Example 1 with Mat33
use of com.almasb.fxgl.physics.box2d.common.Mat33 in project FXGL by AlmasB.
the class WeldJoint method solvePositionConstraints.
@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 Rotation qA = pool.popRot();
final Rotation 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;
Rotation.mulToOutUnsafe(qA, temp.set(m_localAnchorA).subLocal(m_localCenterA), rA);
Rotation.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 = FXGLMath.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 <= JBoxSettings.linearSlop && angularError <= JBoxSettings.angularSlop;
}Example 2 with Mat33
use of com.almasb.fxgl.physics.box2d.common.Mat33 in project FXGL by AlmasB.
the class WeldJoint method initVelocityConstraints.
@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 Rotation qA = pool.popRot();
final Rotation qB = pool.popRot();
final Vec2 temp = pool.popVec2();
qA.set(aA);
qB.set(aB);
// Compute the effective masses.
Rotation.mulToOutUnsafe(qA, temp.set(m_localAnchorA).subLocal(m_localCenterA), m_rA);
Rotation.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 * (float) FXGLMath.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);
}Example 3 with Mat33
use of com.almasb.fxgl.physics.box2d.common.Mat33 in project FXGL by AlmasB.
the class PrismaticJoint method solvePositionConstraints.
@Override
public boolean solvePositionConstraints(final SolverData data) {
final Rotation qA = pool.popRot();
final Rotation qB = pool.popRot();
final Vec2 rA = pool.popVec2();
final Vec2 rB = pool.popVec2();
final Vec2 d = pool.popVec2();
final Vec2 axis = pool.popVec2();
final Vec2 perp = pool.popVec2();
final Vec2 temp = pool.popVec2();
final Vec2 C1 = pool.popVec2();
final Vec3 impulse = pool.popVec3();
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;
qA.set(aA);
qB.set(aB);
float mA = m_invMassA, mB = m_invMassB;
float iA = m_invIA, iB = m_invIB;
// Compute fresh Jacobians
Rotation.mulToOutUnsafe(qA, temp.set(m_localAnchorA).subLocal(m_localCenterA), rA);
Rotation.mulToOutUnsafe(qB, temp.set(m_localAnchorB).subLocal(m_localCenterB), rB);
d.set(cB).addLocal(rB).subLocal(cA).subLocal(rA);
Rotation.mulToOutUnsafe(qA, m_localXAxisA, axis);
float a1 = Vec2.cross(temp.set(d).addLocal(rA), axis);
float a2 = Vec2.cross(rB, axis);
Rotation.mulToOutUnsafe(qA, m_localYAxisA, perp);
float s1 = Vec2.cross(temp.set(d).addLocal(rA), perp);
float s2 = Vec2.cross(rB, perp);
C1.x = Vec2.dot(perp, d);
C1.y = aB - aA - m_referenceAngle;
float linearError = FXGLMath.abs(C1.x);
float angularError = FXGLMath.abs(C1.y);
boolean active = false;
float C2 = 0.0f;
if (m_enableLimit) {
float translation = Vec2.dot(axis, d);
if (FXGLMath.abs(m_upperTranslation - m_lowerTranslation) < 2.0f * JBoxSettings.linearSlop) {
// Prevent large angular corrections
C2 = FXGLMath.clamp(translation, -JBoxSettings.maxLinearCorrection, JBoxSettings.maxLinearCorrection);
linearError = Math.max(linearError, FXGLMath.abs(translation));
active = true;
} else if (translation <= m_lowerTranslation) {
// Prevent large linear corrections and allow some slop.
C2 = FXGLMath.clamp(translation - m_lowerTranslation + JBoxSettings.linearSlop, -JBoxSettings.maxLinearCorrection, 0.0f);
linearError = Math.max(linearError, m_lowerTranslation - translation);
active = true;
} else if (translation >= m_upperTranslation) {
// Prevent large linear corrections and allow some slop.
C2 = FXGLMath.clamp(translation - m_upperTranslation - JBoxSettings.linearSlop, 0.0f, JBoxSettings.maxLinearCorrection);
linearError = Math.max(linearError, translation - m_upperTranslation);
active = true;
}
}
if (active) {
float k11 = mA + mB + iA * s1 * s1 + iB * s2 * s2;
float k12 = iA * s1 + iB * s2;
float k13 = iA * s1 * a1 + iB * s2 * a2;
float k22 = iA + iB;
if (k22 == 0.0f) {
// For fixed rotation
k22 = 1.0f;
}
float k23 = iA * a1 + iB * a2;
float k33 = mA + mB + iA * a1 * a1 + iB * a2 * a2;
final Mat33 K = pool.popMat33();
K.ex.set(k11, k12, k13);
K.ey.set(k12, k22, k23);
K.ez.set(k13, k23, k33);
final Vec3 C = pool.popVec3();
C.x = C1.x;
C.y = C1.y;
C.z = C2;
K.solve33ToOut(C.negateLocal(), impulse);
pool.pushVec3(1);
pool.pushMat33(1);
} else {
float k11 = mA + mB + iA * s1 * s1 + iB * s2 * s2;
float k12 = iA * s1 + iB * s2;
float k22 = iA + iB;
if (k22 == 0.0f) {
k22 = 1.0f;
}
final Mat22 K = pool.popMat22();
K.ex.set(k11, k12);
K.ey.set(k12, k22);
// temp is impulse1
K.solveToOut(C1.negateLocal(), temp);
C1.negateLocal();
impulse.x = temp.x;
impulse.y = temp.y;
impulse.z = 0.0f;
pool.pushMat22(1);
}
float Px = impulse.x * perp.x + impulse.z * axis.x;
float Py = impulse.x * perp.y + impulse.z * axis.y;
float LA = impulse.x * s1 + impulse.y + impulse.z * a1;
float LB = impulse.x * s2 + impulse.y + impulse.z * a2;
cA.x -= mA * Px;
cA.y -= mA * Py;
aA -= iA * LA;
cB.x += mB * Px;
cB.y += mB * Py;
aB += iB * LB;
// 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(7);
pool.pushVec3(1);
pool.pushRot(2);
return linearError <= JBoxSettings.linearSlop && angularError <= JBoxSettings.angularSlop;
}