// Sequential position solver for position constraints.
public bool SolveTOIPositionConstraints(int toiIndexA, int toiIndexB)
{
FP minSeparation = 0.0f;
for (int i = 0; i < _count; ++i)
{
ContactPositionConstraint pc = _positionConstraints[i];
int indexA = pc.indexA;
int indexB = pc.indexB;
FPVector2 localCenterA = pc.localCenterA;
FPVector2 localCenterB = pc.localCenterB;
int pointCount = pc.pointCount;
FP mA = 0.0f;
FP iA = 0.0f;
if (indexA == toiIndexA || indexA == toiIndexB)
{
mA = pc.invMassA;
iA = pc.invIA;
}
FP mB = 0.0f;
FP iB = 0.0f;
if (indexB == toiIndexA || indexB == toiIndexB)
{
mB = pc.invMassB;
iB = pc.invIB;
}
FPVector2 cA = _positions[indexA].c;
FP aA = _positions[indexA].a;
FPVector2 cB = _positions[indexB].c;
FP aB = _positions[indexB].a;
// Solve normal constraints
for (int j = 0; j < pointCount; ++j)
{
Transform xfA = new Transform();
Transform xfB = new Transform();
xfA.q.Set(aA);
xfB.q.Set(aB);
xfA.p = cA - MathUtils.Mul(xfA.q, localCenterA);
xfB.p = cB - MathUtils.Mul(xfB.q, localCenterB);
FPVector2 normal;
FPVector2 point;
FP separation;
PositionSolverManifold.Initialize(pc, xfA, xfB, j, out normal, out point, out separation);
FPVector2 rA = point - cA;
FPVector2 rB = point - cB;
// Track max constraint error.
minSeparation = Spax.FPMath.Min(minSeparation, separation);
// Prevent large corrections and allow slop.
FP C = MathUtils.Clamp(Settings.Baumgarte * (separation + Settings.LinearSlop), -Settings.MaxLinearCorrection, 0.0f);
// Compute the effective mass.
FP rnA = MathUtils.Cross(rA, normal);
FP rnB = MathUtils.Cross(rB, normal);
FP K = mA + mB + iA * rnA * rnA + iB * rnB * rnB;
// Compute normal impulse
FP impulse = K > 0.0f ? -C / K : 0.0f;
FPVector2 P = impulse * normal;
cA -= mA * P;
aA -= iA * MathUtils.Cross(rA, P);
cB += mB * P;
aB += iB * MathUtils.Cross(rB, P);
}
_positions[indexA].c = cA;
_positions[indexA].a = aA;
_positions[indexB].c = cB;
_positions[indexB].a = aB;
}
// We can't expect minSpeparation >= -b2_linearSlop because we don't
// push the separation above -b2_linearSlop.
return(minSeparation >= -1.5f * Settings.LinearSlop);
}
public void Reset(TimeStep step, int count, Contact[] contacts, Position[] positions, Velocity[] velocities, bool warmstarting = Settings.EnableWarmstarting)
{
_step = step;
_count = count;
_positions = positions;
_velocities = velocities;
_contacts = contacts;
// grow the array
if (_velocityConstraints == null || _velocityConstraints.Length < count)
{
_velocityConstraints = new ContactVelocityConstraint[count * 2];
_positionConstraints = new ContactPositionConstraint[count * 2];
for (int i = 0; i < _velocityConstraints.Length; i++)
{
_velocityConstraints[i] = new ContactVelocityConstraint();
}
for (int i = 0; i < _positionConstraints.Length; i++)
{
_positionConstraints[i] = new ContactPositionConstraint();
}
}
// Initialize position independent portions of the constraints.
for (int i = 0; i < _count; ++i)
{
Contact contact = contacts[i];
Fixture fixtureA = contact.FixtureA;
Fixture fixtureB = contact.FixtureB;
Shape shapeA = fixtureA.Shape;
Shape shapeB = fixtureB.Shape;
FP radiusA = shapeA.Radius;
FP radiusB = shapeB.Radius;
Body bodyA = fixtureA.Body;
Body bodyB = fixtureB.Body;
Manifold manifold = contact.Manifold;
int pointCount = manifold.PointCount;
Debug.Assert(pointCount > 0);
ContactVelocityConstraint vc = _velocityConstraints[i];
vc.friction = contact.Friction;
vc.restitution = contact.Restitution;
vc.tangentSpeed = contact.TangentSpeed;
vc.indexA = bodyA.IslandIndex;
vc.indexB = bodyB.IslandIndex;
vc.invMassA = bodyA._invMass;
vc.invMassB = bodyB._invMass;
vc.invIA = bodyA._invI;
vc.invIB = bodyB._invI;
vc.contactIndex = i;
vc.pointCount = pointCount;
vc.K.SetZero();
vc.normalMass.SetZero();
ContactPositionConstraint pc = _positionConstraints[i];
pc.indexA = bodyA.IslandIndex;
pc.indexB = bodyB.IslandIndex;
