paulxstretch/deps/juce/modules/juce_box2d/box2d/Dynamics/Joints/b2PrismaticJoint.cpp

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/*
* 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 "b2PrismaticJoint.h"
#include "../b2Body.h"
#include "../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;
Cdot1.x = b2Dot(m_perp, vB - vA) + m_s2 * wB - m_s1 * wA;
Cdot1.y = wB - wA;
/*if (b2Abs(Cdot1.x) > 0.01f || b2Abs(Cdot1.y) > 0.01f)
{
b2Vec2 test = b2Mul22(m_K, df);
Cdot1.x += 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;
}
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);
}