public float Evaluate(int indexA, int indexB, float t)
{
SweepA.GetTransform(xfa, t);
SweepB.GetTransform(xfb, t);
switch (Type)
{
case Type.Points:
{
Rot.MulTransUnsafe(xfa.Q, Axis, axisA);
Rot.MulTransUnsafe(xfb.Q, Axis.NegateLocal(), axisB);
Axis.NegateLocal();
localPointA.Set(ProxyA.GetVertex(indexA));
localPointB.Set(ProxyB.GetVertex(indexB));
Transform.MulToOutUnsafe(xfa, localPointA, pointA);
Transform.MulToOutUnsafe(xfb, localPointB, pointB);
float separation = Vec2.Dot(pointB.SubLocal(pointA), Axis);
return(separation);
}
case Type.FaceA:
{
// System.out.printf("We're faceA\n");
Rot.MulToOutUnsafe(xfa.Q, Axis, normal);
Transform.MulToOutUnsafe(xfa, LocalPoint, pointA);
Rot.MulTransUnsafe(xfb.Q, normal.NegateLocal(), axisB);
normal.NegateLocal();
localPointB.Set(ProxyB.GetVertex(indexB));
Transform.MulToOutUnsafe(xfb, localPointB, pointB);
float separation = Vec2.Dot(pointB.SubLocal(pointA), normal);
return(separation);
}
case Type.FaceB:
{
// System.out.printf("We're faceB\n");
Rot.MulToOutUnsafe(xfb.Q, Axis, normal);
Transform.MulToOutUnsafe(xfb, LocalPoint, pointB);
Rot.MulTransUnsafe(xfa.Q, normal.NegateLocal(), axisA);
normal.NegateLocal();
localPointA.Set(ProxyA.GetVertex(indexA));
Transform.MulToOutUnsafe(xfa, localPointA, pointA);
float separation = Vec2.Dot(pointA.SubLocal(pointB), normal);
return(separation);
}
default:
Debug.Assert(false);
return(0f);
}
}
public override bool TestPoint(Transform transform, Vec2 p)
{
Vec2 center = pool1;
Rot.MulToOutUnsafe(transform.Q, P, center);
center.AddLocal(transform.P);
Vec2 d = center.SubLocal(p).NegateLocal();
return(Vec2.Dot(d, d) <= Radius * Radius);
}
internal void Advance(float t)
{
// Advance to the new safe time. This doesn't sync the broad-phase.
Sweep.Advance(t);
Sweep.C.Set(Sweep.C0);
Sweep.A = Sweep.A0;
Xf.Q.Set(Sweep.A);
// m_xf.position = m_sweep.c - Mul(m_xf.R, m_sweep.localCenter);
Rot.MulToOutUnsafe(Xf.Q, Sweep.LocalCenter, Xf.P);
Xf.P.MulLocal(-1).AddLocal(Sweep.C);
}
public override void ComputeAABB(AABB aabb, Transform transform, int childIndex)
{
Vec2 p = pool1;
Rot.MulToOutUnsafe(transform.Q, P, p);
p.AddLocal(transform.P);
aabb.LowerBound.X = p.X - Radius;
aabb.LowerBound.Y = p.Y - Radius;
aabb.UpperBound.X = p.X + Radius;
aabb.UpperBound.Y = p.Y + Radius;
}
public override bool SolvePositionConstraints(SolverData data)
{
if (FrequencyHz > 0.0f)
{
return(true);
}
Rot qA = Pool.PopRot();
Rot qB = Pool.PopRot();
Vec2 rA = Pool.PopVec2();
Vec2 rB = Pool.PopVec2();
Vec2 u = Pool.PopVec2();
Vec2 cA = data.Positions[IndexA].C;
float aA = data.Positions[IndexA].A;
Vec2 cB = data.Positions[IndexB].C;
float aB = data.Positions[IndexB].A;
qA.Set(aA);
qB.Set(aB);
Rot.MulToOutUnsafe(qA, u.Set(LocalAnchorA).SubLocal(LocalCenterA), rA);
Rot.MulToOutUnsafe(qB, u.Set(LocalAnchorB).SubLocal(LocalCenterB), rB);
u.Set(cB).AddLocal(rB).SubLocal(cA).SubLocal(rA);
float length = u.Normalize();
float C = length - Length;
C = MathUtils.Clamp(C, -Settings.MAX_LINEAR_CORRECTION, Settings.MAX_LINEAR_CORRECTION);
float impulse = (-Mass) * C;
float Px = impulse * u.X;
float Py = impulse * u.Y;
cA.X -= InvMassA * Px;
cA.Y -= InvMassA * Py;
aA -= InvIA * (rA.X * Py - rA.Y * Px);
cB.X += InvMassB * Px;
cB.Y += InvMassB * Py;
aB += InvIB * (rB.X * Py - rB.Y * Px);
data.Positions[IndexA].C.Set(cA);
data.Positions[IndexA].A = aA;
data.Positions[IndexB].C.Set(cB);
data.Positions[IndexB].A = aB;
Pool.PushVec2(3);
Pool.PushRot(2);
return(MathUtils.Abs(C) < Settings.LINEAR_SLOP);
}
public void Initialize(ContactPositionConstraint pc, Transform xfA, Transform xfB, int index)
{
Debug.Assert(pc.PointCount > 0);
switch (pc.Type)
{
case Manifold.ManifoldType.Circles:
{
Transform.MulToOutUnsafe(xfA, pc.LocalPoint, pointA);
Transform.MulToOutUnsafe(xfB, pc.LocalPoints[0], pointB);
Normal.Set(pointB).SubLocal(pointA);
Normal.Normalize();
Point.Set(pointA).AddLocal(pointB).MulLocal(.5f);
temp.Set(pointB).SubLocal(pointA);
Separation = Vec2.Dot(temp, Normal) - pc.RadiusA - pc.RadiusB;
break;
}
case Manifold.ManifoldType.FaceA:
{
Rot.MulToOutUnsafe(xfA.Q, pc.LocalNormal, Normal);
Transform.MulToOutUnsafe(xfA, pc.LocalPoint, planePoint);
Transform.MulToOutUnsafe(xfB, pc.LocalPoints[index], clipPoint);
temp.Set(clipPoint).SubLocal(planePoint);
Separation = Vec2.Dot(temp, Normal) - pc.RadiusA - pc.RadiusB;
Point.Set(clipPoint);
break;
}
case Manifold.ManifoldType.FaceB:
{
Rot.MulToOutUnsafe(xfB.Q, pc.LocalNormal, Normal);
Transform.MulToOutUnsafe(xfB, pc.LocalPoint, planePoint);
Transform.MulToOutUnsafe(xfA, pc.LocalPoints[index], clipPoint);
temp.Set(clipPoint).SubLocal(planePoint);
Separation = Vec2.Dot(temp, Normal) - pc.RadiusA - pc.RadiusB;
Point.Set(clipPoint);
// Ensure normal points from A to B
Normal.NegateLocal();
}
break;
}
}
// Collision Detection in Interactive 3D Environments by Gino van den Bergen
// From Section 3.1.2
// x = s + a * r
// norm(x) = radius
public override bool Raycast(RayCastOutput output, RayCastInput input, Transform transform, int childIndex)
{
Vec2 position = pool1;
Vec2 s = pool2;
Vec2 r = pool3;
Rot.MulToOutUnsafe(transform.Q, P, position);
position.AddLocal(transform.P);
s.Set(input.P1).SubLocal(position);
float b = Vec2.Dot(s, s) - Radius * Radius;
// Solve quadratic equation.
r.Set(input.P2).SubLocal(input.P1);
float c = Vec2.Dot(s, r);
float rr = Vec2.Dot(r, r);
float sigma = c * c - rr * b;
// Check for negative discriminant and short segment.
if (sigma < 0.0f || rr < Settings.EPSILON)
{
return(false);
}
// Find the point of intersection of the line with the circle.
float a = -(c + MathUtils.Sqrt(sigma));
// Is the intersection point on the segment?
