diff options
author | chai <chaifix@163.com> | 2020-09-10 20:30:31 +0800 |
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committer | chai <chaifix@163.com> | 2020-09-10 20:30:31 +0800 |
commit | 639b34294ffc20721c66db46e59e07d9100ac4b8 (patch) | |
tree | 7e1d45b536fa35e9f1559e468ea66fca99524573 /ThirdParty/Box2D/Dynamics/Joints/b2PrismaticJoint.cpp |
*init
Diffstat (limited to 'ThirdParty/Box2D/Dynamics/Joints/b2PrismaticJoint.cpp')
-rw-r--r-- | ThirdParty/Box2D/Dynamics/Joints/b2PrismaticJoint.cpp | 642 |
1 files changed, 642 insertions, 0 deletions
diff --git a/ThirdParty/Box2D/Dynamics/Joints/b2PrismaticJoint.cpp b/ThirdParty/Box2D/Dynamics/Joints/b2PrismaticJoint.cpp new file mode 100644 index 0000000..5da19b6 --- /dev/null +++ b/ThirdParty/Box2D/Dynamics/Joints/b2PrismaticJoint.cpp @@ -0,0 +1,642 @@ +/* +* 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 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; +} + +// A velocity based solver computes reaction forces(impulses) using the velocity constraint solver.Under this context, +// the position solver is not there to resolve forces.It is only there to cope with integration error. +// +// Therefore, the pseudo impulses in the position solver do not have any physical meaning.Thus it is okay if they suck. +// +// We could take the active state from the velocity solver.However, the joint might push past the limit when the velocity +// solver indicates the limit is inactive. +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) +{ + if (flag != m_enableMotor) + { + m_bodyA->SetAwake(true); + m_bodyB->SetAwake(true); + m_enableMotor = flag; + } +} + +void b2PrismaticJoint::SetMotorSpeed(float32 speed) +{ + if (speed != m_motorSpeed) + { + m_bodyA->SetAwake(true); + m_bodyB->SetAwake(true); + m_motorSpeed = speed; + } +} + +void b2PrismaticJoint::SetMaxMotorForce(float32 force) +{ + if (force != m_maxMotorForce) + { + 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); +} |