internal override void SolveVelocityConstraints(ref SolverData data)
{
Vector2 vA = data.velocities[_indexA].v;
float wA = data.velocities[_indexA].w;
Vector2 vB = data.velocities[_indexB].v;
float wB = data.velocities[_indexB].w;
// Cdot = dot(u, v + cross(w, r))
Vector2 vpA = vA + MathUtils.Cross(wA, ref _rA);
Vector2 vpB = vB + MathUtils.Cross(wB, ref _rB);
float Cdot = Vector2.Dot(_u, vpB - vpA);
float impulse = -_mass * (Cdot + _bias + _gamma * _impulse);
_impulse += impulse;
Vector2 P = impulse * _u;
vA -= _invMassA * P;
wA -= _invIA * MathUtils.Cross(ref _rA, ref P);
vB += _invMassB * P;
wB += _invIB * MathUtils.Cross(ref _rB, ref P);
data.velocities[_indexA].v = vA;
data.velocities[_indexA].w = wA;
data.velocities[_indexB].v = vB;
data.velocities[_indexB].w = wB;
}
public static float DistanceBetweenPointAndLineSegment(ref Vector2 point, ref Vector2 start, ref Vector2 end)
{
if (start == end)
{
return(Vector2.Distance(point, start));
}
Vector2 v = end - start;
Vector2 w = point - start;
float c1 = Vector2.Dot(w, v);
if (c1 <= 0)
{
return(Vector2.Distance(point, start));
}
float c2 = Vector2.Dot(v, v);
if (c2 <= c1)
{
return(Vector2.Distance(point, end));
}
float b = c1 / c2;
Vector2 pointOnLine = start + v * b;
return(Vector2.Distance(point, pointOnLine));
}
internal override void SolveVelocityConstraints(ref SolverData data)
{
Vector2 vA = data.velocities[_indexA].v;
float wA = data.velocities[_indexA].w;
Vector2 vB = data.velocities[_indexB].v;
float wB = data.velocities[_indexB].w;
Vector2 vpA = vA + MathUtils.Cross(wA, ref _rA);
Vector2 vpB = vB + MathUtils.Cross(wB, ref _rB);
float Cdot = -Vector2.Dot(_uA, vpA) - Ratio * Vector2.Dot(_uB, vpB);
float impulse = -_mass * Cdot;
_impulse += impulse;
Vector2 PA = -impulse * _uA;
Vector2 PB = -Ratio * impulse * _uB;
vA += _invMassA * PA;
wA += _invIA * MathUtils.Cross(ref _rA, ref PA);
vB += _invMassB * PB;
wB += _invIB * MathUtils.Cross(ref _rB, ref PB);
data.velocities[_indexA].v = vA;
data.velocities[_indexA].w = wA;
data.velocities[_indexB].v = vB;
data.velocities[_indexB].w = wB;
}
public override float ComputeSubmergedArea(ref Vector2 normal, float offset, ref Transform xf, out Vector2 sc)
{
sc = Vector2.Zero;
Vector2 p = Transform.Multiply(ref _position, ref xf);
float l = -(Vector2.Dot(normal, p) - offset);
if (l < -Radius + Settings.Epsilon)
{
//Completely dry
return(0);
}
if (l > Radius)
{
//Completely wet
sc = p;
return(Constant.Pi * _2radius);
}
//Magic
float l2 = l * l;
float area = _2radius * (float)((Math.Asin(l / Radius) + Constant.Pi / 2) + l * Math.Sqrt(_2radius - l2));
float com = -2.0f / 3.0f * (float)Math.Pow(_2radius - l2, 1.5f) / area;
sc.X = p.X + normal.X * com;
sc.Y = p.Y + normal.Y * com;
return(area);
}
public override bool TestPoint(ref Transform transform, ref Vector2 point)
{
Vector2 center = transform.p + Complex.Multiply(ref _position, ref transform.q);
Vector2 d = point - center;
return(Vector2.Dot(d, d) <= _2radius);
}
/// <summary>
/// Tests if a point lies on a line segment.
/// </summary>
/// <remarks>Used by method <c>CalculateBeta()</c>.</remarks>
private static bool PointOnLineSegment(Vector2 start, Vector2 end, Vector2 point)
{
Vector2 segment = end - start;
return(MathUtils.Area(ref start, ref end, ref point) == 0f &&
Vector2.Dot(point - start, segment) >= 0f &&
Vector2.Dot(point - end, segment) <= 0f);
}
public static void Initialize(ContactPositionConstraint pc, ref Transform xfA, ref Transform xfB, int index, out Vector2 normal, out Vector2 point, out float separation)
{
Debug.Assert(pc.pointCount > 0);
switch (pc.type)
{
case ManifoldType.Circles:
{
Vector2 pointA = Transform.Multiply(ref pc.localPoint, ref xfA);
Vector2 pointB = Transform.Multiply(pc.localPoints[0], ref xfB);
normal = pointB - pointA;
// Handle zero normalization
if (normal != Vector2.Zero)
{
normal.Normalize();
}
point = 0.5f * (pointA + pointB);
separation = Vector2.Dot(pointB - pointA, normal) - pc.radiusA - pc.radiusB;
}
break;
case ManifoldType.FaceA:
{
Complex.Multiply(ref pc.localNormal, ref xfA.q, out normal);
Vector2 planePoint = Transform.Multiply(ref pc.localPoint, ref xfA);
Vector2 clipPoint = Transform.Multiply(pc.localPoints[index], ref xfB);
separation = Vector2.Dot(clipPoint - planePoint, normal) - pc.radiusA - pc.radiusB;
point = clipPoint;
}
break;
case ManifoldType.FaceB:
{
Complex.Multiply(ref pc.localNormal, ref xfB.q, out normal);
Vector2 planePoint = Transform.Multiply(ref pc.localPoint, ref xfB);
Vector2 clipPoint = Transform.Multiply(pc.localPoints[index], ref xfA);
separation = Vector2.Dot(clipPoint - planePoint, normal) - pc.radiusA - pc.radiusB;
point = clipPoint;
// Ensure normal points from A to B
normal = -normal;
}
break;
default:
normal = Vector2.Zero;
point = Vector2.Zero;
separation = 0;
break;
}
}
protected override sealed void ComputeProperties()
{
float area = Constant.Pi * _2radius;
MassData.Area = area;
MassData.Mass = Density * area;
MassData.Centroid = Position;
// inertia about the local origin
MassData.Inertia = MassData.Mass * (0.5f * _2radius + Vector2.Dot(Position, Position));
}
private void ApplyViscosity(FluidParticle p, float timeStep)
{
for (int i = 0; i < p.Neighbours.Count; ++i)
{
FluidParticle neighbour = p.Neighbours[i];
if (p.Index >= neighbour.Index)
{
continue;
}
float q;
Vector2.DistanceSquared(ref p.Position, ref neighbour.Position, out q);
if (q > _influenceRadiusSquared)
{
continue;
}
Vector2 direction;