if (0.0f <= a && a <= input.MaxFraction * rr)
{
a /= rr;
output.Fraction = a;
output.Normal.Set(r).MulLocal(a);
output.Normal.AddLocal(s);
output.Normal.Normalize();
return(true);
}
return(false);
}
public void InitializeVelocityConstraints()
{
//Console.WriteLine("Initializing velocity constraints for " + m_count + " contacts");
// Warm start.
for (int i = 0; i < Count; ++i)
{
ContactVelocityConstraint vc = VelocityConstraints[i];
ContactPositionConstraint pc = PositionConstraints[i];
float radiusA = pc.RadiusA;
float radiusB = pc.RadiusB;
Manifold manifold = Contacts[vc.ContactIndex].Manifold;
int indexA = vc.IndexA;
int indexB = vc.IndexB;
float mA = vc.InvMassA;
float mB = vc.InvMassB;
float iA = vc.InvIA;
float iB = vc.InvIB;
Vec2 localCenterA = pc.LocalCenterA;
Vec2 localCenterB = pc.LocalCenterB;
Vec2 cA = Positions[indexA].C;
float aA = Positions[indexA].A;
Vec2 vA = Velocities[indexA].V;
float wA = Velocities[indexA].W;
Vec2 cB = Positions[indexB].C;
float aB = Positions[indexB].A;
Vec2 vB = Velocities[indexB].V;
float wB = Velocities[indexB].W;
Debug.Assert(manifold.PointCount > 0);
xfA.Q.Set(aA);
xfB.Q.Set(aB);
Rot.MulToOutUnsafe(xfA.Q, localCenterA, temp);
xfA.P.Set(cA).SubLocal(temp);
Rot.MulToOutUnsafe(xfB.Q, localCenterB, temp);
xfB.P.Set(cB).SubLocal(temp);
worldManifold.Initialize(manifold, xfA, radiusA, xfB, radiusB);
vc.Normal.Set(worldManifold.Normal);
int pointCount = vc.PointCount;
for (int j = 0; j < pointCount; ++j)
{
ContactVelocityConstraint.VelocityConstraintPoint vcp = vc.Points[j];
vcp.RA.Set(worldManifold.Points[j]).SubLocal(cA);
vcp.RB.Set(worldManifold.Points[j]).SubLocal(cB);
float rnA = Vec2.Cross(vcp.RA, vc.Normal);
float rnB = Vec2.Cross(vcp.RB, vc.Normal);
float kNormal = mA + mB + iA * rnA * rnA + iB * rnB * rnB;
vcp.NormalMass = kNormal > 0.0f ? 1.0f / kNormal : 0.0f;
Vec2.CrossToOutUnsafe(vc.Normal, 1.0f, tangent);
float rtA = Vec2.Cross(vcp.RA, tangent);
float rtB = Vec2.Cross(vcp.RB, tangent);
float 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;
Vec2.CrossToOutUnsafe(wB, vcp.RB, temp1);
Vec2.CrossToOutUnsafe(wA, vcp.RA, temp2);
temp.Set(vB).AddLocal(temp1).SubLocal(vA).SubLocal(temp2);
float vRel = Vec2.Dot(vc.Normal, temp);
if (vRel < -Settings.VELOCITY_THRESHOLD)
{
vcp.VelocityBias = (-vc.Restitution) * vRel;
}
}
// If we have two points, then prepare the block solver.
if (vc.PointCount == 2)
{
ContactVelocityConstraint.VelocityConstraintPoint vcp1 = vc.Points[0];
ContactVelocityConstraint.VelocityConstraintPoint vcp2 = vc.Points[1];
float rn1A = Vec2.Cross(vcp1.RA, vc.Normal);
float rn1B = Vec2.Cross(vcp1.RB, vc.Normal);
float rn2A = Vec2.Cross(vcp2.RA, vc.Normal);
float rn2B = Vec2.Cross(vcp2.RB, vc.Normal);
float k11 = mA + mB + iA * rn1A * rn1A + iB * rn1B * rn1B;
float k22 = mA + mB + iA * rn2A * rn2A + iB * rn2B * rn2B;
float k12 = mA + mB + iA * rn1A * rn2A + iB * rn1B * rn2B;
if (k11 * k11 < MAX_CONDITION_NUMBER * (k11 * k22 - k12 * k12))
{
// K is safe to invert.
vc.K.Ex.Set(k11, k12);
vc.K.Ey.Set(k12, k22);
vc.K.InvertToOut(vc.NormalMass);
}
else
{
// The constraints are redundant, just use one.
// TODO_ERIN use deepest?
vc.PointCount = 1;
}
}
}
}
/// <seealso cref="Joint.solvePositionConstraints(float)"></seealso>
public override bool SolvePositionConstraints(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;
Rot qA = Pool.PopRot();
Rot qB = Pool.PopRot();
Vec2 temp = Pool.PopVec2();
Vec2 rA = Pool.PopVec2();
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(LocalAnchorA).SubLocal(m_localCenterA), rA);
Rot.MulToOutUnsafe(qB, temp.Set(LocalAnchorB).SubLocal(m_localCenterB), rB);
float positionError, angularError;
Mat33 K = Pool.PopMat33();
Vec2 C1 = Pool.PopVec2();
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 (Frequency > 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);
Vec3 C = Pool.PopVec3();
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);
}
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.LINEAR_SLOP && angularError <= Settings.ANGULAR_SLOP);
}
public override bool Raycast(RayCastOutput output, RayCastInput input, Transform xf, int childIndex)
{
Vec2 p1 = pool1;
Vec2 p2 = pool2;
Vec2 d = pool3;
Vec2 temp = pool4;
p1.Set(input.P1).SubLocal(xf.P);
Rot.MulTrans(xf.Q, p1, p1);
p2.Set(input.P2).SubLocal(xf.P);
Rot.MulTrans(xf.Q, p2, p2);
d.Set(p2).SubLocal(p1);
// if (count == 2) {
// } else {
float lower = 0, upper = input.MaxFraction;
int index = -1;
for (int i = 0; i < VertexCount; ++i)
{
// p = p1 + a * d
// dot(normal, p - v) = 0
// dot(normal, p1 - v) + a * dot(normal, d) = 0
temp.Set(Vertices[i]).SubLocal(p1);
float numerator = Vec2.Dot(Normals[i], temp);
float denominator = Vec2.Dot(Normals[i], d);
if (denominator == 0.0f)
{
if (numerator < 0.0f)
{
return(false);
}
}
else
{
// Note: we want this predicate without division:
// lower < numerator / denominator, where denominator < 0
// Since denominator < 0, we have to flip the inequality:
// lower < numerator / denominator <==> denominator * lower >
// numerator.
if (denominator < 0.0f && numerator < lower * denominator)
{
// Increase lower.
// The segment enters this half-space.
lower = numerator / denominator;
index = i;
}
else if (denominator > 0.0f && numerator < upper * denominator)
{
// Decrease upper.
// The segment exits this half-space.
upper = numerator / denominator;
}
}
if (upper < lower)
{
return(false);
}
}
Debug.Assert(0.0f <= lower && lower <= input.MaxFraction);
if (index >= 0)
{
output.Fraction = lower;
Rot.MulToOutUnsafe(xf.Q, Normals[index], output.Normal);
// normal = Mul(xf.R, m_normals[index]);
return(true);
}
return(false);
}
public override void InitVelocityConstraints(SolverData data)
{
IndexA = BodyA.IslandIndex;
IndexB = BodyB.IslandIndex;
LocalCenterA.Set(BodyA.Sweep.LocalCenter);
LocalCenterB.Set(BodyB.Sweep.LocalCenter);
InvMassA = BodyA.InvMass;
InvMassB = BodyB.InvMass;
InvIA = BodyA.InvI;
InvIB = BodyB.InvI;
Vec2 cA = data.Positions[IndexA].C;
float aA = data.Positions[IndexA].A;
Vec2 vA = data.Velocities[IndexA].V;
float wA = data.Velocities[IndexA].W;
Vec2 cB = data.Positions[IndexB].C;
float aB = data.Positions[IndexB].A;
Vec2 vB = data.Velocities[IndexB].V;
float wB = data.Velocities[IndexB].W;
Rot qA = Pool.PopRot();
Rot qB = Pool.PopRot();
Vec2 d = Pool.PopVec2();
Vec2 temp = Pool.PopVec2();
Vec2 rA = Pool.PopVec2();
Vec2 rB = Pool.PopVec2();
qA.Set(aA);
qB.Set(aB);
// Compute the effective masses.
