/*******************************************************************************
* Copyright (c) 2013, Daniel Murphy
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without modification,
* are permitted provided that the following conditions are met:
* * Redistributions of source code must retain the above copyright notice,
* this list of conditions and the following disclaimer.
* * Redistributions in binary form must reproduce the above copyright notice,
* this list of conditions and the following disclaimer in the documentation
* and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
* WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
* IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT,
* INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
* PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY,
* WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
* POSSIBILITY OF SUCH DAMAGE.
******************************************************************************/
/**
* Created at 3:38:38 AM Jan 15, 2011
*/
package org.jbox2d.dynamics.joints;
import org.jbox2d.common.Mat33;
import org.jbox2d.common.MathUtils;
import org.jbox2d.common.Rot;
import org.jbox2d.common.Settings;
import org.jbox2d.common.Vec2;
import org.jbox2d.common.Vec3;
import org.jbox2d.dynamics.SolverData;
import org.jbox2d.pooling.IWorldPool;
//Point-to-point constraint
//C = p2 - p1
//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)
//Angle constraint
//C = angle2 - angle1 - referenceAngle
//Cdot = w2 - w1
//J = [0 0 -1 0 0 1]
//K = invI1 + invI2
/**
* A weld joint essentially glues two bodies together. A weld joint may distort somewhat because the
* island constraint solver is approximate.
*
* @author Daniel Murphy
*/
public class WeldJoint extends Joint {
private float m_frequencyHz;
private float m_dampingRatio;
private float m_bias;
// Solver shared
private final Vec2 m_localAnchorA;
private final Vec2 m_localAnchorB;
private float m_referenceAngle;
private float m_gamma;
private final Vec3 m_impulse;
// Solver temp
private int m_indexA;
private int m_indexB;
private final Vec2 m_rA = new Vec2();
private final Vec2 m_rB = new Vec2();
private final Vec2 m_localCenterA = new Vec2();
private final Vec2 m_localCenterB = new Vec2();
private float m_invMassA;
private float m_invMassB;
private float m_invIA;
private float m_invIB;
private final Mat33 m_mass = new Mat33();
protected WeldJoint(IWorldPool argWorld, WeldJointDef def) {
super(argWorld, def);
m_localAnchorA = new Vec2(def.localAnchorA);
m_localAnchorB = new Vec2(def.localAnchorB);
m_referenceAngle = def.referenceAngle;
m_frequencyHz = def.frequencyHz;
m_dampingRatio = def.dampingRatio;
m_impulse = new Vec3();
m_impulse.setZero();
}
public float getReferenceAngle() {
return m_referenceAngle;
}
public Vec2 getLocalAnchorA() {
return m_localAnchorA;
}
public Vec2 getLocalAnchorB() {
return m_localAnchorB;
}
public float getFrequency() {
return m_frequencyHz;
}
public void setFrequency(float frequencyHz) {
this.m_frequencyHz = frequencyHz;
}
public float getDampingRatio() {
return m_dampingRatio;
}
public void setDampingRatio(float dampingRatio) {
this.m_dampingRatio = dampingRatio;
}
@Override
public void getAnchorA(Vec2 argOut) {
m_bodyA.getWorldPointToOut(m_localAnchorA, argOut);
}
@Override
public void getAnchorB(Vec2 argOut) {
m_bodyB.getWorldPointToOut(m_localAnchorB, argOut);
}
@Override
public void getReactionForce(float inv_dt, Vec2 argOut) {
argOut.set(m_impulse.x, m_impulse.y);
argOut.mulLocal(inv_dt);
}
@Override
public float getReactionTorque(float inv_dt) {
return inv_dt * m_impulse.z;
}
@Override
public void initVelocityConstraints(final SolverData data) {
m_indexA = m_bodyA.m_islandIndex;
m_indexB = m_bodyB.m_islandIndex;
m_localCenterA.set(m_bodyA.m_sweep.localCenter);
m_localCenterB.set(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;
// Vec2 cA = data.positions[m_indexA].c;
float aA = data.positions[m_indexA].a;
Vec2 vA = data.velocities[m_indexA].v;
float wA = data.velocities[m_indexA].w;
// Vec2 cB = data.positions[m_indexB].c;
float aB = data.positions[m_indexB].a;
Vec2 vB = data.velocities[m_indexB].v;
float wB = data.velocities[m_indexB].w;
final Rot qA = pool.popRot();
final Rot qB = pool.popRot();
final Vec2 temp = pool.popVec2();
qA.set(aA);
qB.set(aB);
// Compute the effective masses.