Vector2.Subtract(ref neighbour.Position, ref p.Position, out direction);
if (direction.LengthSquared() < float.Epsilon)
{
continue;
}
direction.Normalize();
Vector2 deltaVelocity;
Vector2.Subtract(ref p.Velocity, ref neighbour.Velocity, out deltaVelocity);
float u;
Vector2.Dot(ref deltaVelocity, ref direction, out u);
if (u > 0.0f)
{
q = 1.0f - (float)Math.Sqrt(q) / Definition.InfluenceRadius;
float impulseFactor = 0.5f * timeStep * q * (u * (Definition.ViscositySigma + Definition.ViscosityBeta * u));
Vector2 impulse;
Vector2.Multiply(ref direction, -impulseFactor, out impulse);
p.ApplyImpulse(ref impulse);
Vector2.Multiply(ref direction, impulseFactor, out impulse);
neighbour.ApplyImpulse(ref impulse);
}
}
}
public static float Evaluate(int indexA, int indexB, float t)
{
Transform xfA, xfB;
_sweepA.GetTransform(out xfA, t);
_sweepB.GetTransform(out xfB, t);
switch (_type)
{
case SeparationFunctionType.Points:
{
Vector2 localPointA = _proxyA.Vertices[indexA];
Vector2 localPointB = _proxyB.Vertices[indexB];
Vector2 pointA = Transform.Multiply(ref localPointA, ref xfA);
Vector2 pointB = Transform.Multiply(ref localPointB, ref xfB);
float separation = Vector2.Dot(pointB - pointA, _axis);
return(separation);
}
case SeparationFunctionType.FaceA:
{
Vector2 normal = Complex.Multiply(ref _axis, ref xfA.q);
Vector2 pointA = Transform.Multiply(ref _localPoint, ref xfA);
Vector2 localPointB = _proxyB.Vertices[indexB];
Vector2 pointB = Transform.Multiply(ref localPointB, ref xfB);
float separation = Vector2.Dot(pointB - pointA, normal);
return(separation);
}
case SeparationFunctionType.FaceB:
{
Vector2 normal = Complex.Multiply(ref _axis, ref xfB.q);
Vector2 pointB = Transform.Multiply(ref _localPoint, ref xfB);
Vector2 localPointA = _proxyA.Vertices[indexA];
Vector2 pointA = Transform.Multiply(ref localPointA, ref xfA);
float separation = Vector2.Dot(pointA - pointB, normal);
return(separation);
}
default:
Debug.Assert(false);
return(0.0f);
}
}
internal override bool SolvePositionConstraints(ref SolverData data)
{
Vector2 cA = data.positions[_indexA].c;
float aA = data.positions[_indexA].a;
Vector2 cB = data.positions[_indexB].c;
float aB = data.positions[_indexB].a;
Complex qA = Complex.FromAngle(aA);
Complex qB = Complex.FromAngle(aB);
Vector2 rA = Complex.Multiply(LocalAnchorA - _localCenterA, ref qA);
Vector2 rB = Complex.Multiply(LocalAnchorB - _localCenterB, ref qB);
Vector2 d = (cB - cA) + rB - rA;
Vector2 ay = Complex.Multiply(ref _localYAxis, ref qA);
float sAy = MathUtils.Cross(d + rA, ay);
float sBy = MathUtils.Cross(ref rB, ref ay);
float C = Vector2.Dot(d, ay);
float k = _invMassA + _invMassB + _invIA * _sAy * _sAy + _invIB * _sBy * _sBy;
float impulse;
if (k != 0.0f)
{
impulse = -C / k;
}
else
{
impulse = 0.0f;
}
Vector2 P = impulse * ay;
float LA = impulse * sAy;
float LB = impulse * sBy;
cA -= _invMassA * P;
aA -= _invIA * LA;
cB += _invMassB * P;
aB += _invIB * LB;
data.positions[_indexA].c = cA;
data.positions[_indexA].a = aA;
data.positions[_indexB].c = cB;
data.positions[_indexB].a = aB;
return(Math.Abs(C) <= Settings.LinearSlop);
}
public override bool TestPoint(ref Transform transform, ref Vector2 point)
{
Vector2 pLocal = Complex.Divide(point - transform.p, ref transform.q);
for (int i = 0; i < Vertices.Count; ++i)
{
float dot = Vector2.Dot(Normals[i], pLocal - Vertices[i]);
if (dot > 0.0f)
{
return(false);
}
}
return(true);
}
/// <summary>
/// Get the supporting vertex in the given direction.
/// </summary>
/// <param name="direction">The direction.</param>
/// <returns></returns>
public Vector2 GetSupportVertex(Vector2 direction)
{
int bestIndex = 0;
float bestValue = Vector2.Dot(Vertices[0], direction);
for (int i = 1; i < Vertices.Count; ++i)
{
float value = Vector2.Dot(Vertices[i], direction);
if (value > bestValue)
{
bestIndex = i;
bestValue = value;
}
}
return Vertices[bestIndex];
}
private void ApplyViscosity(float deltaTime)
{
float u, q;
for (int i = 0; i < Particles.Count; i++)
{
Particle particle = Particles[i];
_tempParticles = Particles.GetNearby(particle);
int len2 = _tempParticles.Count;
if (len2 > MaxNeighbors)
{
len2 = MaxNeighbors;
}
for (int j = 0; j < len2; j++)
{
Particle tempParticle = _tempParticles[j];
Vector2.DistanceSquared(ref particle.Position, ref tempParticle.Position, out q);
if ((q < InfluenceRadiusSquared) && (q != 0))
{
q = (float)Math.Sqrt(q);
Vector2.Subtract(ref tempParticle.Position, ref particle.Position, out _rij);
Vector2.Divide(ref _rij, q, out _rij);
Vector2.Subtract(ref particle.Velocity, ref tempParticle.Velocity, out _tempVect);
Vector2.Dot(ref _tempVect, ref _rij, out u);
if (u <= 0.0f)
{
continue;
}
q /= InfluenceRadius;
float I = (deltaTime * (1 - q) * (ViscositySigma * u + ViscosityBeta * u * u));
Vector2.Multiply(ref _rij, (I * 0.5f), out _rij);
Vector2.Subtract(ref particle.Velocity, ref _rij, out _tempVect);
particle.Velocity = _tempVect;
_tempVect = tempParticle.Velocity;
_tempVect += _rij;
tempParticle.Velocity = _tempVect;
}
}
}
}
public override bool RayCast(out RayCastOutput output, ref RayCastInput input, ref Transform transform, int childIndex)
{
// Collision Detection in Interactive 3D Environments by Gino van den Bergen
// From Section 3.1.2
// x = s + a * r
// norm(x) = radius
output = new RayCastOutput();
Vector2 position = transform.p + Complex.Multiply(ref _position, ref transform.q);
Vector2 s = input.Point1 - position;
float b = Vector2.Dot(s, s) - _2radius;
// Solve quadratic equation.