Rot.MulToOutUnsafe(qA, d.Set(LocalAnchorA).SubLocal(LocalCenterA), rA);
Rot.MulToOutUnsafe(qB, d.Set(LocalAnchorB).SubLocal(LocalCenterB), rB);
d.Set(cB).SubLocal(cA).AddLocal(rB).SubLocal(rA);
float mA = InvMassA, mB = InvMassB;
float iA = InvIA, iB = InvIB;
// Compute motor Jacobian and effective mass.
{
Rot.MulToOutUnsafe(qA, LocalXAxisA, Axis);
temp.Set(d).AddLocal(rA);
A1 = Vec2.Cross(temp, Axis);
A2 = Vec2.Cross(rB, Axis);
MotorMass = mA + mB + iA * A1 * A1 + iB * A2 * A2;
if (MotorMass > 0.0f)
{
MotorMass = 1.0f / MotorMass;
}
}
// Prismatic constraint.
{
Rot.MulToOutUnsafe(qA, LocalYAxisA, Perp);
temp.Set(d).AddLocal(rA);
S1 = Vec2.Cross(temp, Perp);
S2 = Vec2.Cross(rB, Perp);
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 bodies with fixed rotation.
k22 = 1.0f;
}
float k23 = iA * A1 + iB * A2;
float k33 = mA + mB + iA * A1 * A1 + iB * A2 * A2;
K.Ex.Set(k11, k12, k13);
K.Ey.Set(k12, k22, k23);
K.Ez.Set(k13, k23, k33);
}
// Compute motor and limit terms.
if (m_limitEnabled)
{
float jointTranslation = Vec2.Dot(Axis, d);
if (MathUtils.Abs(UpperTranslation - LowerTranslation) < 2.0f * Settings.LINEAR_SLOP)
{
LimitState = LimitState.Equal;
}
else if (jointTranslation <= LowerTranslation)
{
if (LimitState != LimitState.AtLower)
{
LimitState = LimitState.AtLower;
Impulse.Z = 0.0f;
}
}
else if (jointTranslation >= UpperTranslation)
{
if (LimitState != LimitState.AtUpper)
{
LimitState = LimitState.AtUpper;
Impulse.Z = 0.0f;
}
}
else
{
LimitState = LimitState.Inactive;
Impulse.Z = 0.0f;
}
}
else
{
LimitState = LimitState.Inactive;
Impulse.Z = 0.0f;
}
if (m_motorEnabled == false)
{
MotorImpulse = 0.0f;
}
if (data.Step.WarmStarting)
{
// Account for variable time step.
Impulse.MulLocal(data.Step.DtRatio);
MotorImpulse *= data.Step.DtRatio;
Vec2 P = Pool.PopVec2();
temp.Set(Axis).MulLocal(MotorImpulse + Impulse.Z);
P.Set(Perp).MulLocal(Impulse.X).AddLocal(temp);
float LA = Impulse.X * S1 + Impulse.Y + (MotorImpulse + Impulse.Z) * A1;
float LB = Impulse.X * S2 + Impulse.Y + (MotorImpulse + Impulse.Z) * A2;
vA.X -= mA * P.X;
vA.Y -= mA * P.Y;
wA -= iA * LA;
vB.X += mB * P.X;
vB.Y += mB * P.Y;
wB += iB * LB;
Pool.PushVec2(1);
}
else
{
Impulse.SetZero();
MotorImpulse = 0.0f;
}
data.Velocities[IndexA].V.Set(vA);
data.Velocities[IndexA].W = wA;
data.Velocities[IndexB].V.Set(vB);
data.Velocities[IndexB].W = wB;
Pool.PushRot(2);
Pool.PushVec2(4);
}
/// <seealso cref="Joint.initVelocityConstraints(TimeStep)"></seealso>
public override void InitVelocityConstraints(SolverData data)
{
m_indexA = BodyA.IslandIndex;
m_indexB = BodyB.IslandIndex;
m_localCenterA.Set(BodyA.Sweep.LocalCenter);
m_localCenterB.Set(BodyB.Sweep.LocalCenter);
m_invMassA = BodyA.InvMass;
m_invMassB = BodyB.InvMass;
m_invIA = BodyA.InvI;
m_invIB = BodyB.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;
Rot qA = Pool.PopRot();
Rot qB = Pool.PopRot();
Vec2 temp = Pool.PopVec2();
qA.Set(aA);
qB.Set(aB);
// Compute the effective masses.
Rot.MulToOutUnsafe(qA, temp.Set(LocalAnchorA).SubLocal(m_localCenterA), m_rA);
Rot.MulToOutUnsafe(qB, temp.Set(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;
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 (Frequency > 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 * Frequency;
// Damping coefficient
float d = 2.0f * 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)
{
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);
}
public void Initialize(Manifold manifold, Transform xfA, float radiusA, Transform xfB, float radiusB)
{
if (manifold.PointCount == 0)
{
return;
}
switch (manifold.Type)
{
case Manifold.ManifoldType.Circles:
{
// final Vec2 pointA = pool3;
// final Vec2 pointB = pool4;
//
// normal.set(1, 0);
// Transform.mulToOut(xfA, manifold.localPoint, pointA);
// Transform.mulToOut(xfB, manifold.points[0].localPoint, pointB);
//
// if (MathUtils.distanceSquared(pointA, pointB) > Settings.EPSILON * Settings.EPSILON) {
// normal.set(pointB).subLocal(pointA);
// normal.normalize();
// }
//
// cA.set(normal).mulLocal(radiusA).addLocal(pointA);
// cB.set(normal).mulLocal(radiusB).subLocal(pointB).negateLocal();
// points[0].set(cA).addLocal(cB).mulLocal(0.5f);
Vec2 pointA = pool3;
Vec2 pointB = pool4;
Normal.X = 1;
Normal.Y = 0;
// pointA.x = xfA.p.x + xfA.q.ex.x * manifold.localPoint.x + xfA.q.ey.x *
// manifold.localPoint.y;
// pointA.y = xfA.p.y + xfA.q.ex.y * manifold.localPoint.x + xfA.q.ey.y *
// manifold.localPoint.y;
// pointB.x = xfB.p.x + xfB.q.ex.x * manifold.points[0].localPoint.x + xfB.q.ey.x *
// manifold.points[0].localPoint.y;
// pointB.y = xfB.p.y + xfB.q.ex.y * manifold.points[0].localPoint.x + xfB.q.ey.y *
// manifold.points[0].localPoint.y;
Transform.MulToOut(xfA, manifold.LocalPoint, pointA);
Transform.MulToOut(xfB, manifold.Points[0].LocalPoint, pointB);
if (MathUtils.DistanceSquared(pointA, pointB) > Settings.EPSILON * Settings.EPSILON)
{
Normal.X = pointB.X - pointA.X;
Normal.Y = pointB.Y - pointA.Y;
Normal.Normalize();
}
float cAx = Normal.X * radiusA + pointA.X;
float cAy = Normal.Y * radiusA + pointA.Y;
float cBx = (-Normal.X) * radiusB + pointB.X;
float cBy = (-Normal.Y) * radiusB + pointB.Y;
Points[0].X = (cAx + cBx) * .5f;
Points[0].Y = (cAy + cBy) * .5f;
}
break;
case Manifold.ManifoldType.FaceA:
{
Vec2 planePoint = pool3;
Rot.MulToOutUnsafe(xfA.Q, manifold.LocalNormal, Normal);
Transform.MulToOut(xfA, manifold.LocalPoint, planePoint);
Vec2 clipPoint = pool4;
for (int i = 0; i < manifold.PointCount; i++)
{
// b2Vec2 clipPoint = b2Mul(xfB, manifold->points[i].localPoint);
// b2Vec2 cA = clipPoint + (radiusA - b2Dot(clipPoint - planePoint,
// normal)) * normal;
// b2Vec2 cB = clipPoint - radiusB * normal;
