m_motorImpulse;
         float32 maxImpulse = data.step.dt * m_maxMotorForce;
         m_motorImpulse = b2Clamp(m_motorImpulse + impulse, -maxImpulse, maxImpulse);
         impulse = m_motorImpulse - oldImpulse;
 
         b2Vec2 P = impulse * m_axis;
         float32 LA = impulse * m_a1;
         float32 LB = impulse * m_a2;
 
         vA -= mA * P;
         wA -= iA * LA;
 
         vB += mB * P;
         wB += iB * LB;
     }
 
     b2Vec2 Cdot1;
     Cdot1.x = b2Dot(m_perp, vB - vA) + m_s2 * wB - m_s1 * wA;
     Cdot1.y = wB - wA;
 
     if (m_enableLimit && m_limitState != e_inactiveLimit)
     {
         // Solve prismatic and limit constraint in block form.
         float32 Cdot2;
         Cdot2 = b2Dot(m_axis, vB - vA) + m_a2 * wB - m_a1 * wA;
         b2Vec3 Cdot(Cdot1.x, Cdot1.y, Cdot2);
 
         b2Vec3 f1 = m_impulse;
         b2Vec3 df =  m_K.Solve33(-Cdot);
         m_impulse += df;
 
         if (m_limitState == e_atLowerLimit)
         {
             m_impulse.z = b2Max(m_impulse.z, 0.0f);
         }
         else if (m_limitState == e_atUpperLimit)
         {
             m_impulse.z = b2Min(m_impulse.z, 0.0f);
         }
 
         // f2(1:2) = invK(1:2,1:2) * (-Cdot(1:2) - K(1:2,3) * (f2(3) - f1(3))) + f1(1:2)
         b2Vec2 b = -Cdot1 - (m_impulse.z - f1.z) * b2Vec2(m_K.ez.x, m_K.ez.y);
         b2Vec2 f2r = m_K.Solve22(b) + b2Vec2(f1.x, f1.y);
         m_impulse.x = f2r.x;
         m_impulse.y = f2r.y;
 
         df = m_impulse - f1;
 
         b2Vec2 P = df.x * m_perp + df.z * m_axis;
         float32 LA = df.x * m_s1 + df.y + df.z * m_a1;
         float32 LB = df.x * m_s2 + df.y + df.z * m_a2;
 
         vA -= mA * P;
         wA -= iA * LA;
 
         vB += mB * P;
         wB += iB * LB;
     }
     else
     {
         // Limit is inactive, just solve the prismatic constraint in block form.
         b2Vec2 df = m_K.Solve22(-Cdot1);
         m_impulse.x += df.x;
         m_impulse.y += df.y;
 
         b2Vec2 P = df.x * m_perp;
         float32 LA = df.x * m_s1 + df.y;
         float32 LB = df.x * m_s2 + df.y;
 
         vA -= mA * P;
         wA -= iA * LA;
 
         vB += mB * P;
         wB += iB * LB;
     }
 
     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;
 }
 
 b2Vec2 b2PrismaticJoint::GetAnchorA() const
 {
     return m_bodyA->GetWorldPoint(m_localAnchorA);
 }
 
 b2Vec2 b2PrismaticJoint::GetAnchorB() const
 {
     return m_bodyB->GetWorldPoint(m_localAnchorB);
 }
 
 b2Vec2 b2PrismaticJoint::GetReactionForce(float32 inv_dt) const
 {
     return inv_dt * (m_impulse.x * m_perp + (m_motorImpulse + m_impulse.z) * m_axis);
 }
 
 float32 b2PrismaticJoint::GetReactionTorque(float32 inv_dt) const
 {
     return inv_dt * m_impulse.y;
 }
 
 float32 b2PrismaticJoint::GetJointTranslation() const
 {
     b2Vec2 pA = m_bodyA->GetWorldPoint(m_localAnchorA);
     b2Vec2 pB = m_bodyB->GetWorldPoint(m_localAnchorB);
     b2Vec2 d = pB - pA;
     b2Vec2 axis = m_bodyA->GetWorldVector(m_localXAxisA);
 
     float32 translation = b2Dot(d, axis);
     return translation;
 }
 
 float32 b2PrismaticJoint::GetJointSpeed() const
 {
     b2Body* bA = m_bodyA;
     b2Body* bB = m_bodyB;
 