Vector2 r = input.Point2 - input.Point1;
float c = Vector2.Dot(s, r);
float rr = Vector2.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 + (float)Math.Sqrt(sigma));
// Is the intersection point on the segment?
if (0.0f <= a && a <= input.MaxFraction * rr)
{
a /= rr;
output.Fraction = a;
//TODO: Check results here
output.Normal = s + a * r;
output.Normal.Normalize();
return(true);
}
return(false);
}
/// <summary>
/// tests if ray intersects AABB
/// </summary>
/// <param name="aabb"></param>
/// <returns></returns>
public static bool RayCastAABB(AABB aabb, Vector2 p1, Vector2 p2)
{
AABB segmentAABB = new AABB();
{
Vector2.Min(ref p1, ref p2, out segmentAABB.LowerBound);
Vector2.Max(ref p1, ref p2, out segmentAABB.UpperBound);
}
if (!AABB.TestOverlap(ref aabb, ref segmentAABB))
{
return(false);
}
Vector2 rayDir = p2 - p1;
Vector2 rayPos = p1;
Vector2 norm = new Vector2(-rayDir.Y, rayDir.X); //normal to ray
if (norm.Length() == 0.0f)
{
return(true); //if ray is just a point, return true (iff point is within aabb, as tested earlier)
}
norm.Normalize();
float dPos = Vector2.Dot(rayPos, norm);
var verts = aabb.Vertices;
float d0 = Vector2.Dot(verts[0], norm) - dPos;
for (int i = 1; i < 4; i++)
{
float d = Vector2.Dot(verts[i], norm) - dPos;
if (Math.Sign(d) != Math.Sign(d0))
{
//return true if the ray splits the vertices (ie: sign of dot products with normal are not all same)
return(true);
}
}
return(false);
}
// Solve a line segment using barycentric coordinates.
//
// p = a1 * w1 + a2 * w2
// a1 + a2 = 1
//
// The vector from the origin to the closest point on the line is
// perpendicular to the line.
// e12 = w2 - w1
// dot(p, e) = 0
// a1 * dot(w1, e) + a2 * dot(w2, e) = 0
//
// 2-by-2 linear system
// [1 1 ][a1] = [1]
// [w1.e12 w2.e12][a2] = [0]
//
// Define
// d12_1 = dot(w2, e12)
// d12_2 = -dot(w1, e12)
// d12 = d12_1 + d12_2
//
// Solution
// a1 = d12_1 / d12
// a2 = d12_2 / d12
internal void Solve2()
{
Vector2 w1 = V[0].W;
Vector2 w2 = V[1].W;
Vector2 e12 = w2 - w1;
// w1 region
float d12_2 = -Vector2.Dot(w1, e12);
if (d12_2 <= 0.0f)
{
// a2 <= 0, so we clamp it to 0
SimplexVertex v0 = V[0];
v0.A = 1.0f;
V[0] = v0;
Count = 1;
return;
}
// w2 region
float d12_1 = Vector2.Dot(w2, e12);
if (d12_1 <= 0.0f)
{
// a1 <= 0, so we clamp it to 0
SimplexVertex v1 = V[1];
v1.A = 1.0f;
V[1] = v1;
Count = 1;
V[0] = V[1];
return;
}
// Must be in e12 region.
float inv_d12 = 1.0f / (d12_1 + d12_2);
SimplexVertex v0_2 = V[0];
SimplexVertex v1_2 = V[1];
v0_2.A = d12_1 * inv_d12;
v1_2.A = d12_2 * inv_d12;
V[0] = v0_2;
V[1] = v1_2;
Count = 2;
}
public void ProjectParentVelocityOnLastMoveCollisionTangent(float minimumVectorLengthSquared)
{
#if FRB_MDX
if (LastMoveCollisionReposition.LengthSq() > minimumVectorLengthSquared &&
#else
if (LastMoveCollisionReposition.LengthSquared() > minimumVectorLengthSquared &&
#endif
Vector2.Dot(
new Vector2(TopParent.Velocity.X, TopParent.Velocity.Y), LastMoveCollisionReposition) < 0)
{
Vector2 collisionAdjustmentNormalized = LastMoveCollisionReposition;
collisionAdjustmentNormalized.Normalize();
float temporaryFloat = collisionAdjustmentNormalized.X;
collisionAdjustmentNormalized.X = -collisionAdjustmentNormalized.Y;
collisionAdjustmentNormalized.Y = temporaryFloat;
float length = Vector2.Dot(
new Vector2(TopParent.Velocity.X, TopParent.Velocity.Y), collisionAdjustmentNormalized);
TopParent.Velocity.X = collisionAdjustmentNormalized.X * length;
TopParent.Velocity.Y = collisionAdjustmentNormalized.Y * length;
}
}
internal override void SolveVelocityConstraints(ref SolverData data)
{
Vector2 vA = data.velocities[_indexA].v;
float wA = data.velocities[_indexA].w;
Vector2 vB = data.velocities[_indexB].v;
float wB = data.velocities[_indexB].w;
// Cdot = dot(u, v + cross(w, r))
Vector2 vpA = vA + MathUtils.Cross(wA, ref _rA);
Vector2 vpB = vB + MathUtils.Cross(wB, ref _rB);
float C = _length - MaxLength;
float Cdot = Vector2.Dot(_u, vpB - vpA);
// Predictive constraint.
if (C < 0.0f)
{
Cdot += data.step.inv_dt * C;
}
float impulse = -_mass * Cdot;
float oldImpulse = _impulse;
_impulse = Math.Min(0.0f, _impulse + impulse);
impulse = _impulse - oldImpulse;
Vector2 P = impulse * _u;
vA -= _invMassA * P;
wA -= _invIA * MathUtils.Cross(ref _rA, ref P);
vB += _invMassB * P;
wB += _invIB * MathUtils.Cross(ref _rB, ref P);
data.velocities[_indexA].v = vA;
data.velocities[_indexA].w = wA;
data.velocities[_indexB].v = vB;
data.velocities[_indexB].w = wB;
}
internal override void SolveVelocityConstraints(ref SolverData data)
{
Vector2 vA = data.velocities[_indexA].v;
float wA = data.velocities[_indexA].w;
Vector2 vB = data.velocities[_indexB].v;
float wB = data.velocities[_indexB].w;
Vector2 vC = data.velocities[_indexC].v;
float wC = data.velocities[_indexC].w;
Vector2 vD = data.velocities[_indexD].v;
float wD = data.velocities[_indexD].w;
float Cdot = Vector2.Dot(_JvAC, vA - vC) + Vector2.Dot(_JvBD, vB - vD);
Cdot += (_JwA * wA - _JwC * wC) + (_JwB * wB - _JwD * wD);
float impulse = -_mass * Cdot;
_impulse += impulse;
vA += (_mA * impulse) * _JvAC;
wA += _iA * impulse * _JwA;
vB += (_mB * impulse) * _JvBD;
wB += _iB * impulse * _JwB;
vC -= (_mC * impulse) * _JvAC;
wC -= _iC * impulse * _JwC;
vD -= (_mD * impulse) * _JvBD;
wD -= _iD * impulse * _JwD;
data.velocities[_indexA].v = vA;
data.velocities[_indexA].w = wA;
data.velocities[_indexB].v = vB;
data.velocities[_indexB].w = wB;
data.velocities[_indexC].v = vC;
data.velocities[_indexC].w = wC;
data.velocities[_indexD].v = vD;
data.velocities[_indexD].w = wD;
}
internal void Solve(ref TimeStep step, ref Vector2 gravity)
{
float h = step.dt;
// Integrate velocities and apply damping. Initialize the body state.
for (int i = 0; i < BodyCount; ++i)
{
Body b = Bodies[i];
Vector2 c = b._sweep.C;
float a = b._sweep.A;
Vector2 v = b._linearVelocity;
float w = b._angularVelocity;
// Store positions for continuous collision.
b._sweep.C0 = b._sweep.C;
b._sweep.A0 = b._sweep.A;
if (b.BodyType == BodyType.Dynamic)
{
// Integrate velocities.