// points[i] = 0.5f * (cA + cB);
Transform.MulToOut(xfB, manifold.Points[i].LocalPoint, clipPoint);
// use cA as temporary for now
// cA.set(clipPoint).subLocal(planePoint);
// float scalar = radiusA - Vec2.dot(cA, normal);
// cA.set(normal).mulLocal(scalar).addLocal(clipPoint);
// cB.set(normal).mulLocal(radiusB).subLocal(clipPoint).negateLocal();
// points[i].set(cA).addLocal(cB).mulLocal(0.5f);
float scalar = radiusA - ((clipPoint.X - planePoint.X) * Normal.X + (clipPoint.Y - planePoint.Y) * Normal.Y);
float cAx = Normal.X * scalar + clipPoint.X;
float cAy = Normal.Y * scalar + clipPoint.Y;
float cBx = (-Normal.X) * radiusB + clipPoint.X;
float cBy = (-Normal.Y) * radiusB + clipPoint.Y;
Points[i].X = (cAx + cBx) * .5f;
Points[i].Y = (cAy + cBy) * .5f;
}
}
break;
case Manifold.ManifoldType.FaceB:
Vec2 planePoint2 = pool3;
Rot.MulToOutUnsafe(xfB.Q, manifold.LocalNormal, Normal);
Transform.MulToOut(xfB, manifold.LocalPoint, planePoint2);
// final Mat22 R = xfB.q;
// normal.x = R.ex.x * manifold.localNormal.x + R.ey.x * manifold.localNormal.y;
// normal.y = R.ex.y * manifold.localNormal.x + R.ey.y * manifold.localNormal.y;
// final Vec2 v = manifold.localPoint;
// planePoint.x = xfB.p.x + xfB.q.ex.x * v.x + xfB.q.ey.x * v.y;
// planePoint.y = xfB.p.y + xfB.q.ex.y * v.x + xfB.q.ey.y * v.y;
Vec2 clipPoint2 = pool4;
for (int i = 0; i < manifold.PointCount; i++)
{
// b2Vec2 clipPoint = b2Mul(xfA, manifold->points[i].localPoint);
// b2Vec2 cB = clipPoint + (radiusB - b2Dot(clipPoint - planePoint,
// normal)) * normal;
// b2Vec2 cA = clipPoint - radiusA * normal;
// points[i] = 0.5f * (cA + cB);
Transform.MulToOut(xfA, manifold.Points[i].LocalPoint, clipPoint2);
// cB.set(clipPoint).subLocal(planePoint);
// float scalar = radiusB - Vec2.dot(cB, normal);
// cB.set(normal).mulLocal(scalar).addLocal(clipPoint);
// cA.set(normal).mulLocal(radiusA).subLocal(clipPoint).negateLocal();
// points[i].set(cA).addLocal(cB).mulLocal(0.5f);
// points[i] = 0.5f * (cA + cB);
//
// clipPoint.x = xfA.p.x + xfA.q.ex.x * manifold.points[i].localPoint.x + xfA.q.ey.x *
// manifold.points[i].localPoint.y;
// clipPoint.y = xfA.p.y + xfA.q.ex.y * manifold.points[i].localPoint.x + xfA.q.ey.y *
// manifold.points[i].localPoint.y;
float scalar = radiusB - ((clipPoint2.X - planePoint2.X) * Normal.X + (clipPoint2.Y - planePoint2.Y) * Normal.Y);
float cBx = Normal.X * scalar + clipPoint2.X;
float cBy = Normal.Y * scalar + clipPoint2.Y;
float cAx = (-Normal.X) * radiusA + clipPoint2.X;
float cAy = (-Normal.Y) * radiusA + clipPoint2.Y;
Points[i].X = (cAx + cBx) * .5f;
Points[i].Y = (cAy + cBy) * .5f;
}
// Ensure normal points from A to B.
Normal.X = -Normal.X;
Normal.Y = -Normal.Y;
break;
}
}
public override void InitVelocityConstraints(SolverData data)
{
IndexA = BodyA.IslandIndex;
IndexB = BodyB.IslandIndex;
LocalCenterA.Set(BodyA.Sweep.LocalCenter);
LocalCenterB.Set(BodyB.Sweep.LocalCenter);
InvMassA = BodyA.InvMass;
InvMassB = BodyB.InvMass;
InvIA = BodyA.InvI;
InvIB = BodyB.InvI;
Vec2 cA = data.Positions[IndexA].C;
float aA = data.Positions[IndexA].A;
Vec2 vA = data.Velocities[IndexA].V;
float wA = data.Velocities[IndexA].W;
Vec2 cB = data.Positions[IndexB].C;
float aB = data.Positions[IndexB].A;
Vec2 vB = data.Velocities[IndexB].V;
float wB = data.Velocities[IndexB].W;
Rot qA = Pool.PopRot();
Rot qB = Pool.PopRot();
qA.Set(aA);
qB.Set(aB);
// use m_u as temporary variable
Rot.MulToOutUnsafe(qA, U.Set(LocalAnchorA).SubLocal(LocalCenterA), RA);
Rot.MulToOutUnsafe(qB, U.Set(LocalAnchorB).SubLocal(LocalCenterB), RB);
U.Set(cB).AddLocal(RB).SubLocal(cA).SubLocal(RA);
Pool.PushRot(2);
// Handle singularity.
float length = U.Length();
if (length > Settings.LINEAR_SLOP)
{
U.X *= 1.0f / length;
U.Y *= 1.0f / length;
}
else
{
U.Set(0.0f, 0.0f);
}
float crAu = Vec2.Cross(RA, U);
float crBu = Vec2.Cross(RB, U);
float invMass = InvMassA + InvIA * crAu * crAu + InvMassB + InvIB * crBu * crBu;
// Compute the effective mass matrix.
Mass = invMass != 0.0f ? 1.0f / invMass : 0.0f;
if (FrequencyHz > 0.0f)
{
float C = length - Length;
// Frequency
float omega = 2.0f * MathUtils.PI * FrequencyHz;
// Damping coefficient
float d = 2.0f * Mass * DampingRatio * omega;
// Spring stiffness
float k = Mass * omega * omega;
// magic formulas
float h = data.Step.Dt;
Gamma = h * (d + h * k);
Gamma = Gamma != 0.0f ? 1.0f / Gamma : 0.0f;
Bias = C * h * k * Gamma;
invMass += Gamma;
Mass = invMass != 0.0f ? 1.0f / invMass : 0.0f;
}
else
{
Gamma = 0.0f;
Bias = 0.0f;
}
if (data.Step.WarmStarting)
{
// Scale the impulse to support a variable time step.
Impulse *= data.Step.DtRatio;
Vec2 P = Pool.PopVec2();
P.Set(U).MulLocal(Impulse);
vA.X -= InvMassA * P.X;
vA.Y -= InvMassA * P.Y;
wA -= InvIA * Vec2.Cross(RA, P);
vB.X += InvMassB * P.X;
vB.Y += InvMassB * P.Y;
wB += InvIB * Vec2.Cross(RB, P);
Pool.PushVec2(1);
}
else
{
Impulse = 0.0f;
}
data.Velocities[IndexA].V.Set(vA);
data.Velocities[IndexA].W = wA;
data.Velocities[IndexB].V.Set(vB);
data.Velocities[IndexB].W = wB;
}
public override void InitVelocityConstraints(SolverData data)
{
IndexA = BodyA.IslandIndex;
IndexB = BodyB.IslandIndex;
LocalCenterB.Set(BodyB.Sweep.LocalCenter);
InvMassB = BodyB.InvMass;
InvIB = BodyB.InvI;
Vec2 cB = data.Positions[IndexB].C;
float aB = data.Positions[IndexB].A;
Vec2 vB = data.Velocities[IndexB].V;
float wB = data.Velocities[IndexB].W;
Rot qB = Pool.PopRot();
qB.Set(aB);
float mass = BodyB.Mass;
// Frequency
float omega = 2.0f * MathUtils.PI * Frequency;
// Damping coefficient
float d = 2.0f * mass * DampingRatio * omega;
// Spring stiffness
float k = mass * (omega * omega);
// magic formulas
// gamma has units of inverse mass.