Rot.mulToOutUnsafe(qA, temp.set(m_localAnchorA).subLocal(m_localCenterA), m_rA);
Rot.mulToOutUnsafe(qB, temp.set(m_localAnchorB).subLocal(m_localCenterB), m_rB);
// J = [-I -r1_skew I r2_skew]
// [ 0 -1 0 1]
// 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;
final Mat33 K = pool.popMat33();
K.ex.x = mA + mB + m_rA.y * m_rA.y * iA + m_rB.y * m_rB.y * iB;
K.ey.x = -m_rA.y * m_rA.x * iA - m_rB.y * m_rB.x * iB;
K.ez.x = -m_rA.y * iA - m_rB.y * iB;
K.ex.y = K.ey.x;
K.ey.y = mA + mB + m_rA.x * m_rA.x * iA + m_rB.x * m_rB.x * iB;
K.ez.y = m_rA.x * iA + m_rB.x * iB;
K.ex.z = K.ez.x;
K.ey.z = K.ez.y;
K.ez.z = iA + iB;
if (m_frequencyHz > 0.0f) {
K.getInverse22(m_mass);
float invM = iA + iB;
float m = invM > 0.0f ? 1.0f / invM : 0.0f;
float C = aB - aA - m_referenceAngle;
// Frequency
float omega = 2.0f * MathUtils.PI * m_frequencyHz;
// Damping coefficient
float d = 2.0f * m * m_dampingRatio * omega;
// Spring stiffness
float k = m * omega * omega;
// magic formulas
float h = data.step.dt;
m_gamma = h * (d + h * k);
m_gamma = m_gamma != 0.0f ? 1.0f / m_gamma : 0.0f;
m_bias = C * h * k * m_gamma;
invM += m_gamma;
m_mass.ez.z = invM != 0.0f ? 1.0f / invM : 0.0f;
} else {
K.getSymInverse33(m_mass);
m_gamma = 0.0f;
m_bias = 0.0f;
}
if (data.step.warmStarting) {
final Vec2 P = pool.popVec2();
// Scale impulses to support a variable time step.
m_impulse.mulLocal(data.step.dtRatio);
P.set(m_impulse.x, m_impulse.y);
vA.x -= mA * P.x;
vA.y -= mA * P.y;
wA -= iA * (Vec2.cross(m_rA, P) + m_impulse.z);
vB.x += mB * P.x;
vB.y += mB * P.y;
wB += iB * (Vec2.cross(m_rB, P) + m_impulse.z);
pool.pushVec2(1);
} else {
m_impulse.setZero();
}
// data.velocities[m_indexA].v.set(vA);
data.velocities[m_indexA].w = wA;
// data.velocities[m_indexB].v.set(vB);
data.velocities[m_indexB].w = wB;
pool.pushVec2(1);
pool.pushRot(2);
pool.pushMat33(1);
}
@Override
public void solveVelocityConstraints(final SolverData data) {
Vec2 vA = data.velocities[m_indexA].v;
float wA = data.velocities[m_indexA].w;
Vec2 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;
final Vec2 Cdot1 = pool.popVec2();
final Vec2 P = pool.popVec2();
final Vec2 temp = pool.popVec2();
if (m_frequencyHz > 0.0f) {
float Cdot2 = wB - wA;
float impulse2 = -m_mass.ez.z * (Cdot2 + m_bias + m_gamma * m_impulse.z);
m_impulse.z += impulse2;
wA -= iA * impulse2;
wB += iB * impulse2;
Vec2.crossToOutUnsafe(wB, m_rB, Cdot1);
Vec2.crossToOutUnsafe(wA, m_rA, temp);
Cdot1.addLocal(vB).subLocal(vA).subLocal(temp);
final Vec2 impulse1 = P;
Mat33.mul22ToOutUnsafe(m_mass, Cdot1, impulse1);
impulse1.negateLocal();
m_impulse.x += impulse1.x;
m_impulse.y += impulse1.y;
vA.x -= mA * P.x;
vA.y -= mA * P.y;
wA -= iA * Vec2.cross(m_rA, P);
vB.x += mB * P.x;
vB.y += mB * P.y;
wB += iB * Vec2.cross(m_rB, P);
} else {
Vec2.crossToOutUnsafe(wA, m_rA, temp);
Vec2.crossToOutUnsafe(wB, m_rB, Cdot1);