// FPE: Only apply gravity if the body wants it.
if (b.IgnoreGravity)
{
v += h * (b._invMass * b._force);
}
else
{
v += h * (gravity + b._invMass * b._force);
}
w += h * b._invI * b._torque;
// Apply damping.
// ODE: dv/dt + c * v = 0
// Solution: v(t) = v0 * exp(-c * t)
// Time step: v(t + dt) = v0 * exp(-c * (t + dt)) = v0 * exp(-c * t) * exp(-c * dt) = v * exp(-c * dt)
// v2 = exp(-c * dt) * v1
// Taylor expansion:
// v2 = (1.0f - c * dt) * v1
v *= MathUtils.Clamp(1.0f - h * b.LinearDamping, 0.0f, 1.0f);
w *= MathUtils.Clamp(1.0f - h * b.AngularDamping, 0.0f, 1.0f);
}
_positions[i].c = c;
_positions[i].a = a;
_velocities[i].v = v;
_velocities[i].w = w;
}
// Solver data
SolverData solverData = new SolverData();
solverData.step = step;
solverData.positions = _positions;
solverData.velocities = _velocities;
solverData.locks = _locks;
_contactSolver.Reset(ref step, ContactCount, _contacts, _positions, _velocities,
_locks, _contactManager.VelocityConstraintsMultithreadThreshold, _contactManager.PositionConstraintsMultithreadThreshold);
_contactSolver.InitializeVelocityConstraints();
if (step.warmStarting)
{
_contactSolver.WarmStart();
}
if (Settings.EnableDiagnostics)
{
_watch.Start();
}
for (int i = 0; i < JointCount; ++i)
{
if (_joints[i].Enabled)
{
_joints[i].InitVelocityConstraints(ref solverData);
}
}
if (Settings.EnableDiagnostics)
{
_watch.Stop();
}
// Solve velocity constraints.
for (int i = 0; i < step.velocityIterations; ++i)
{
for (int j = 0; j < JointCount; ++j)
{
Joint joint = _joints[j];
if (!joint.Enabled)
{
continue;
}
if (Settings.EnableDiagnostics)
{
_watch.Start();
}
joint.SolveVelocityConstraints(ref solverData);
joint.Validate(step.inv_dt);
if (Settings.EnableDiagnostics)
{
_watch.Stop();
}
}
_contactSolver.SolveVelocityConstraints();
}
// Store impulses for warm starting.
_contactSolver.StoreImpulses();
// Integrate positions
for (int i = 0; i < BodyCount; ++i)
{
Vector2 c = _positions[i].c;
float a = _positions[i].a;
Vector2 v = _velocities[i].v;
float w = _velocities[i].w;
// Check for large velocities
Vector2 translation = h * v;
if (Vector2.Dot(translation, translation) > Settings.MaxTranslationSquared)
{
float ratio = Settings.MaxTranslation / translation.Length();
v *= ratio;
}
float rotation = h * w;
if (rotation * rotation > Settings.MaxRotationSquared)
{
float ratio = Settings.MaxRotation / Math.Abs(rotation);
w *= ratio;
}
// Integrate
c += h * v;
a += h * w;
_positions[i].c = c;
_positions[i].a = a;
_velocities[i].v = v;
_velocities[i].w = w;
}
// Solve position constraints
bool positionSolved = false;
for (int i = 0; i < step.positionIterations; ++i)
{
bool contactsOkay = _contactSolver.SolvePositionConstraints();
bool jointsOkay = true;
for (int j = 0; j < JointCount; ++j)
{
Joint joint = _joints[j];
if (!joint.Enabled)
{
continue;
}
if (Settings.EnableDiagnostics)
{
_watch.Start();
}
bool jointOkay = joint.SolvePositionConstraints(ref solverData);
if (Settings.EnableDiagnostics)
{
_watch.Stop();
}
jointsOkay = jointsOkay && jointOkay;
}
if (contactsOkay && jointsOkay)
{
// Exit early if the position errors are small.
positionSolved = true;
break;
}
}
if (Settings.EnableDiagnostics)
{
JointUpdateTime = TimeSpan.FromTicks(_watch.ElapsedTicks);
_watch.Reset();
}
// Copy state buffers back to the bodies
for (int i = 0; i < BodyCount; ++i)
{
Body body = Bodies[i];
body._sweep.C = _positions[i].c;
body._sweep.A = _positions[i].a;
body._linearVelocity = _velocities[i].v;
body._angularVelocity = _velocities[i].w;
body.SynchronizeTransform();
}
Report(_contactSolver._velocityConstraints);
if (Settings.AllowSleep)
{
float minSleepTime = Settings.MaxFloat;
for (int i = 0; i < BodyCount; ++i)
{
Body b = Bodies[i];
if (b.BodyType == BodyType.Static)
{
continue;
}
if (!b.SleepingAllowed || b._angularVelocity * b._angularVelocity > AngTolSqr || Vector2.Dot(b._linearVelocity, b._linearVelocity) > LinTolSqr)
{
b._sleepTime = 0.0f;
minSleepTime = 0.0f;
}
else
{
b._sleepTime += h;
minSleepTime = Math.Min(minSleepTime, b._sleepTime);
}
}
if (minSleepTime >= Settings.TimeToSleep && positionSolved)
{
for (int i = 0; i < BodyCount; ++i)
{
Body b = Bodies[i];
b.Awake = false;
}
}
}
}
/// <summary>
/// This resets the mass properties to the sum of the mass properties of the fixtures.
/// This normally does not need to be called unless you called SetMassData to override
/// the mass and you later want to reset the mass.
/// </summary>
public void ResetMassData()
{
// Compute mass data from shapes. Each shape has its own density.
_mass = 0.0f;
_invMass = 0.0f;
_inertia = 0.0f;
_invI = 0.0f;
_sweep.LocalCenter = Vector2.Zero;
// Kinematic bodies have zero mass.
if (BodyType == BodyType.Kinematic)
{
_sweep.C0 = _xf.p;
_sweep.C = _xf.p;
_sweep.A0 = _sweep.A;
return;
}
Debug.Assert(BodyType == BodyType.Dynamic || BodyType == BodyType.Static);
// Accumulate mass over all fixtures.
Vector2 localCenter = Vector2.Zero;
foreach (Fixture f in FixtureList)
{
if (f.Shape._density == 0)
{
continue;
}
MassData massData = f.Shape.MassData;
_mass += massData.Mass;
localCenter += massData.Mass * massData.Centroid;
_inertia += massData.Inertia;
}
//FPE: Static bodies only have mass, they don't have other properties. A little hacky tho...
if (BodyType == BodyType.Static)
{
_sweep.C0 = _sweep.C = _xf.p;
return;
}
// Compute center of mass.
if (_mass > 0.0f)
{
_invMass = 1.0f / _mass;
localCenter *= _invMass;
}
else
{
// Force all dynamic bodies to have a positive mass.