// beta has units of inverse time.
float h = data.Step.Dt;
Debug.Assert(d + h * k > Settings.EPSILON);
m_gamma = h * (d + h * k);
if (m_gamma != 0.0f)
{
m_gamma = 1.0f / m_gamma;
}
m_beta = h * k * m_gamma;
Vec2 temp = Pool.PopVec2();
// Compute the effective mass matrix.
Rot.MulToOutUnsafe(qB, temp.Set(m_localAnchorB).SubLocal(LocalCenterB), RB);
// 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]
Mat22 K = Pool.PopMat22();
K.Ex.X = InvMassB + InvIB * RB.Y * RB.Y + m_gamma;
K.Ex.Y = (-InvIB) * RB.X * RB.Y;
K.Ey.X = K.Ex.Y;
K.Ey.Y = InvMassB + InvIB * RB.X * RB.X + m_gamma;
K.InvertToOut(m_mass);
m_C.Set(cB).AddLocal(RB).SubLocal(m_targetA);
m_C.MulLocal(m_beta);
// Cheat with some damping
wB *= 0.98f;
if (data.Step.WarmStarting)
{
m_impulse.MulLocal(data.Step.DtRatio);
vB.X += InvMassB * m_impulse.X;
vB.Y += InvMassB * m_impulse.Y;
wB += InvIB * Vec2.Cross(RB, m_impulse);
}
else
{
m_impulse.SetZero();
}
data.Velocities[IndexB].V.Set(vB);
data.Velocities[IndexB].W = wB;
Pool.PushVec2(1);
Pool.PushMat22(1);
Pool.PushRot(1);
}
public override bool SolvePositionConstraints(SolverData data)
{
Rot qA = Pool.PopRot();
Rot qB = Pool.PopRot();
Vec2 rA = Pool.PopVec2();
Vec2 rB = Pool.PopVec2();
Vec2 d = Pool.PopVec2();
Vec2 axis = Pool.PopVec2();
Vec2 perp = Pool.PopVec2();
Vec2 temp = Pool.PopVec2();
Vec2 C1 = Pool.PopVec2();
Vec3 impulse = Pool.PopVec3();
Vec2 cA = data.Positions[IndexA].C;
float aA = data.Positions[IndexA].A;
Vec2 cB = data.Positions[IndexB].C;
float aB = data.Positions[IndexB].A;
qA.Set(aA);
qB.Set(aB);
float mA = InvMassA, mB = InvMassB;
float iA = InvIA, iB = InvIB;
// Compute fresh Jacobians
Rot.MulToOutUnsafe(qA, temp.Set(LocalAnchorA).SubLocal(LocalCenterA), rA);
Rot.MulToOutUnsafe(qB, temp.Set(LocalAnchorB).SubLocal(LocalCenterB), rB);
d.Set(cB).AddLocal(rB).SubLocal(cA).SubLocal(rA);
Rot.MulToOutUnsafe(qA, LocalXAxisA, axis);
float a1 = Vec2.Cross(temp.Set(d).AddLocal(rA), axis);
float a2 = Vec2.Cross(rB, axis);
Rot.MulToOutUnsafe(qA, 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 - ReferenceAngle;
float linearError = MathUtils.Abs(C1.X);
float angularError = MathUtils.Abs(C1.Y);
bool active = false;
float C2 = 0.0f;
if (m_limitEnabled)
{
float translation = Vec2.Dot(axis, d);
if (MathUtils.Abs(UpperTranslation - LowerTranslation) < 2.0f * Settings.LINEAR_SLOP)
{
// Prevent large angular corrections
C2 = MathUtils.Clamp(translation, -Settings.MAX_LINEAR_CORRECTION, Settings.MAX_LINEAR_CORRECTION);
linearError = MathUtils.Max(linearError, MathUtils.Abs(translation));
active = true;
}
else if (translation <= LowerTranslation)
{
// Prevent large linear corrections and allow some slop.
C2 = MathUtils.Clamp(translation - LowerTranslation + Settings.LINEAR_SLOP, -Settings.MAX_LINEAR_CORRECTION, 0.0f);
linearError = MathUtils.Max(linearError, LowerTranslation - translation);
active = true;
}
else if (translation >= UpperTranslation)
{
// Prevent large linear corrections and allow some slop.
C2 = MathUtils.Clamp(translation - UpperTranslation - Settings.LINEAR_SLOP, 0.0f, Settings.MAX_LINEAR_CORRECTION);
linearError = MathUtils.Max(linearError, translation - 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;
Mat33 K = Pool.PopMat33();
K.Ex.Set(k11, k12, k13);
K.Ey.Set(k12, k22, k23);
K.Ez.Set(k13, k23, k33);
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;
}
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[IndexA].C.Set(cA);
data.Positions[IndexA].A = aA;
data.Positions[IndexB].C.Set(cB);
data.Positions[IndexB].A = aB;
Pool.PushVec2(7);
Pool.PushVec3(1);
Pool.PushRot(2);
return(linearError <= Settings.LINEAR_SLOP && angularError <= Settings.ANGULAR_SLOP);
}
// Sequential position solver for position constraints.
public bool SolveTOIPositionConstraints(int toiIndexA, int toiIndexB)
{
float minSeparation = 0.0f;
for (int i = 0; i < Count; ++i)
{
ContactPositionConstraint pc = PositionConstraints[i];
int indexA = pc.IndexA;
int indexB = pc.IndexB;
Vec2 localCenterA = pc.LocalCenterA;
Vec2 localCenterB = pc.LocalCenterB;
int pointCount = pc.PointCount;
float mA = 0.0f;
float iA = 0.0f;
if (indexA == toiIndexA || indexA == toiIndexB)
{
mA = pc.InvMassA;
iA = pc.InvIA;
}
float mB = pc.InvMassB;
float iB = pc.InvIB;
if (indexB == toiIndexA || indexB == toiIndexB)
{
mB = pc.InvMassB;
iB = pc.InvIB;
}
Vec2 cA = Positions[indexA].C;
float aA = Positions[indexA].A;
Vec2 cB = Positions[indexB].C;
float aB = Positions[indexB].A;
// Solve normal constraints
for (int j = 0; j < pointCount; ++j)
{
xfA.Q.Set(aA);
xfB.Q.Set(aB);
Rot.MulToOutUnsafe(xfA.Q, localCenterA, xfA.P);
xfA.P.NegateLocal().AddLocal(cA);
Rot.MulToOutUnsafe(xfB.Q, localCenterB, xfB.P);
xfB.P.NegateLocal().AddLocal(cB);
PositionSolverManifold psm = psolver;
psm.Initialize(pc, xfA, xfB, j);
Vec2 normal = psm.Normal;
Vec2 point = psm.Point;
float separation = psm.Separation;
rA.Set(point).SubLocal(cA);
rB.Set(point).SubLocal(cB);
// Track max constraint error.
minSeparation = MathUtils.Min(minSeparation, separation);
// Prevent large corrections and allow slop.
float C = MathUtils.Clamp(Settings.TOI_BAUGARTE * (separation + Settings.LINEAR_SLOP), -Settings.MAX_LINEAR_CORRECTION, 0.0f);
// Compute the effective mass.
