File indexing completed on 2025-08-03 03:49:59

 /*
 * Copyright (c) 2006-2007 Erin Catto http://www.gphysics.com
 *
 * 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* b1, b2Body* b2, const b2Vec2& anchor, const b2Vec2& axis)
 {
     bodyA = b1;
     bodyB = b2;
     localAnchorA = bodyA->GetLocalPoint(anchor);
     localAnchorB = bodyB->GetLocalPoint(anchor);
     localAxis1 = bodyA->GetLocalVector(axis);
     referenceAngle = bodyB->GetAngle() - bodyA->GetAngle();
 }
 
 b2PrismaticJoint::b2PrismaticJoint(const b2PrismaticJointDef* def)
 : b2Joint(def)
 {
     m_localAnchor1 = def->localAnchorA;
     m_localAnchor2 = def->localAnchorB;
     m_localXAxis1 = def->localAxis1;
     m_localYAxis1 = b2Cross(1.0f, m_localXAxis1);
     m_refAngle = def->referenceAngle;
 
     m_impulse.SetZero();
     m_motorMass = 0.0;
     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 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);
 
         qreal m1 = m_invMassA, m2 = m_invMassB;
         qreal i1 = m_invIA, i2 = m_invIB;
 
         qreal k11 = m1 + m2 + i1 * m_s1 * m_s1 + i2 * m_s2 * m_s2;
         qreal k12 = i1 * m_s1 + i2 * m_s2;
         qreal k13 = i1 * m_s1 * m_a1 + i2 * m_s2 * m_a2;
         qreal k22 = i1 + i2;
         if (k22 == 0.0f)
         {
             k22 = 1.0f;
         }
         qreal k23 = i1 * m_a1 + i2 * m_a2;
         qreal 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)
     {
         qreal 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;
         qreal L1 = m_impulse.x * m_s1 + m_impulse.y + (m_motorImpulse + m_impulse.z) * m_a1;
         qreal 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 b2PrismaticJoint::SolveVelocityConstraints(const b2TimeStep& step)
 {
     b2Body* b1 = m_bodyA;
     b2Body* b2 = m_bodyB;
 
     b2Vec2 v1 = b1->m_linearVelocity;
     qreal w1 = b1->m_angularVelocity;
     b2Vec2 v2 = b2->m_linearVelocity;
     qreal w2 = b2->m_angularVelocity;
 
     // Solve linear motor constraint.
     if (m_enableMotor && m_limitState != e_equalLimits)
     {
         qreal Cdot = b2Dot(m_axis, v2 - v1) + m_a2 * w2 - m_a1 * w1;
         qreal impulse = m_motorMass * (m_motorSpeed - Cdot);
         qreal oldImpulse = m_motorImpulse;
         qreal maxImpulse = step.dt * m_maxMotorForce;
         m_motorImpulse = b2Clamp(m_motorImpulse + impulse, -maxImpulse, maxImpulse);
         impulse = m_motorImpulse - oldImpulse;
 
         b2Vec2 P = impulse * m_axis;
         qreal L1 = impulse * m_a1;
         qreal L2 = impulse * m_a2;
 
         v1 -= m_invMassA * P;
         w1 -= m_invIA * L1;
 
         v2 += m_invMassB * P;
         w2 += m_invIB * L2;
     }
 
     b2Vec2 Cdot1;
     Cdot1.x = b2Dot(m_perp, v2 - v1) + m_s2 * w2 - m_s1 * w1;
     Cdot1.y = w2 - w1;
 
     if (m_enableLimit && m_limitState != e_inactiveLimit)
     {
         // Solve prismatic and limit constraint in block form.
         qreal Cdot2;
         Cdot2 = b2Dot(m_axis, v2 - v1) + m_a2 * w2 - m_a1 * w1;
         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.col3.x, m_K.col3.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;
         qreal L1 = df.x * m_s1 + df.y + df.z * m_a1;
         qreal L2 = df.x * m_s2 + df.y + df.z * m_a2;
 
         v1 -= m_invMassA * P;
         w1 -= m_invIA * L1;
 
         v2 += m_invMassB * P;
         w2 += m_invIB * L2;
     }
     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;
         qreal L1 = df.x * m_s1 + df.y;
         qreal L2 = df.x * m_s2 + df.y;
 
         v1 -= m_invMassA * P;
         w1 -= m_invIA * L1;
 
         v2 += m_invMassB * P;
         w2 += m_invIB * L2;
     }
 
     b1->m_linearVelocity = v1;
     b1->m_angularVelocity = w1;
     b2->m_linearVelocity = v2;
     b2->m_angularVelocity = w2;
 }
 
 bool b2PrismaticJoint::SolvePositionConstraints(qreal baumgarte)
 {
     B2_NOT_USED(baumgarte);
 
     b2Body* b1 = m_bodyA;
     b2Body* b2 = m_bodyB;
 
     b2Vec2 c1 = b1->m_sweep.c;
     qreal a1 = b1->m_sweep.a;
 
     b2Vec2 c2 = b2->m_sweep.c;
     qreal a2 = b2->m_sweep.a;
 