_mass = 1.0f;
_invMass = 1.0f;
}
if (_inertia > 0.0f && !_fixedRotation)
{
// Center the inertia about the center of mass.
_inertia -= _mass * Vector2.Dot(localCenter, localCenter);
Debug.Assert(_inertia > 0.0f);
_invI = 1.0f / _inertia;
}
else
{
_inertia = 0.0f;
_invI = 0.0f;
}
// Move center of mass.
Vector2 oldCenter = _sweep.C;
_sweep.LocalCenter = localCenter;
_sweep.C0 = _sweep.C = Transform.Multiply(ref _sweep.LocalCenter, ref _xf);
// Update center of mass velocity.
Vector2 a = _sweep.C - oldCenter;
_linearVelocity += new Vector2(-_angularVelocity * a.Y, _angularVelocity * a.X);
}
internal override bool SolvePositionConstraints(ref SolverData data)
{
Vector2 cA = data.positions[_indexA].c;
float aA = data.positions[_indexA].a;
Vector2 cB = data.positions[_indexB].c;
float aB = data.positions[_indexB].a;
Complex qA = Complex.FromAngle(aA);
Complex qB = Complex.FromAngle(aB);
float mA = _invMassA, mB = _invMassB;
float iA = _invIA, iB = _invIB;
// Compute fresh Jacobians
Vector2 rA = Complex.Multiply(LocalAnchorA - _localCenterA, ref qA);
Vector2 rB = Complex.Multiply(LocalAnchorB - _localCenterB, ref qB);
Vector2 d = cB + rB - cA - rA;
Vector2 axis = Complex.Multiply(ref _localXAxis, ref qA);
float a1 = MathUtils.Cross(d + rA, axis);
float a2 = MathUtils.Cross(ref rB, ref axis);
Vector2 perp = Complex.Multiply(ref _localYAxisA, ref qA);
float s1 = MathUtils.Cross(d + rA, perp);
float s2 = MathUtils.Cross(ref rB, ref perp);
Vector3 impulse;
Vector2 C1 = new Vector2();
C1.X = Vector2.Dot(perp, d);
C1.Y = aB - aA - ReferenceAngle;
float linearError = Math.Abs(C1.X);
float angularError = Math.Abs(C1.Y);
bool active = false;
float C2 = 0.0f;
if (_enableLimit)
{
float translation = Vector2.Dot(axis, d);
if (Math.Abs(_upperTranslation - _lowerTranslation) < 2.0f * Settings.LinearSlop)
{
// Prevent large angular corrections
C2 = MathUtils.Clamp(translation, -Settings.MaxLinearCorrection, Settings.MaxLinearCorrection);
linearError = Math.Max(linearError, Math.Abs(translation));
active = true;
}
else if (translation <= _lowerTranslation)
{
// Prevent large linear corrections and allow some slop.
C2 = MathUtils.Clamp(translation - _lowerTranslation + Settings.LinearSlop, -Settings.MaxLinearCorrection, 0.0f);
linearError = Math.Max(linearError, _lowerTranslation - translation);
active = true;
}
else if (translation >= _upperTranslation)
{
// Prevent large linear corrections and allow some slop.
C2 = MathUtils.Clamp(translation - _upperTranslation - Settings.LinearSlop, 0.0f, Settings.MaxLinearCorrection);
linearError = Math.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 = new Mat33();
K.ex = new Vector3(k11, k12, k13);
K.ey = new Vector3(k12, k22, k23);
K.ez = new Vector3(k13, k23, k33);
Vector3 C = new Vector3();
C.X = C1.X;
C.Y = C1.Y;
C.Z = C2;
impulse = K.Solve33(-C);
}
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 = new Mat22();
K.ex = new Vector2(k11, k12);
K.ey = new Vector2(k12, k22);
Vector2 impulse1 = K.Solve(-C1);
impulse = new Vector3();
impulse.X = impulse1.X;
impulse.Y = impulse1.Y;
impulse.Z = 0.0f;
}
Vector2 P = impulse.X * perp + impulse.Z * axis;
float LA = impulse.X * s1 + impulse.Y + impulse.Z * a1;
float LB = impulse.X * s2 + impulse.Y + impulse.Z * a2;
cA -= mA * P;
aA -= iA * LA;
cB += mB * P;
aB += iB * LB;
data.positions[_indexA].c = cA;
data.positions[_indexA].a = aA;
data.positions[_indexB].c = cB;
data.positions[_indexB].a = aB;
return(linearError <= Settings.LinearSlop && angularError <= Settings.AngularSlop);
}
internal override void SolveVelocityConstraints(ref SolverData data)
{
Vector2 vA = data.velocities[_indexA].v;
float wA = data.velocities[_indexA].w;
Vector2 vB = data.velocities[_indexB].v;
float wB = data.velocities[_indexB].w;
float mA = _invMassA, mB = _invMassB;
float iA = _invIA, iB = _invIB;
// Solve linear motor constraint.
if (_enableMotor && _limitState != LimitState.Equal)
{
float Cdot = Vector2.Dot(_axis, vB - vA) + _a2 * wB - _a1 * wA;
float impulse = _motorMass * (_motorSpeed - Cdot);
float oldImpulse = MotorImpulse;
float maxImpulse = data.step.dt * _maxMotorForce;
MotorImpulse = MathUtils.Clamp(MotorImpulse + impulse, -maxImpulse, maxImpulse);
impulse = MotorImpulse - oldImpulse;
Vector2 P = impulse * _axis;
float LA = impulse * _a1;
float LB = impulse * _a2;
vA -= mA * P;
wA -= iA * LA;
vB += mB * P;
wB += iB * LB;
}
Vector2 Cdot1 = new Vector2();
Cdot1.X = Vector2.Dot(_perp, vB - vA) + _s2 * wB - _s1 * wA;
Cdot1.Y = wB - wA;
if (_enableLimit && _limitState != LimitState.Inactive)
{
// Solve prismatic and limit constraint in block form.
float Cdot2;
Cdot2 = Vector2.Dot(_axis, vB - vA) + _a2 * wB - _a1 * wA;
Vector3 Cdot = new Vector3(Cdot1.X, Cdot1.Y, Cdot2);
Vector3 f1 = _impulse;
Vector3 df = _K.Solve33(-Cdot);
_impulse += df;
if (_limitState == LimitState.AtLower)
{
_impulse.Z = Math.Max(_impulse.Z, 0.0f);
}
else if (_limitState == LimitState.AtUpper)
{
_impulse.Z = Math.Min(_impulse.Z, 0.0f);
}
// f2(1:2) = invK(1:2,1:2) * (-Cdot(1:2) - K(1:2,3) * (f2(3) - f1(3))) + f1(1:2)
Vector2 b = -Cdot1 - (_impulse.Z - f1.Z) * new Vector2(_K.ez.X, _K.ez.Y);
Vector2 f2r = _K.Solve22(b) + new Vector2(f1.X, f1.Y);
_impulse.X = f2r.X;
_impulse.Y = f2r.Y;
df = _impulse - f1;
Vector2 P = df.X * _perp + df.Z * _axis;
float LA = df.X * _s1 + df.Y + df.Z * _a1;
float LB = df.X * _s2 + df.Y + df.Z * _a2;
vA -= mA * P;
wA -= iA * LA;
vB += mB * P;
wB += iB * LB;
}
else
{
// Limit is inactive, just solve the prismatic constraint in block form.