float rnA = Vec2.Cross(rA, normal);
float rnB = Vec2.Cross(rB, normal);
float K = mA + mB + iA * rnA * rnA + iB * rnB * rnB;
// Compute normal impulse
float impulse = K > 0.0f ? (-C) / K : 0.0f;
P.Set(normal).MulLocal(impulse);
cA.SubLocal(temp.Set(P).MulLocal(mA));
aA -= iA * Vec2.Cross(rA, P);
cB.AddLocal(temp.Set(P).MulLocal(mB));
aB += iB * Vec2.Cross(rB, P);
}
Positions[indexA].C.Set(cA);
Positions[indexA].A = aA;
Positions[indexB].C.Set(cB);
Positions[indexB].A = aB;
}
// We can't expect minSpeparation >= -_linearSlop because we don't
// push the separation above -_linearSlop.
return(minSeparation >= (-1.5f) * Settings.LINEAR_SLOP);
}
// float FindMinSeparation(int* indexA, int* indexB, float t) const
public float FindMinSeparation(int[] indexes, float t)
{
SweepA.GetTransform(xfa, t);
SweepB.GetTransform(xfb, t);
switch (Type)
{
case Type.Points:
{
Rot.MulTransUnsafe(xfa.Q, Axis, axisA);
Rot.MulTransUnsafe(xfb.Q, Axis.NegateLocal(), axisB);
Axis.NegateLocal();
indexes[0] = ProxyA.GetSupport(axisA);
indexes[1] = ProxyB.GetSupport(axisB);
localPointA.Set(ProxyA.GetVertex(indexes[0]));
localPointB.Set(ProxyB.GetVertex(indexes[1]));
Transform.MulToOutUnsafe(xfa, localPointA, pointA);
Transform.MulToOutUnsafe(xfb, localPointB, pointB);
float separation = Vec2.Dot(pointB.SubLocal(pointA), Axis);
return(separation);
}
case Type.FaceA:
{
Rot.MulToOutUnsafe(xfa.Q, Axis, normal);
Transform.MulToOutUnsafe(xfa, LocalPoint, pointA);
Rot.MulTransUnsafe(xfb.Q, normal.NegateLocal(), axisB);
normal.NegateLocal();
indexes[0] = -1;
indexes[1] = ProxyB.GetSupport(axisB);
localPointB.Set(ProxyB.GetVertex(indexes[1]));
Transform.MulToOutUnsafe(xfb, localPointB, pointB);
float separation = Vec2.Dot(pointB.SubLocal(pointA), normal);
return(separation);
}
case Type.FaceB:
{
Rot.MulToOutUnsafe(xfb.Q, Axis, normal);
Transform.MulToOutUnsafe(xfb, LocalPoint, pointB);
Rot.MulTransUnsafe(xfa.Q, normal.NegateLocal(), axisA);
normal.NegateLocal();
indexes[1] = -1;
indexes[0] = ProxyA.GetSupport(axisA);
localPointA.Set(ProxyA.GetVertex(indexes[0]));
Transform.MulToOutUnsafe(xfa, localPointA, pointA);
float separation = Vec2.Dot(pointA.SubLocal(pointB), normal);
return(separation);
}
default:
Debug.Assert(false);
indexes[0] = -1;
indexes[1] = -1;
return(0f);
}
}
// TODO_ERIN might not need to return the separation
public float Initialize(Distance.SimplexCache cache, Distance.DistanceProxy proxyA, Sweep sweepA, Distance.DistanceProxy proxyB, Sweep sweepB, float t1)
{
ProxyA = proxyA;
ProxyB = proxyB;
int count = cache.Count;
Debug.Assert(0 < count && count < 3);
SweepA = sweepA;
SweepB = sweepB;
SweepA.GetTransform(xfa, t1);
SweepB.GetTransform(xfb, t1);
// log.debug("initializing separation.\n" +
// "cache: "+cache.count+"-"+cache.metric+"-"+cache.indexA+"-"+cache.indexB+"\n"
// "distance: "+proxyA.
if (count == 1)
{
Type = Type.Points;
/*
* Vec2 localPointA = m_proxyA.GetVertex(cache.indexA[0]); Vec2 localPointB =
* m_proxyB.GetVertex(cache.indexB[0]); Vec2 pointA = Mul(transformA, localPointA); Vec2
* pointB = Mul(transformB, localPointB); m_axis = pointB - pointA; m_axis.Normalize();
*/
localPointA.Set(ProxyA.GetVertex(cache.IndexA[0]));
localPointB.Set(ProxyB.GetVertex(cache.IndexB[0]));
Transform.MulToOutUnsafe(xfa, localPointA, pointA);
Transform.MulToOutUnsafe(xfb, localPointB, pointB);
Axis.Set(pointB).SubLocal(pointA);
float s = Axis.Normalize();
return(s);
}
else if (cache.IndexA[0] == cache.IndexA[1])
{
// Two points on B and one on A.
Type = Type.FaceB;
localPointB1.Set(ProxyB.GetVertex(cache.IndexB[0]));
localPointB2.Set(ProxyB.GetVertex(cache.IndexB[1]));
temp.Set(localPointB2).SubLocal(localPointB1);
Vec2.CrossToOutUnsafe(temp, 1f, Axis);
Axis.Normalize();
Rot.MulToOutUnsafe(xfb.Q, Axis, normal);
LocalPoint.Set(localPointB1).AddLocal(localPointB2).MulLocal(.5f);
Transform.MulToOutUnsafe(xfb, LocalPoint, pointB);
localPointA.Set(proxyA.GetVertex(cache.IndexA[0]));
Transform.MulToOutUnsafe(xfa, localPointA, pointA);
temp.Set(pointA).SubLocal(pointB);
float s = Vec2.Dot(temp, normal);
if (s < 0.0f)
{
Axis.NegateLocal();
s = -s;
}
return(s);
}
else
{
// Two points on A and one or two points on B.
Type = Type.FaceA;
localPointA1.Set(ProxyA.GetVertex(cache.IndexA[0]));
localPointA2.Set(ProxyA.GetVertex(cache.IndexA[1]));
temp.Set(localPointA2).SubLocal(localPointA1);
Vec2.CrossToOutUnsafe(temp, 1.0f, Axis);
Axis.Normalize();
Rot.MulToOutUnsafe(xfa.Q, Axis, normal);
LocalPoint.Set(localPointA1).AddLocal(localPointA2).MulLocal(.5f);
Transform.MulToOutUnsafe(xfa, LocalPoint, pointA);
localPointB.Set(ProxyB.GetVertex(cache.IndexB[0]));
Transform.MulToOutUnsafe(xfb, localPointB, pointB);
temp.Set(pointB).SubLocal(pointA);
float s = Vec2.Dot(temp, normal);
if (s < 0.0f)
{
Axis.NegateLocal();
s = -s;
}
return(s);
}
}
public override bool SolvePositionConstraints(SolverData data)
{
Rot qA = Pool.PopRot();
Rot qB = Pool.PopRot();
Vec2 rA = Pool.PopVec2();
Vec2 rB = Pool.PopVec2();
Vec2 uA = Pool.PopVec2();
Vec2 uB = Pool.PopVec2();
Vec2 temp = Pool.PopVec2();
Vec2 PA = Pool.PopVec2();
Vec2 PB = Pool.PopVec2();
Vec2 cA = data.Positions[IndexA].C;
float aA = data.Positions[IndexA].A;
Vec2 cB = data.Positions[IndexB].C;
float aB = data.Positions[IndexB].A;
qA.Set(aA);
qB.Set(aB);
Rot.MulToOutUnsafe(qA, temp.Set(LocalAnchorA).SubLocal(m_localCenterA), rA);
Rot.MulToOutUnsafe(qB, temp.Set(LocalAnchorB).SubLocal(m_localCenterB), rB);
uA.Set(cA).AddLocal(rA).SubLocal(m_groundAnchorA);
uB.Set(cB).AddLocal(rB).SubLocal(m_groundAnchorB);
float lengthA = uA.Length();
float lengthB = uB.Length();
if (lengthA > 10.0f * Settings.LINEAR_SLOP)
{
uA.MulLocal(1.0f / lengthA);
}
else
{
uA.SetZero();
}
if (lengthB > 10.0f * Settings.LINEAR_SLOP)
{
uB.MulLocal(1.0f / lengthB);
}
else
{
uB.SetZero();
}
// Compute effective mass.