Cdot1.addLocal(vB).subLocal(vA).subLocal(temp);
float Cdot2 = wB - wA;
final Vec3 Cdot = pool.popVec3();
Cdot.set(Cdot1.x, Cdot1.y, Cdot2);
final Vec3 impulse = pool.popVec3();
Mat33.mulToOutUnsafe(m_mass, Cdot, impulse);
impulse.negateLocal();
m_impulse.addLocal(impulse);
P.set(impulse.x, impulse.y);
vA.x -= mA * P.x;
vA.y -= mA * P.y;
wA -= iA * (Vec2.cross(m_rA, P) + impulse.z);
vB.x += mB * P.x;
vB.y += mB * P.y;
wB += iB * (Vec2.cross(m_rB, P) + impulse.z);
pool.pushVec3(2);
}
// data.velocities[m_indexA].v.set(vA);
data.velocities[m_indexA].w = wA;
// data.velocities[m_indexB].v.set(vB);
data.velocities[m_indexB].w = wB;
pool.pushVec2(3);
}
@Override
public boolean solvePositionConstraints(final SolverData data) {
Vec2 cA = data.positions[m_indexA].c;
float aA = data.positions[m_indexA].a;
Vec2 cB = data.positions[m_indexB].c;
float aB = data.positions[m_indexB].a;
final Rot qA = pool.popRot();
final Rot qB = pool.popRot();
final Vec2 temp = pool.popVec2();
final Vec2 rA = pool.popVec2();
final Vec2 rB = pool.popVec2();
qA.set(aA);
qB.set(aB);
float mA = m_invMassA, mB = m_invMassB;
float iA = m_invIA, iB = m_invIB;
Rot.mulToOutUnsafe(qA, temp.set(m_localAnchorA).subLocal(m_localCenterA), rA);
Rot.mulToOutUnsafe(qB, temp.set(m_localAnchorB).subLocal(m_localCenterB), rB);
float positionError, angularError;
final Mat33 K = pool.popMat33();
final Vec2 C1 = pool.popVec2();
final Vec2 P = pool.popVec2();
K.ex.x = mA + mB + rA.y * rA.y * iA + rB.y * rB.y * iB;
K.ey.x = -rA.y * rA.x * iA - rB.y * rB.x * iB;
K.ez.x = -rA.y * iA - rB.y * iB;
K.ex.y = K.ey.x;
K.ey.y = mA + mB + rA.x * rA.x * iA + rB.x * rB.x * iB;
K.ez.y = rA.x * iA + rB.x * iB;
K.ex.z = K.ez.x;
K.ey.z = K.ez.y;
K.ez.z = iA + iB;
if (m_frequencyHz > 0.0f) {
C1.set(cB).addLocal(rB).subLocal(cA).subLocal(rA);
positionError = C1.length();
angularError = 0.0f;
K.solve22ToOut(C1, P);
P.negateLocal();
cA.x -= mA * P.x;
cA.y -= mA * P.y;
aA -= iA * Vec2.cross(rA, P);
cB.x += mB * P.x;
cB.y += mB * P.y;
aB += iB * Vec2.cross(rB, P);
} else {
C1.set(cB).addLocal(rB).subLocal(cA).subLocal(rA);
float C2 = aB - aA - m_referenceAngle;
positionError = C1.length();
angularError = MathUtils.abs(C2);
final Vec3 C = pool.popVec3();
final Vec3 impulse = pool.popVec3();
C.set(C1.x, C1.y, C2);
K.solve33ToOut(C, impulse);
impulse.negateLocal();
P.set(impulse.x, impulse.y);
cA.x -= mA * P.x;
cA.y -= mA * P.y;
aA -= iA * (Vec2.cross(rA, P) + impulse.z);
cB.x += mB * P.x;
cB.y += mB * P.y;
aB += iB * (Vec2.cross(rB, P) + impulse.z);
pool.pushVec3(2);
}
// data.positions[m_indexA].c.set(cA);
data.positions[m_indexA].a = aA;
// data.positions[m_indexB].c.set(cB);
data.positions[m_indexB].a = aB;
pool.pushVec2(5);
pool.pushRot(2);
pool.pushMat33(1);
return positionError <= Settings.linearSlop && angularError <= Settings.angularSlop;
}
}