Vector2 df = _K.Solve22(-Cdot1);
_impulse.X += df.X;
_impulse.Y += df.Y;
Vector2 P = df.X * _perp;
float LA = df.X * _s1 + df.Y;
float LB = df.X * _s2 + df.Y;
vA -= mA * P;
wA -= iA * LA;
vB += mB * P;
wB += iB * LB;
}
data.velocities[_indexA].v = vA;
data.velocities[_indexA].w = wA;
data.velocities[_indexB].v = vB;
data.velocities[_indexB].w = wB;
}
private void SolveVelocityConstraints(int start, int end)
{
for (int i = start; i < end; ++i)
{
ContactVelocityConstraint vc = _velocityConstraints[i];
#if NET40 || NET45 || NETSTANDARD2_0 || PORTABLE40 || PORTABLE45 || W10 || W8_1 || WP8_1
// find lower order item
int orderedIndexA = vc.indexA;
int orderedIndexB = vc.indexB;
if (orderedIndexB < orderedIndexA)
{
orderedIndexA = vc.indexB;
orderedIndexB = vc.indexA;
}
for (; ;)
{
if (Interlocked.CompareExchange(ref _locks[orderedIndexA], 1, 0) == 0)
{
if (Interlocked.CompareExchange(ref _locks[orderedIndexB], 1, 0) == 0)
{
break;
}
System.Threading.Interlocked.Exchange(ref _locks[orderedIndexA], 0);
}
#if NET40 || NET45 || NETSTANDARD2_0
Thread.Sleep(0);
#endif
}
#endif
int indexA = vc.indexA;
int indexB = vc.indexB;
float mA = vc.invMassA;
float iA = vc.invIA;
float mB = vc.invMassB;
float iB = vc.invIB;
int pointCount = vc.pointCount;
Vector2 vA = _velocities[indexA].v;
float wA = _velocities[indexA].w;
Vector2 vB = _velocities[indexB].v;
float wB = _velocities[indexB].w;
Vector2 normal = vc.normal;
Vector2 tangent = MathUtils.Rot270(ref normal);
float friction = vc.friction;
Debug.Assert(pointCount == 1 || pointCount == 2);
// Solve tangent constraints first because non-penetration is more important
// than friction.
for (int j = 0; j < pointCount; ++j)
{
VelocityConstraintPoint vcp = vc.points[j];
// Relative velocity at contact
Vector2 dv = vB + MathUtils.Cross(wB, ref vcp.rB) - vA - MathUtils.Cross(wA, ref vcp.rA);
// Compute tangent force
float vt = Vector2.Dot(dv, tangent) - vc.tangentSpeed;
float lambda = vcp.tangentMass * (-vt);
// b2Clamp the accumulated force
float maxFriction = friction * vcp.normalImpulse;
float newImpulse = MathUtils.Clamp(vcp.tangentImpulse + lambda, -maxFriction, maxFriction);
lambda = newImpulse - vcp.tangentImpulse;
vcp.tangentImpulse = newImpulse;
// Apply contact impulse
Vector2 P = lambda * tangent;
vA -= mA * P;
wA -= iA * MathUtils.Cross(ref vcp.rA, ref P);
vB += mB * P;
wB += iB * MathUtils.Cross(ref vcp.rB, ref P);
}
// Solve normal constraints
if (vc.pointCount == 1)
{
VelocityConstraintPoint vcp = vc.points[0];
// Relative velocity at contact
Vector2 dv = vB + MathUtils.Cross(wB, ref vcp.rB) - vA - MathUtils.Cross(wA, ref vcp.rA);
// Compute normal impulse
float vn = Vector2.Dot(dv, normal);
float lambda = -vcp.normalMass * (vn - vcp.velocityBias);
// b2Clamp the accumulated impulse
float newImpulse = Math.Max(vcp.normalImpulse + lambda, 0.0f);
lambda = newImpulse - vcp.normalImpulse;
vcp.normalImpulse = newImpulse;
// Apply contact impulse
Vector2 P = lambda * normal;
vA -= mA * P;
wA -= iA * MathUtils.Cross(ref vcp.rA, ref P);
vB += mB * P;
wB += iB * MathUtils.Cross(ref vcp.rB, ref P);
}
else
{
// Block solver developed in collaboration with Dirk Gregorius (back in 01/07 on Box2D_Lite).
// Build the mini LCP for this contact patch
//
// vn = A * x + b, vn >= 0, , vn >= 0, x >= 0 and vn_i * x_i = 0 with i = 1..2
//
// A = J * W * JT and J = ( -n, -r1 x n, n, r2 x n )
// b = vn0 - velocityBias
//
// The system is solved using the "Total enumeration method" (s. Murty). The complementary constraint vn_i * x_i
// implies that we must have in any solution either vn_i = 0 or x_i = 0. So for the 2D contact problem the cases
// vn1 = 0 and vn2 = 0, x1 = 0 and x2 = 0, x1 = 0 and vn2 = 0, x2 = 0 and vn1 = 0 need to be tested. The first valid
// solution that satisfies the problem is chosen.
//
// In order to account of the accumulated impulse 'a' (because of the iterative nature of the solver which only requires
// that the accumulated impulse is clamped and not the incremental impulse) we change the impulse variable (x_i).