float ruA = Vec2.Cross(rA, uA);
float ruB = Vec2.Cross(rB, uB);
float mA = InvMassA + InvIA * ruA * ruA;
float mB = InvMassB + InvIB * ruB * ruB;
float mass = mA + m_ratio * m_ratio * mB;
if (mass > 0.0f)
{
mass = 1.0f / mass;
}
float C = m_constant - lengthA - m_ratio * lengthB;
float linearError = MathUtils.Abs(C);
float impulse = (-mass) * C;
PA.Set(uA).MulLocal(-impulse);
PB.Set(uB).MulLocal((-m_ratio) * impulse);
cA.X += InvMassA * PA.X;
cA.Y += InvMassA * PA.Y;
aA += InvIA * Vec2.Cross(rA, PA);
cB.X += InvMassB * PB.X;
cB.Y += InvMassB * PB.Y;
aB += InvIB * Vec2.Cross(rB, PB);
data.Positions[IndexA].C.Set(cA);
data.Positions[IndexA].A = aA;
data.Positions[IndexB].C.Set(cB);
data.Positions[IndexB].A = aB;
Pool.PushRot(2);
Pool.PushVec2(7);
return(linearError < Settings.LINEAR_SLOP);
}
public override void InitVelocityConstraints(SolverData data)
{
IndexA = BodyA.IslandIndex;
IndexB = BodyB.IslandIndex;
m_localCenterA.Set(BodyA.Sweep.LocalCenter);
m_localCenterB.Set(BodyB.Sweep.LocalCenter);
InvMassA = BodyA.InvMass;
InvMassB = BodyB.InvMass;
InvIA = BodyA.InvI;
InvIB = BodyB.InvI;
Vec2 cA = data.Positions[IndexA].C;
float aA = data.Positions[IndexA].A;
Vec2 vA = data.Velocities[IndexA].V;
float wA = data.Velocities[IndexA].W;
Vec2 cB = data.Positions[IndexB].C;
float aB = data.Positions[IndexB].A;
Vec2 vB = data.Velocities[IndexB].V;
float wB = data.Velocities[IndexB].W;
Rot qA = Pool.PopRot();
Rot qB = Pool.PopRot();
Vec2 temp = Pool.PopVec2();
qA.Set(aA);
qB.Set(aB);
// Compute the effective masses.
Rot.MulToOutUnsafe(qA, temp.Set(LocalAnchorA).SubLocal(m_localCenterA), RA);
Rot.MulToOutUnsafe(qB, temp.Set(LocalAnchorB).SubLocal(m_localCenterB), RB);
m_uA.Set(cA).AddLocal(RA).SubLocal(m_groundAnchorA);
m_uB.Set(cB).AddLocal(RB).SubLocal(m_groundAnchorB);
float lengthA = m_uA.Length();
float lengthB = m_uB.Length();
if (lengthA > 10f * Settings.LINEAR_SLOP)
{
m_uA.MulLocal(1.0f / lengthA);
}
else
{
m_uA.SetZero();
}
if (lengthB > 10f * Settings.LINEAR_SLOP)
{
m_uB.MulLocal(1.0f / lengthB);
}
else
{
m_uB.SetZero();
}
// Compute effective mass.
float ruA = Vec2.Cross(RA, m_uA);
float ruB = Vec2.Cross(RB, m_uB);
float mA = InvMassA + InvIA * ruA * ruA;
float mB = InvMassB + InvIB * ruB * ruB;
m_mass = mA + m_ratio * m_ratio * mB;
if (m_mass > 0.0f)
{
m_mass = 1.0f / m_mass;
}
if (data.Step.WarmStarting)
{
// Scale impulses to support variable time steps.
m_impulse *= data.Step.DtRatio;
// Warm starting.
Vec2 PA = Pool.PopVec2();
Vec2 PB = Pool.PopVec2();
PA.Set(m_uA).MulLocal(-m_impulse);
PB.Set(m_uB).MulLocal((-m_ratio) * m_impulse);
vA.X += InvMassA * PA.X;
vA.Y += InvMassA * PA.Y;
wA += InvIA * Vec2.Cross(RA, PA);
vB.X += InvMassB * PB.X;
vB.Y += InvMassB * PB.Y;
wB += InvIB * Vec2.Cross(RB, PB);
Pool.PushVec2(2);
}
else
{
m_impulse = 0.0f;
}
data.Velocities[IndexA].V.Set(vA);
data.Velocities[IndexA].W = wA;
data.Velocities[IndexB].V.Set(vB);
data.Velocities[IndexB].W = wB;
Pool.PushVec2(1);
Pool.PushRot(2);
}
public override void InitVelocityConstraints(SolverData data)
{
IndexA = BodyA.IslandIndex;
IndexB = BodyB.IslandIndex;
LocalCenterA.Set(BodyA.Sweep.LocalCenter);
LocalCenterB.Set(BodyB.Sweep.LocalCenter);
InvMassA = BodyA.InvMass;
InvMassB = BodyB.InvMass;
InvIA = BodyA.InvI;
InvIB = BodyB.InvI;
// Vec2 cA = data.positions[m_indexA].c;
float aA = data.Positions[IndexA].A;
Vec2 vA = data.Velocities[IndexA].V;
float wA = data.Velocities[IndexA].W;
// Vec2 cB = data.positions[m_indexB].c;
float aB = data.Positions[IndexB].A;
Vec2 vB = data.Velocities[IndexB].V;
float wB = data.Velocities[IndexB].W;
Rot qA = Pool.PopRot();
Rot qB = Pool.PopRot();
Vec2 temp = Pool.PopVec2();
qA.Set(aA);
qB.Set(aB);
// Compute the effective masses.
Rot.MulToOutUnsafe(qA, temp.Set(LocalAnchorA).SubLocal(LocalCenterA), RA);
Rot.MulToOutUnsafe(qB, temp.Set(LocalAnchorB).SubLocal(LocalCenterB), 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 = InvMassA, mB = InvMassB;
float iA = InvIA, iB = InvIB;
bool fixedRotation = (iA + iB == 0.0f);
Mass.Ex.X = mA + mB + RA.Y * RA.Y * iA + RB.Y * RB.Y * iB;
Mass.Ey.X = (-RA.Y) * RA.X * iA - RB.Y * RB.X * iB;
Mass.Ez.X = (-RA.Y) * iA - RB.Y * iB;
Mass.Ex.Y = Mass.Ey.X;
Mass.Ey.Y = mA + mB + RA.X * RA.X * iA + RB.X * RB.X * iB;
Mass.Ez.Y = RA.X * iA + RB.X * iB;
Mass.Ex.Z = Mass.Ez.X;
Mass.Ey.Z = Mass.Ez.Y;
Mass.Ez.Z = iA + iB;
MotorMass = iA + iB;
if (MotorMass > 0.0f)
{
MotorMass = 1.0f / MotorMass;
}
if (m_motorEnabled == false || fixedRotation)
{
MotorImpulse = 0.0f;
}
if (m_limitEnabled && fixedRotation == false)
{
float jointAngle = aB - aA - ReferenceAngle;
if (MathUtils.Abs(UpperAngle - LowerAngle) < 2.0f * Settings.ANGULAR_SLOP)
{
LimitState = LimitState.Equal;
}
else if (jointAngle <= LowerAngle)
{
if (LimitState != LimitState.AtLower)
{
Impulse.Z = 0.0f;
}
LimitState = LimitState.AtLower;
}
else if (jointAngle >= UpperAngle)
{
if (LimitState != LimitState.AtUpper)
{
Impulse.Z = 0.0f;
}
LimitState = LimitState.AtUpper;
}
else
{
LimitState = LimitState.Inactive;
Impulse.Z = 0.0f;
}
}
else
{
LimitState = LimitState.Inactive;
}
if (data.Step.WarmStarting)
{
Vec2 P = Pool.PopVec2();
// Scale impulses to support a variable time step.
