b2PrismaticJoint.cpp
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- /*
- * 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);
- 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 b2PrismaticJoint::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;
- // Solve linear motor constraint.
- if (m_enableMotor && m_limitState != e_equalLimits)
- {
- float32 Cdot = b2Dot(m_axis, v2 - v1) + m_a2 * w2 - m_a1 * w1;
- float32 impulse = m_motorMass * (m_motorSpeed - Cdot);
- float32 oldImpulse = m_motorImpulse;
- float32 maxImpulse = step.dt * m_maxMotorForce;
- m_motorImpulse = b2Clamp(m_motorImpulse + impulse, -maxImpulse, maxImpulse);
- impulse = m_motorImpulse - oldImpulse;
- b2Vec2 P = impulse * m_axis;
- float32 L1 = impulse * m_a1;
- float32 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.
- float32 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;
- float32 L1 = df.x * m_s1 + df.y + df.z * m_a1;
- float32 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;
- float32 L1 = df.x * m_s1 + df.y;
- float32 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(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;
- }
- b2Vec2 b2PrismaticJoint::GetAnchorA() const
- {
- return m_bodyA->GetWorldPoint(m_localAnchor1);
- }
- b2Vec2 b2PrismaticJoint::GetAnchorB() const
- {
- return m_bodyB->GetWorldPoint(m_localAnchor2);
- }
- 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
- {
- 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);
- float32 translation = b2Dot(d, axis);
- return translation;
- }
- float32 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;
- float32 w1 = b1->m_angularVelocity;
- float32 w2 = b2->m_angularVelocity;
- float32 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;
- }
- float32 b2PrismaticJoint::GetLowerLimit() const
- {
- return m_lowerTranslation;
- }
- float32 b2PrismaticJoint::GetUpperLimit() const
- {
- return m_upperTranslation;
- }
- void b2PrismaticJoint::SetLimits(float32 lower, float32 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(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() const
- {
- return m_motorImpulse;
- }