//
// Substitute:
//
// x = a + d
//
// a := old total impulse
// x := new total impulse
// d := incremental impulse
//
// For the current iteration we extend the formula for the incremental impulse
// to compute the new total impulse:
//
// vn = A * d + b
// = A * (x - a) + b
// = A * x + b - A * a
// = A * x + b'
// b' = b - A * a;
VelocityConstraintPoint cp1 = vc.points[0];
VelocityConstraintPoint cp2 = vc.points[1];
Vector2 a = new Vector2(cp1.normalImpulse, cp2.normalImpulse);
Debug.Assert(a.X >= 0.0f && a.Y >= 0.0f);
// Relative velocity at contact
Vector2 dv1 = vB + MathUtils.Cross(wB, ref cp1.rB) - vA - MathUtils.Cross(wA, ref cp1.rA);
Vector2 dv2 = vB + MathUtils.Cross(wB, ref cp2.rB) - vA - MathUtils.Cross(wA, ref cp2.rA);
// Compute normal velocity
float vn1 = Vector2.Dot(dv1, normal);
float vn2 = Vector2.Dot(dv2, normal);
Vector2 b = new Vector2();
b.X = vn1 - cp1.velocityBias;
b.Y = vn2 - cp2.velocityBias;
// Compute b'
b -= MathUtils.Mul(ref vc.K, ref a);
const float k_errorTol = 1e-3f;
//B2_NOT_USED(k_errorTol);
for (; ;)
{
//
// Case 1: vn = 0
//
// 0 = A * x + b'
//
// Solve for x:
//
// x = - inv(A) * b'
//
Vector2 x = -MathUtils.Mul(ref vc.normalMass, ref b);
if (x.X >= 0.0f && x.Y >= 0.0f)
{
// Get the incremental impulse
Vector2 d = x - a;
// Apply incremental impulse
Vector2 P1 = d.X * normal;
Vector2 P2 = d.Y * normal;
vA -= mA * (P1 + P2);
wA -= iA * (MathUtils.Cross(ref cp1.rA, ref P1) + MathUtils.Cross(ref cp2.rA, ref P2));
vB += mB * (P1 + P2);
wB += iB * (MathUtils.Cross(ref cp1.rB, ref P1) + MathUtils.Cross(ref cp2.rB, ref P2));
// Accumulate
cp1.normalImpulse = x.X;
cp2.normalImpulse = x.Y;
#if B2_DEBUG_SOLVER
// Postconditions
dv1 = vB + MathUtils.Cross(wB, cp1.rB) - vA - MathUtils.Cross(wA, cp1.rA);
dv2 = vB + MathUtils.Cross(wB, cp2.rB) - vA - MathUtils.Cross(wA, cp2.rA);
// Compute normal velocity
vn1 = Vector2.Dot(dv1, normal);
vn2 = Vector2.Dot(dv2, normal);
b2Assert(b2Abs(vn1 - cp1.velocityBias) < k_errorTol);
b2Assert(b2Abs(vn2 - cp2.velocityBias) < k_errorTol);
#endif
break;
}
//
// Case 2: vn1 = 0 and x2 = 0
//
// 0 = a11 * x1 + a12 * 0 + b1'
// vn2 = a21 * x1 + a22 * 0 + b2'
//
x.X = -cp1.normalMass * b.X;
x.Y = 0.0f;
vn1 = 0.0f;
vn2 = vc.K.ex.Y * x.X + b.Y;
if (x.X >= 0.0f && vn2 >= 0.0f)
{
// Get the incremental impulse
Vector2 d = x - a;
// Apply incremental impulse
Vector2 P1 = d.X * normal;
Vector2 P2 = d.Y * normal;
vA -= mA * (P1 + P2);
wA -= iA * (MathUtils.Cross(ref cp1.rA, ref P1) + MathUtils.Cross(ref cp2.rA, ref P2));
vB += mB * (P1 + P2);
wB += iB * (MathUtils.Cross(ref cp1.rB, ref P1) + MathUtils.Cross(ref cp2.rB, ref P2));
// Accumulate
cp1.normalImpulse = x.X;
cp2.normalImpulse = x.Y;
#if B2_DEBUG_SOLVER
// Postconditions
dv1 = vB + MathUtils.Cross(wB, cp1.rB) - vA - MathUtils.Cross(wA, cp1.rA);
// Compute normal velocity
vn1 = Vector2.Dot(dv1, normal);
b2Assert(b2Abs(vn1 - cp1.velocityBias) < k_errorTol);
#endif
break;
}
//
// Case 3: vn2 = 0 and x1 = 0
//
// vn1 = a11 * 0 + a12 * x2 + b1'
// 0 = a21 * 0 + a22 * x2 + b2'
//
x.X = 0.0f;
x.Y = -cp2.normalMass * b.Y;
vn1 = vc.K.ey.X * x.Y + b.X;
vn2 = 0.0f;
if (x.Y >= 0.0f && vn1 >= 0.0f)
{
// Resubstitute for the incremental impulse
Vector2 d = x - a;
// Apply incremental impulse
Vector2 P1 = d.X * normal;
Vector2 P2 = d.Y * normal;
vA -= mA * (P1 + P2);
wA -= iA * (MathUtils.Cross(ref cp1.rA, ref P1) + MathUtils.Cross(ref cp2.rA, ref P2));
vB += mB * (P1 + P2);
wB += iB * (MathUtils.Cross(ref cp1.rB, ref P1) + MathUtils.Cross(ref cp2.rB, ref P2));
// Accumulate
cp1.normalImpulse = x.X;
cp2.normalImpulse = x.Y;
#if B2_DEBUG_SOLVER
// Postconditions
dv2 = vB + MathUtils.Cross(wB, cp2.rB) - vA - MathUtils.Cross(wA, cp2.rA);
// Compute normal velocity
vn2 = Vector2.Dot(dv2, normal);
b2Assert(b2Abs(vn2 - cp2.velocityBias) < k_errorTol);
#endif
break;
}
//
// Case 4: x1 = 0 and x2 = 0
//
// vn1 = b1
// vn2 = b2;
x.X = 0.0f;
x.Y = 0.0f;
vn1 = b.X;
vn2 = b.Y;
if (vn1 >= 0.0f && vn2 >= 0.0f)
{
// Resubstitute for the incremental impulse
Vector2 d = x - a;
// Apply incremental impulse
Vector2 P1 = d.X * normal;
Vector2 P2 = d.Y * normal;
vA -= mA * (P1 + P2);
wA -= iA * (MathUtils.Cross(ref cp1.rA, ref P1) + MathUtils.Cross(ref cp2.rA, ref P2));
vB += mB * (P1 + P2);
wB += iB * (MathUtils.Cross(ref cp1.rB, ref P1) + MathUtils.Cross(ref cp2.rB, ref P2));
// Accumulate
cp1.normalImpulse = x.X;
cp2.normalImpulse = x.Y;
break;
}
// No solution, give up. This is hit sometimes, but it doesn't seem to matter.
break;
}
}
_velocities[indexA].v = vA;
_velocities[indexA].w = wA;
_velocities[indexB].v = vB;
_velocities[indexB].w = wB;
#if NET40 || NET45 || NETSTANDARD2_0 || PORTABLE40 || PORTABLE45 || W10 || W8_1 || WP8_1
System.Threading.Interlocked.Exchange(ref _locks[orderedIndexB], 0);
System.Threading.Interlocked.Exchange(ref _locks[orderedIndexA], 0);
#endif
}
}
public static float Dot(Vector2 a, Vector2 b)
{
return(MonoGameVector2.Dot(a.MonoGameVector, b.MonoGameVector));
}
public static float Dot(Vector2 v1, Vector2 v2)
{
return(Vector.Dot(v1, v2));
}
internal void SolveTOI(ref TimeStep subStep, int toiIndexA, int toiIndexB)
{
Debug.Assert(toiIndexA < BodyCount);
Debug.Assert(toiIndexB < BodyCount);
// Initialize the body state.
for (int i = 0; i < BodyCount; ++i)
{
Body b = Bodies[i];
_positions[i].c = b._sweep.C;
_positions[i].a = b._sweep.A;
_velocities[i].v = b._linearVelocity;
_velocities[i].w = b._angularVelocity;
}
_contactSolver.Reset(ref subStep, ContactCount, _contacts, _positions, _velocities,
_locks, _contactManager.VelocityConstraintsMultithreadThreshold, _contactManager.PositionConstraintsMultithreadThreshold);
// Solve position constraints.
for (int i = 0; i < subStep.positionIterations; ++i)
{
bool contactsOkay = _contactSolver.SolveTOIPositionConstraints(toiIndexA, toiIndexB);
if (contactsOkay)
{
break;
}
}
// Leap of faith to new safe state.
