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+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#include "box2d/b2_body.h"
+#include "box2d/b2_motor_joint.h"
+#include "box2d/b2_time_step.h"
+
+// Point-to-point constraint
+// Cdot = v2 - v1
+// = v2 + cross(w2, r2) - v1 - cross(w1, r1)
+// J = [-I -r1_skew I r2_skew ]
+// Identity used:
+// w k % (rx i + ry j) = w * (-ry i + rx j)
+//
+// r1 = offset - c1
+// r2 = -c2
+
+// Angle constraint
+// Cdot = w2 - w1
+// J = [0 0 -1 0 0 1]
+// K = invI1 + invI2
+
+void b2MotorJointDef::Initialize(b2Body* bA, b2Body* bB)
+{
+ bodyA = bA;
+ bodyB = bB;
+ b2Vec2 xB = bodyB->GetPosition();
+ linearOffset = bodyA->GetLocalPoint(xB);
+
+ float angleA = bodyA->GetAngle();
+ float angleB = bodyB->GetAngle();
+ angularOffset = angleB - angleA;
+}
+
+b2MotorJoint::b2MotorJoint(const b2MotorJointDef* def)
+: b2Joint(def)
+{
+ m_linearOffset = def->linearOffset;
+ m_angularOffset = def->angularOffset;
+
+ m_linearImpulse.SetZero();
+ m_angularImpulse = 0.0f;
+
+ m_maxForce = def->maxForce;
+ m_maxTorque = def->maxTorque;
+ m_correctionFactor = def->correctionFactor;
+}
+
+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;
+ 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);
+
+ // Compute the effective mass matrix.
+ m_rA = b2Mul(qA, m_linearOffset - m_localCenterA);
+ m_rB = b2Mul(qB, -m_localCenterB);
+
+ // J = [-I -r1_skew I r2_skew]
+ // 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;
+
+ // Upper 2 by 2 of K for point to point
+ 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;
+ 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 b2MotorJoint::SolveVelocityConstraints(const b2SolverData& data)
+{
+ b2Vec2 vA = data.velocities[m_indexA].v;
+ float wA = data.velocities[m_indexA].w;
+ b2Vec2 vB = data.velocities[m_indexB].v;
+ float wB = data.velocities[m_indexB].w;
+
+ float mA = m_invMassA, mB = m_invMassB;
+ float iA = m_invIA, iB = m_invIB;
+
+ float h = data.step.dt;
+ float inv_h = data.step.inv_dt;
+
+ // Solve angular friction
+ {
+ float Cdot = wB - wA + inv_h * m_correctionFactor * m_angularError;
+ float impulse = -m_angularMass * Cdot;
+
+ float oldImpulse = m_angularImpulse;
+ float maxImpulse = h * m_maxTorque;
+ m_angularImpulse = b2Clamp(m_angularImpulse + impulse, -maxImpulse, maxImpulse);
+ impulse = m_angularImpulse - oldImpulse;
+
+ wA -= iA * impulse;
+ wB += iB * impulse;
+ }
+
+ // Solve linear friction
+ {
+ b2Vec2 Cdot = vB + b2Cross(wB, m_rB) - vA - b2Cross(wA, m_rA) + inv_h * m_correctionFactor * m_linearError;
+
+ b2Vec2 impulse = -b2Mul(m_linearMass, Cdot);
+ b2Vec2 oldImpulse = m_linearImpulse;
+ m_linearImpulse += impulse;
+
+ float maxImpulse = h * m_maxForce;
+
+ if (m_linearImpulse.LengthSquared() > maxImpulse * maxImpulse)
+ {
+ m_linearImpulse.Normalize();
+ m_linearImpulse *= maxImpulse;
+ }
+
+ impulse = m_linearImpulse - oldImpulse;
+
+ 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;
+}
+
+bool b2MotorJoint::SolvePositionConstraints(const b2SolverData& data)
+{
+ B2_NOT_USED(data);
+
+ return true;
+}
+
+b2Vec2 b2MotorJoint::GetAnchorA() const
+{
+ return m_bodyA->GetPosition();
+}
+
+b2Vec2 b2MotorJoint::GetAnchorB() const
+{
+ return m_bodyB->GetPosition();
+}
+
+b2Vec2 b2MotorJoint::GetReactionForce(float inv_dt) const
+{
+ return inv_dt * m_linearImpulse;
+}
+
+float b2MotorJoint::GetReactionTorque(float inv_dt) const
+{
+ return inv_dt * m_angularImpulse;
+}
+
+void b2MotorJoint::SetMaxForce(float force)
+{
+ b2Assert(b2IsValid(force) && force >= 0.0f);
+ m_maxForce = force;
+}
+
+float b2MotorJoint::GetMaxForce() const
+{
+ return m_maxForce;
+}
+
+void b2MotorJoint::SetMaxTorque(float torque)
+{
+ b2Assert(b2IsValid(torque) && torque >= 0.0f);
+ m_maxTorque = torque;
+}
+
+float b2MotorJoint::GetMaxTorque() const
+{
+ return m_maxTorque;
+}
+
+void b2MotorJoint::SetCorrectionFactor(float factor)
+{
+ b2Assert(b2IsValid(factor) && 0.0f <= factor && factor <= 1.0f);
+ m_correctionFactor = factor;
+}
+
+float b2MotorJoint::GetCorrectionFactor() const
+{
+ return m_correctionFactor;
+}
+
+void b2MotorJoint::SetLinearOffset(const b2Vec2& linearOffset)
+{
+ if (linearOffset.x != m_linearOffset.x || linearOffset.y != m_linearOffset.y)
+ {
+ m_bodyA->SetAwake(true);
+ m_bodyB->SetAwake(true);
+ m_linearOffset = linearOffset;
+ }
+}
+
+const b2Vec2& b2MotorJoint::GetLinearOffset() const
+{
+ return m_linearOffset;
+}
+
+void b2MotorJoint::SetAngularOffset(float angularOffset)
+{
+ if (angularOffset != m_angularOffset)
+ {
+ m_bodyA->SetAwake(true);
+ m_bodyB->SetAwake(true);
+ m_angularOffset = angularOffset;
+ }
+}
+
+float b2MotorJoint::GetAngularOffset() const
+{
+ return m_angularOffset;
+}
+
+void b2MotorJoint::Dump()
+{
+ int32 indexA = m_bodyA->m_islandIndex;
+ int32 indexB = m_bodyB->m_islandIndex;
+
+ b2Dump(" b2MotorJointDef jd;\n");
+ b2Dump(" jd.bodyA = bodies[%d];\n", indexA);
+ b2Dump(" jd.bodyB = bodies[%d];\n", indexB);
+ b2Dump(" jd.collideConnected = bool(%d);\n", m_collideConnected);
+ b2Dump(" jd.linearOffset.Set(%.9g, %.9g);\n", m_linearOffset.x, m_linearOffset.y);
+ b2Dump(" jd.angularOffset = %.9g;\n", m_angularOffset);
+ b2Dump(" jd.maxForce = %.9g;\n", m_maxForce);
+ b2Dump(" jd.maxTorque = %.9g;\n", m_maxTorque);
+ b2Dump(" jd.correctionFactor = %.9g;\n", m_correctionFactor);
+ b2Dump(" joints[%d] = m_world->CreateJoint(&jd);\n", m_index);
+}