Impulse.X *= data.Step.DtRatio;
Impulse.Y *= data.Step.DtRatio;
MotorImpulse *= data.Step.DtRatio;
P.X = Impulse.X;
P.Y = Impulse.Y;
vA.X -= mA * P.X;
vA.Y -= mA * P.Y;
wA -= iA * (Vec2.Cross(RA, P) + MotorImpulse + Impulse.Z);
vB.X += mB * P.X;
vB.Y += mB * P.Y;
wB += iB * (Vec2.Cross(RB, P) + MotorImpulse + Impulse.Z);
Pool.PushVec2(1);
}
else
{
Impulse.SetZero();
MotorImpulse = 0.0f;
}
data.Velocities[IndexA].V.Set(vA);
data.Velocities[IndexA].W = wA;
data.Velocities[IndexB].V.Set(vB);
data.Velocities[IndexB].W = wB;
Pool.PushVec2(1);
Pool.PushRot(2);
}
public override bool SolvePositionConstraints(SolverData data)
{
Rot qA = Pool.PopRot();
Rot qB = Pool.PopRot();
Vec2 cA = data.Positions[IndexA].C;
float aA = data.Positions[IndexA].A;
Vec2 cB = data.Positions[IndexB].C;
float aB = data.Positions[IndexB].A;
qA.Set(aA);
qB.Set(aB);
float angularError = 0.0f;
float positionError = 0.0f;
bool fixedRotation = (InvIA + InvIB == 0.0f);
// Solve angular limit constraint.
if (m_limitEnabled && LimitState != LimitState.Inactive && fixedRotation == false)
{
float angle = aB - aA - ReferenceAngle;
float limitImpulse = 0.0f;
if (LimitState == LimitState.Equal)
{
// Prevent large angular corrections
float C = MathUtils.Clamp(angle - LowerAngle, -Settings.MAX_ANGULAR_CORRECTION, Settings.MAX_ANGULAR_CORRECTION);
limitImpulse = (-MotorMass) * C;
angularError = MathUtils.Abs(C);
}
else if (LimitState == LimitState.AtLower)
{
float C = angle - LowerAngle;
angularError = -C;
// Prevent large angular corrections and allow some slop.
C = MathUtils.Clamp(C + Settings.ANGULAR_SLOP, -Settings.MAX_ANGULAR_CORRECTION, 0.0f);
limitImpulse = (-MotorMass) * C;
}
else if (LimitState == LimitState.AtUpper)
{
float C = angle - UpperAngle;
angularError = C;
// Prevent large angular corrections and allow some slop.
C = MathUtils.Clamp(C - Settings.ANGULAR_SLOP, 0.0f, Settings.MAX_ANGULAR_CORRECTION);
limitImpulse = (-MotorMass) * C;
}
aA -= InvIA * limitImpulse;
aB += InvIB * limitImpulse;
}
// Solve point-to-point constraint.
{
qA.Set(aA);
qB.Set(aB);
Vec2 rA = Pool.PopVec2();
Vec2 rB = Pool.PopVec2();
Vec2 C = Pool.PopVec2();
Vec2 impulse = Pool.PopVec2();
Rot.MulToOutUnsafe(qA, C.Set(LocalAnchorA).SubLocal(LocalCenterA), rA);
Rot.MulToOutUnsafe(qB, C.Set(LocalAnchorB).SubLocal(LocalCenterB), rB);
C.Set(cB).AddLocal(rB).SubLocal(cA).SubLocal(rA);
positionError = C.Length();
float mA = InvMassA, mB = InvMassB;
float iA = InvIA, iB = InvIB;
Mat22 K = Pool.PopMat22();
K.Ex.X = mA + mB + iA * rA.Y * rA.Y + iB * rB.Y * rB.Y;
K.Ex.Y = (-iA) * rA.X * rA.Y - iB * rB.X * rB.Y;
K.Ey.X = K.Ex.Y;
K.Ey.Y = mA + mB + iA * rA.X * rA.X + iB * rB.X * rB.X;
K.SolveToOut(C, impulse);
impulse.NegateLocal();
cA.X -= mA * impulse.X;
cA.Y -= mA * impulse.Y;
aA -= iA * Vec2.Cross(rA, impulse);
cB.X += mB * impulse.X;
cB.Y += mB * impulse.Y;
aB += iB * Vec2.Cross(rB, impulse);
Pool.PushVec2(4);
Pool.PushMat22(1);
}
data.Positions[IndexA].C.Set(cA);
data.Positions[IndexA].A = aA;
data.Positions[IndexB].C.Set(cB);
data.Positions[IndexB].A = aB;
Pool.PushRot(2);
return(positionError <= Settings.LINEAR_SLOP && angularError <= Settings.ANGULAR_SLOP);
}
public void GetWorldVectorToOutUnsafe(Vec2 localVector, Vec2 result)
{
Rot.MulToOutUnsafe(Xf.Q, localVector, result);
}
/// <seealso cref="Joint.initVelocityConstraints(TimeStep)"></seealso>
public override void InitVelocityConstraints(SolverData data)
{
IndexA = BodyA.IslandIndex;
IndexB = BodyB.IslandIndex;
LocalCenterA.Set(BodyA.Sweep.LocalCenter);
LocalCenterB.Set(BodyB.Sweep.LocalCenter);
InvMassA = BodyA.InvMass;
InvMassB = BodyB.InvMass;
InvIA = BodyA.InvI;
InvIB = BodyB.InvI;
float aA = data.Positions[IndexA].A;
Vec2 vA = data.Velocities[IndexA].V;
float wA = data.Velocities[IndexA].W;
float aB = data.Positions[IndexB].A;
Vec2 vB = data.Velocities[IndexB].V;
float wB = data.Velocities[IndexB].W;
Vec2 temp = Pool.PopVec2();
Rot qA = Pool.PopRot();
Rot qB = Pool.PopRot();
qA.Set(aA);
qB.Set(aB);
// Compute the effective mass matrix.
Rot.MulToOutUnsafe(qA, temp.Set(m_localAnchorA).SubLocal(LocalCenterA), RA);
Rot.MulToOutUnsafe(qB, temp.Set(m_localAnchorB).SubLocal(LocalCenterB), 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 = InvMassA, mB = InvMassB;
float iA = InvIA, iB = InvIB;
Mat22 K = Pool.PopMat22();
K.Ex.X = mA + mB + iA * RA.Y * RA.Y + iB * RB.Y * RB.Y;
K.Ex.Y = (-iA) * RA.X * RA.Y - iB * RB.X * RB.Y;
K.Ey.X = K.Ex.Y;
K.Ey.Y = mA + mB + iA * RA.X * RA.X + iB * RB.X * RB.X;
K.InvertToOut(LinearMass);
AngularMass = iA + iB;
if (AngularMass > 0.0f)
{
AngularMass = 1.0f / AngularMass;
}
if (data.Step.WarmStarting)
{
// Scale impulses to support a variable time step.
m_linearImpulse.MulLocal(data.Step.DtRatio);
m_angularImpulse *= data.Step.DtRatio;
Vec2 P = Pool.PopVec2();
P.Set(m_linearImpulse);
temp.Set(P).MulLocal(mA);
vA.SubLocal(temp);
wA -= iA * (Vec2.Cross(RA, P) + m_angularImpulse);
temp.Set(P).MulLocal(mB);
vB.AddLocal(temp);
wB += iB * (Vec2.Cross(RB, P) + m_angularImpulse);
Pool.PushVec2(1);
}
else
{
m_linearImpulse.SetZero();
m_angularImpulse = 0.0f;
}
data.Velocities[IndexA].V.Set(vA);
if (data.Velocities[IndexA].W != wA)
{
Debug.Assert(data.Velocities[IndexA].W != wA);
}
data.Velocities[IndexA].W = wA;
data.Velocities[IndexB].V.Set(vB);
data.Velocities[IndexB].W = wB;
Pool.PushRot(2);
Pool.PushVec2(1);
Pool.PushMat22(1);
}