     b2Vec2 rA = b2Mul(bA->m_xf.q, m_localAnchorA - bA->m_sweep.localCenter);
     b2Vec2 rB = b2Mul(bB->m_xf.q, m_localAnchorB - bB->m_sweep.localCenter);
     b2Vec2 p1 = bA->m_sweep.c + rA;
     b2Vec2 p2 = bB->m_sweep.c + rB;
     b2Vec2 d = p2 - p1;
     b2Vec2 axis = b2Mul(bA->m_xf.q, m_localXAxisA);
 
     b2Vec2 vA = bA->m_linearVelocity;
     b2Vec2 vB = bB->m_linearVelocity;
     float32 wA = bA->m_angularVelocity;
     float32 wB = bB->m_angularVelocity;
 
     float32 speed = b2Dot(d, b2Cross(wA, axis)) + b2Dot(axis, vB + b2Cross(wB, rB) - vA - b2Cross(wA, rA));
     return speed;
 }
 
 bool b2PrismaticJoint::IsLimitEnabled() const
 {
     return m_enableLimit;
 }
 
 void b2PrismaticJoint::EnableLimit(bool flag)
 {
     if (flag != m_enableLimit)
     {
         m_bodyA->SetAwake(true);
         m_bodyB->SetAwake(true);
         m_enableLimit = flag;
         m_impulse.z = 0.0f;
     }
 }
 
 float32 b2PrismaticJoint::GetLowerLimit() const
 {
     return m_lowerTranslation;
 }
 
 float32 b2PrismaticJoint::GetUpperLimit() const
 {
     return m_upperTranslation;
 }
 
 void b2PrismaticJoint::SetLimits(float32 lower, float32 upper)
 {
     b2Assert(lower <= upper);
     if (lower != m_lowerTranslation || upper != m_upperTranslation)
     {
         m_bodyA->SetAwake(true);
         m_bodyB->SetAwake(true);
         m_lowerTranslation = lower;
         m_upperTranslation = upper;
         m_impulse.z = 0.0f;
     }
 }
 
 bool b2PrismaticJoint::IsMotorEnabled() const
 {
     return m_enableMotor;
 }
 
 void b2PrismaticJoint::EnableMotor(bool flag)
 {
     m_bodyA->SetAwake(true);
     m_bodyB->SetAwake(true);
     m_enableMotor = flag;
 }
 
 void b2PrismaticJoint::SetMotorSpeed(float32 speed)
 {
     m_bodyA->SetAwake(true);
     m_bodyB->SetAwake(true);
     m_motorSpeed = speed;
 }
 
 void b2PrismaticJoint::SetMaxMotorForce(float32 force)
 {
     m_bodyA->SetAwake(true);
     m_bodyB->SetAwake(true);
     m_maxMotorForce = force;
 }
 
 float32 b2PrismaticJoint::GetMotorForce(float32 inv_dt) const
 {
     return inv_dt * m_motorImpulse;
 }
 
 void b2PrismaticJoint::Dump()
 {
     int32 indexA = m_bodyA->m_islandIndex;
     int32 indexB = m_bodyB->m_islandIndex;
 
     b2Log("  b2PrismaticJointDef jd;\n");
     b2Log("  jd.bodyA = bodies[%d];\n", indexA);
     b2Log("  jd.bodyB = bodies[%d];\n", indexB);
     b2Log("  jd.collideConnected = bool(%d);\n", m_collideConnected);
     b2Log("  jd.localAnchorA.Set(%.15lef, %.15lef);\n", m_localAnchorA.x, m_localAnchorA.y);
     b2Log("  jd.localAnchorB.Set(%.15lef, %.15lef);\n", m_localAnchorB.x, m_localAnchorB.y);
     b2Log("  jd.localAxisA.Set(%.15lef, %.15lef);\n", m_localXAxisA.x, m_localXAxisA.y);
     b2Log("  jd.referenceAngle = %.15lef;\n", m_referenceAngle);
     b2Log("  jd.enableLimit = bool(%d);\n", m_enableLimit);
     b2Log("  jd.lowerTranslation = %.15lef;\n", m_lowerTranslation);
     b2Log("  jd.upperTranslation = %.15lef;\n", m_upperTranslation);
     b2Log("  jd.enableMotor = bool(%d);\n", m_enableMotor);
     b2Log("  jd.motorSpeed = %.15lef;\n", m_motorSpeed);
     b2Log("  jd.maxMotorForce = %.15lef;\n", m_maxMotorForce);
     b2Log("  joints[%d] = m_world->CreateJoint(&jd);\n", m_index);
 }