     // Solve linear limit constraint.
     qreal linearError = 0.0f, angularError = 0.0f;
     bool active = false;
     qreal 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);
 
         qreal 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)
     {
         qreal m1 = m_invMassA, m2 = m_invMassB;
         qreal i1 = m_invIA, i2 = m_invIB;
 
         qreal k11 = m1 + m2 + i1 * m_s1 * m_s1 + i2 * m_s2 * m_s2;
         qreal k12 = i1 * m_s1 + i2 * m_s2;
         qreal k13 = i1 * m_s1 * m_a1 + i2 * m_s2 * m_a2;
         qreal k22 = i1 + i2;
         if (k22 == 0.0f)
         {
             k22 = 1.0f;
         }
         qreal k23 = i1 * m_a1 + i2 * m_a2;
         qreal 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
     {
         qreal m1 = m_invMassA, m2 = m_invMassB;
         qreal i1 = m_invIA, i2 = m_invIB;
 
         qreal k11 = m1 + m2 + i1 * m_s1 * m_s1 + i2 * m_s2 * m_s2;
         qreal k12 = i1 * m_s1 + i2 * m_s2;
         qreal k22 = i1 + i2;
         if (k22 == 0.0f)
         {
             k22 = 1.0f;
         }
 
         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;
     qreal L1 = impulse.x * m_s1 + impulse.y + impulse.z * m_a1;
     qreal 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;
 }
 
 b2Vec2 b2PrismaticJoint::GetAnchorA() const
 {
     return m_bodyA->GetWorldPoint(m_localAnchor1);
 }
 
 b2Vec2 b2PrismaticJoint::GetAnchorB() const
 {
     return m_bodyB->GetWorldPoint(m_localAnchor2);
 }
 
 b2Vec2 b2PrismaticJoint::GetReactionForce(qreal inv_dt) const
 {
     return inv_dt * (m_impulse.x * m_perp + (m_motorImpulse + m_impulse.z) * m_axis);
 }
 
 qreal b2PrismaticJoint::GetReactionTorque(qreal inv_dt) const
 {
     return inv_dt * m_impulse.y;
 }
 
 qreal b2PrismaticJoint::GetJointTranslation() const
 {
     b2Body* b1 = m_bodyA;
     b2Body* b2 = m_bodyB;
 
     b2Vec2 p1 = b1->GetWorldPoint(m_localAnchor1);
     b2Vec2 p2 = b2->GetWorldPoint(m_localAnchor2);
     b2Vec2 d = p2 - p1;
     b2Vec2 axis = b1->GetWorldVector(m_localXAxis1);
 
     qreal translation = b2Dot(d, axis);
     return translation;
 }
 
 qreal b2PrismaticJoint::GetJointSpeed() const
 {
     b2Body* b1 = m_bodyA;
     b2Body* b2 = m_bodyB;
 
     b2Vec2 r1 = b2Mul(b1->GetTransform().R, m_localAnchor1 - b1->GetLocalCenter());
     b2Vec2 r2 = b2Mul(b2->GetTransform().R, m_localAnchor2 - b2->GetLocalCenter());
     b2Vec2 p1 = b1->m_sweep.c + r1;
     b2Vec2 p2 = b2->m_sweep.c + r2;
     b2Vec2 d = p2 - p1;
     b2Vec2 axis = b1->GetWorldVector(m_localXAxis1);
 
     b2Vec2 v1 = b1->m_linearVelocity;
     b2Vec2 v2 = b2->m_linearVelocity;
     qreal w1 = b1->m_angularVelocity;
     qreal w2 = b2->m_angularVelocity;
 
     qreal speed = b2Dot(d, b2Cross(w1, axis)) + b2Dot(axis, v2 + b2Cross(w2, r2) - v1 - b2Cross(w1, r1));
     return speed;
 }
 
 bool b2PrismaticJoint::IsLimitEnabled() const
 {
     return m_enableLimit;
 }
 
 void b2PrismaticJoint::EnableLimit(bool flag)
 {
     m_bodyA->SetAwake(true);
     m_bodyB->SetAwake(true);
     m_enableLimit = flag;
 }
 
 qreal b2PrismaticJoint::GetLowerLimit() const
 {
     return m_lowerTranslation;
 }
 
 qreal b2PrismaticJoint::GetUpperLimit() const
 {
     return m_upperTranslation;
 }
 
 void b2PrismaticJoint::SetLimits(qreal lower, qreal upper)
 {
     b2Assert(lower <= upper);
     m_bodyA->SetAwake(true);
     m_bodyB->SetAwake(true);
     m_lowerTranslation = lower;
     m_upperTranslation = upper;
 }
 
 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(qreal speed)
 {
     m_bodyA->SetAwake(true);
     m_bodyB->SetAwake(true);
     m_motorSpeed = speed;
 }
 
 void b2PrismaticJoint::SetMaxMotorForce(qreal force)
 {
     m_bodyA->SetAwake(true);
     m_bodyB->SetAwake(true);
     m_maxMotorForce = force;
 }
 
 qreal b2PrismaticJoint::GetMotorForce(qreal inv_dt) const
 {
     return inv_dt * m_motorImpulse;
 }