@Override
public void solveVelocityConstraints(TimeStep step) {
Body b = m_bodyB;
Vec2 r = pool.popVec2();
r.set(m_localAnchor).subLocal(b.getLocalCenter());
Mat22.mulToOut(b.getTransform().R, r, r);
// Cdot = v + cross(w, r)
Vec2 Cdot = pool.popVec2();
Vec2.crossToOut(b.m_angularVelocity, r, Cdot);
Cdot.addLocal(b.m_linearVelocity);
Vec2 impulse = pool.popVec2();
Vec2 temp = pool.popVec2();
// Mul(m_mass, -(Cdot + m_beta * m_C + m_gamma * m_impulse));
impulse.set(m_C).mulLocal(m_beta);
temp.set(m_impulse).mulLocal(m_gamma);
temp.addLocal(impulse).addLocal(Cdot).mulLocal(-1);
Mat22.mulToOut(m_mass, temp, impulse);
Vec2 oldImpulse = temp;
oldImpulse.set(m_impulse);
m_impulse.addLocal(impulse);
float maxImpulse = step.dt * m_maxForce;
if (m_impulse.lengthSquared() > maxImpulse * maxImpulse) {
m_impulse.mulLocal(maxImpulse / m_impulse.length());
}
impulse.set(m_impulse).subLocal(oldImpulse);
// pooling
oldImpulse.set(impulse).mulLocal(b.m_invMass);
b.m_linearVelocity.addLocal(oldImpulse);
b.m_angularVelocity += b.m_invI * Vec2.cross(r, impulse);
pool.pushVec2(4);
}
@Override
public void initVelocityConstraints(TimeStep step) {
Body b = m_bodyB;
float mass = b.getMass();
// Frequency
float omega = 2.0f * MathUtils.PI * m_frequencyHz;
// Damping coefficient
float d = 2.0f * mass * m_dampingRatio * omega;
// Spring stiffness
float k = mass * (omega * omega);
// magic formulas
// gamma has units of inverse mass.
// beta has units of inverse time.
assert (d + step.dt * k > Settings.EPSILON);
m_gamma = step.dt * (d + step.dt * k);
if (m_gamma != 0.0f) {
m_gamma = 1.0f / m_gamma;
}
m_beta = step.dt * k * m_gamma;
Vec2 r = pool.popVec2();
// Compute the effective mass matrix.
// Vec2 r = Mul(b.getTransform().R, m_localAnchor - b.getLocalCenter());
r.set(m_localAnchor).subLocal(b.getLocalCenter());
Mat22.mulToOut(b.getTransform().R, r, r);
// K = [(1/m1 + 1/m2) * eye(2) - skew(r1) * invI1 * skew(r1) - skew(r2) * invI2 * skew(r2)]
// = [1/m1+1/m2 0 ] + invI1 * [r1.y*r1.y -r1.x*r1.y] + invI2 * [r1.y*r1.y
// -r1.x*r1.y]
// [ 0 1/m1+1/m2] [-r1.x*r1.y r1.x*r1.x] [-r1.x*r1.y
// r1.x*r1.x]
float invMass = b.m_invMass;
float invI = b.m_invI;
Mat22 K1 = pool.popMat22();
K1.m11 = invMass;
K1.m21 = 0.0f;
K1.m12 = 0.0f;
K1.m22 = invMass;
Mat22 K2 = pool.popMat22();
K2.m11 = invI * r.y * r.y;
K2.m21 = -invI * r.x * r.y;
K2.m12 = -invI * r.x * r.y;
K2.m22 = invI * r.x * r.x;
Mat22 K = pool.popMat22();
K.set(K1).addLocal(K2);
K.m11 += m_gamma;
K.m22 += m_gamma;
K.invertToOut(m_mass);
m_C.set(b.m_sweep.c).addLocal(r).subLocal(m_target);
// Cheat with some damping
b.m_angularVelocity *= 0.98f;
// Warm starting.
m_impulse.mulLocal(step.dtRatio);
// pool
Vec2 temp = pool.popVec2();
temp.set(m_impulse).mulLocal(invMass);
b.m_linearVelocity.addLocal(temp);
b.m_angularVelocity += invI * Vec2.cross(r, m_impulse);
pool.pushVec2(2);
pool.pushMat22(3);
}