pc.invMassA = bodyA._invMass;
pc.invMassB = bodyB._invMass;
pc.localCenterA = bodyA._sweep.LocalCenter;
pc.localCenterB = bodyB._sweep.LocalCenter;
pc.invIA = bodyA._invI;
pc.invIB = bodyB._invI;
pc.localNormal = manifold.LocalNormal;
pc.localPoint = manifold.LocalPoint;
pc.pointCount = pointCount;
pc.radiusA = radiusA;
pc.radiusB = radiusB;
pc.type = manifold.Type;
for (int j = 0; j < pointCount; ++j)
{
ManifoldPoint cp = manifold.Points[j];
VelocityConstraintPoint vcp = vc.points[j];
if (Settings.EnableWarmstarting)
{
vcp.normalImpulse = _step.dtRatio * cp.NormalImpulse;
vcp.tangentImpulse = _step.dtRatio * cp.TangentImpulse;
}
else
{
vcp.normalImpulse = 0.0f;
vcp.tangentImpulse = 0.0f;
}
vcp.rA = FPVector2.zero;
vcp.rB = FPVector2.zero;
vcp.normalMass = 0.0f;
vcp.tangentMass = 0.0f;
vcp.velocityBias = 0.0f;
pc.localPoints[j] = cp.LocalPoint;
}
}
}
public void InitializeVelocityConstraints()
{
for (int i = 0; i < _count; ++i)
{
ContactVelocityConstraint vc = _velocityConstraints[i];
ContactPositionConstraint pc = _positionConstraints[i];
FP radiusA = pc.radiusA;
FP radiusB = pc.radiusB;
Manifold manifold = _contacts[vc.contactIndex].Manifold;
int indexA = vc.indexA;
int indexB = vc.indexB;
FP mA = vc.invMassA;
FP mB = vc.invMassB;
FP iA = vc.invIA;
FP iB = vc.invIB;
FPVector2 localCenterA = pc.localCenterA;
FPVector2 localCenterB = pc.localCenterB;
FPVector2 cA = _positions[indexA].c;
FP aA = _positions[indexA].a;
FPVector2 vA = _velocities[indexA].v;
FP wA = _velocities[indexA].w;
FPVector2 cB = _positions[indexB].c;
FP aB = _positions[indexB].a;
FPVector2 vB = _velocities[indexB].v;
FP wB = _velocities[indexB].w;
Debug.Assert(manifold.PointCount > 0);
Transform xfA = new Transform();
Transform xfB = new Transform();
xfA.q.Set(aA);
xfB.q.Set(aB);
xfA.p = cA - MathUtils.Mul(xfA.q, localCenterA);
xfB.p = cB - MathUtils.Mul(xfB.q, localCenterB);
FPVector2 normal;
FixedArray2 <FPVector2> points;
WorldManifold.Initialize(ref manifold, ref xfA, radiusA, ref xfB, radiusB, out normal, out points);
vc.normal = normal;
int pointCount = vc.pointCount;
for (int j = 0; j < pointCount; ++j)
{
VelocityConstraintPoint vcp = vc.points[j];
vcp.rA = points[j] - cA;
vcp.rB = points[j] - cB;
FP rnA = MathUtils.Cross(vcp.rA, vc.normal);
FP rnB = MathUtils.Cross(vcp.rB, vc.normal);
FP kNormal = mA + mB + iA * rnA * rnA + iB * rnB * rnB;
vcp.normalMass = kNormal > 0.0f ? 1.0f / kNormal : 0.0f;
FPVector2 tangent = MathUtils.Cross(vc.normal, 1.0f);
FP rtA = MathUtils.Cross(vcp.rA, tangent);
FP rtB = MathUtils.Cross(vcp.rB, tangent);
FP kTangent = mA + mB + iA * rtA * rtA + iB * rtB * rtB;
vcp.tangentMass = kTangent > 0.0f ? 1.0f / kTangent : 0.0f;
// Setup a velocity bias for restitution.
vcp.velocityBias = 0.0f;
FP vRel = FPVector2.Dot(vc.normal, vB + MathUtils.Cross(wB, vcp.rB) - vA - MathUtils.Cross(wA, vcp.rA));
if (vRel < -Settings.VelocityThreshold)
{
vcp.velocityBias = -vc.restitution * vRel;
}
}
// If we have two points, then prepare the block solver.
if (vc.pointCount == 2)
{
VelocityConstraintPoint vcp1 = vc.points[0];
VelocityConstraintPoint vcp2 = vc.points[1];
FP rn1A = MathUtils.Cross(vcp1.rA, vc.normal);
FP rn1B = MathUtils.Cross(vcp1.rB, vc.normal);
FP rn2A = MathUtils.Cross(vcp2.rA, vc.normal);
FP rn2B = MathUtils.Cross(vcp2.rB, vc.normal);
FP k11 = mA + mB + iA * rn1A * rn1A + iB * rn1B * rn1B;
FP k22 = mA + mB + iA * rn2A * rn2A + iB * rn2B * rn2B;
FP k12 = mA + mB + iA * rn1A * rn2A + iB * rn1B * rn2B;
// Ensure a reasonable condition number.
FP k_maxConditionNumber = 1000.0f;
if (k11 * k11 < k_maxConditionNumber * (k11 * k22 - k12 * k12))
{
// K is safe to invert.
vc.K.ex = new FPVector2(k11, k12);
vc.K.ey = new FPVector2(k12, k22);
vc.normalMass = vc.K.Inverse;
}
else
{
// The constraints are redundant, just use one.
// TODO_ERIN use deepest?
vc.pointCount = 1;
}
}
}
}