Bodies[toiIndexA]._sweep.C0 = _positions[toiIndexA].c;
Bodies[toiIndexA]._sweep.A0 = _positions[toiIndexA].a;
Bodies[toiIndexB]._sweep.C0 = _positions[toiIndexB].c;
Bodies[toiIndexB]._sweep.A0 = _positions[toiIndexB].a;
// No warm starting is needed for TOI events because warm
// starting impulses were applied in the discrete solver.
_contactSolver.InitializeVelocityConstraints();
// Solve velocity constraints.
for (int i = 0; i < subStep.velocityIterations; ++i)
{
_contactSolver.SolveVelocityConstraints();
}
// Don't store the TOI contact forces for warm starting
// because they can be quite large.
float h = subStep.dt;
// Integrate positions.
for (int i = 0; i < BodyCount; ++i)
{
Vector2 c = _positions[i].c;
float a = _positions[i].a;
Vector2 v = _velocities[i].v;
float w = _velocities[i].w;
// Check for large velocities
Vector2 translation = h * v;
if (Vector2.Dot(translation, translation) > Settings.MaxTranslationSquared)
{
float ratio = Settings.MaxTranslation / translation.Length();
v *= ratio;
}
float rotation = h * w;
if (rotation * rotation > Settings.MaxRotationSquared)
{
float ratio = Settings.MaxRotation / Math.Abs(rotation);
w *= ratio;
}
// Integrate
c += h * v;
a += h * w;
_positions[i].c = c;
_positions[i].a = a;
_velocities[i].v = v;
_velocities[i].w = w;
// Sync bodies
Body body = Bodies[i];
body._sweep.C = c;
body._sweep.A = a;
body._linearVelocity = v;
body._angularVelocity = w;
body.SynchronizeTransform();
}
Report(_contactSolver._velocityConstraints);
}
public override bool RayCast(out RayCastOutput output, ref RayCastInput input, ref Transform transform, int childIndex)
{
// p = p1 + t * d
// v = v1 + s * e
// p1 + t * d = v1 + s * e
// s * e - t * d = p1 - v1
output = new RayCastOutput();
// Put the ray into the edge's frame of reference.
Vector2 p1 = Complex.Divide(input.Point1 - transform.p, ref transform.q);
Vector2 p2 = Complex.Divide(input.Point2 - transform.p, ref transform.q);
Vector2 d = p2 - p1;
Vector2 v1 = _vertex1;
Vector2 v2 = _vertex2;
Vector2 e = v2 - v1;
Vector2 normal = new Vector2(e.Y, -e.X); //TODO: Could possibly cache the normal.
normal.Normalize();
// q = p1 + t * d
// dot(normal, q - v1) = 0
// dot(normal, p1 - v1) + t * dot(normal, d) = 0
float numerator = Vector2.Dot(normal, v1 - p1);
float denominator = Vector2.Dot(normal, d);
if (denominator == 0.0f)
{
return(false);
}
float t = numerator / denominator;
if (t < 0.0f || input.MaxFraction < t)
{
return(false);
}
Vector2 q = p1 + t * d;
// q = v1 + s * r
// s = dot(q - v1, r) / dot(r, r)
Vector2 r = v2 - v1;
float rr = Vector2.Dot(r, r);
if (rr == 0.0f)
{
return(false);
}
float s = Vector2.Dot(q - v1, r) / rr;
if (s < 0.0f || 1.0f < s)
{
return(false);
}
output.Fraction = t;
if (numerator > 0.0f)
{
output.Normal = -normal;
}
else
{
output.Normal = normal;
}
return(true);
}
internal override void InitVelocityConstraints(ref SolverData data)
{
_indexA = BodyA.IslandIndex;
_indexB = BodyB.IslandIndex;
_localCenterA = BodyA._sweep.LocalCenter;
_localCenterB = BodyB._sweep.LocalCenter;
_invMassA = BodyA._invMass;
_invMassB = BodyB._invMass;
_invIA = BodyA._invI;
_invIB = BodyB._invI;
Vector2 cA = data.positions[_indexA].c;
float aA = data.positions[_indexA].a;
Vector2 vA = data.velocities[_indexA].v;
float wA = data.velocities[_indexA].w;
Vector2 cB = data.positions[_indexB].c;
float aB = data.positions[_indexB].a;
Vector2 vB = data.velocities[_indexB].v;
float wB = data.velocities[_indexB].w;
Complex qA = Complex.FromAngle(aA);
Complex qB = Complex.FromAngle(aB);
// Compute the effective masses.
Vector2 rA = Complex.Multiply(LocalAnchorA - _localCenterA, ref qA);
Vector2 rB = Complex.Multiply(LocalAnchorB - _localCenterB, ref qB);
Vector2 d = (cB - cA) + rB - rA;
float mA = _invMassA, mB = _invMassB;
float iA = _invIA, iB = _invIB;
// Compute motor Jacobian and effective mass.
{
_axis = Complex.Multiply(ref _localXAxis, ref qA);
_a1 = MathUtils.Cross(d + rA, _axis);
_a2 = MathUtils.Cross(ref rB, ref _axis);
_motorMass = mA + mB + iA * _a1 * _a1 + iB * _a2 * _a2;
if (_motorMass > 0.0f)
{
_motorMass = 1.0f / _motorMass;
}
}
// Prismatic constraint.
{
_perp = Complex.Multiply(ref _localYAxisA, ref qA);
_s1 = MathUtils.Cross(d + rA, _perp);
_s2 = MathUtils.Cross(ref rB, ref _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 = new Vector3(k11, k12, k13);
_K.ey = new Vector3(k12, k22, k23);
_K.ez = new Vector3(k13, k23, k33);
}
// Compute motor and limit terms.
if (_enableLimit)
{
float jointTranslation = Vector2.Dot(_axis, d);
if (Math.Abs(_upperTranslation - _lowerTranslation) < 2.0f * Settings.LinearSlop)
{
_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 (_enableMotor == false)
{
MotorImpulse = 0.0f;
}
if (data.step.warmStarting)
{
// Account for variable time step.
_impulse *= data.step.dtRatio;
MotorImpulse *= data.step.dtRatio;
Vector2 P = _impulse.X * _perp + (MotorImpulse + _impulse.Z) * _axis;
float LA = _impulse.X * _s1 + _impulse.Y + (MotorImpulse + _impulse.Z) * _a1;
float LB = _impulse.X * _s2 + _impulse.Y + (MotorImpulse + _impulse.Z) * _a2;
vA -= mA * P;
wA -= iA * LA;
vB += mB * P;
wB += iB * LB;
}
else
{
_impulse = Vector3.Zero;
MotorImpulse = 0.0f;
}
data.velocities[_indexA].v = vA;
data.velocities[_indexA].w = wA;
data.velocities[_indexB].v = vB;
data.velocities[_indexB].w = wB;
}