internal override void SolveVelocityConstraints(ref SolverData data)
{
FPVector2 vA = data.velocities[_indexA].v;
FP wA = data.velocities[_indexA].w;
// Cdot = v + cross(w, r)
FPVector2 Cdot = vA + MathUtils.Cross(wA, _rA);
FPVector2 impulse = MathUtils.Mul(ref _mass, -(Cdot + _C + _gamma * _impulse));
FPVector2 oldImpulse = _impulse;
_impulse += impulse;
FP maxImpulse = data.step.dt * MaxForce;
if (_impulse.LengthSquared() > maxImpulse * maxImpulse)
{
_impulse *= maxImpulse / _impulse.magnitude;
}
impulse = _impulse - oldImpulse;
vA += _invMassA * impulse;
wA += _invIA * MathUtils.Cross(_rA, impulse);
data.velocities[_indexA].v = vA;
data.velocities[_indexA].w = wA;
}
internal override void SolveVelocityConstraints(ref SolverData data)
{
FPVector2 vA = data.velocities[_indexA].v;
FP wA = data.velocities[_indexA].w;
FPVector2 vB = data.velocities[_indexB].v;
FP wB = data.velocities[_indexB].w;
FP mA = _invMassA, mB = _invMassB;
FP iA = _invIA, iB = _invIB;
FP h = data.step.dt;
FP inv_h = data.step.inv_dt;
// Solve angular friction
{
FP Cdot = wB - wA + inv_h * CorrectionFactor * _angularError;
FP impulse = -_angularMass * Cdot;
FP oldImpulse = _angularImpulse;
FP maxImpulse = h * _maxTorque;
_angularImpulse = MathUtils.Clamp(_angularImpulse + impulse, -maxImpulse, maxImpulse);
impulse = _angularImpulse - oldImpulse;
wA -= iA * impulse;
wB += iB * impulse;
}
// Solve linear friction
{
FPVector2 Cdot = vB + MathUtils.Cross(wB, _rB) - vA - MathUtils.Cross(wA, _rA) + inv_h * CorrectionFactor * _linearError;
FPVector2 impulse = -MathUtils.Mul(ref _linearMass, ref Cdot);
FPVector2 oldImpulse = _linearImpulse;
_linearImpulse += impulse;
FP maxImpulse = h * _maxForce;
if (_linearImpulse.LengthSquared() > maxImpulse * maxImpulse)
{
_linearImpulse.Normalize();
_linearImpulse *= maxImpulse;
}
impulse = _linearImpulse - oldImpulse;
vA -= mA * impulse;
wA -= iA * MathUtils.Cross(_rA, impulse);
vB += mB * impulse;
wB += iB * MathUtils.Cross(_rB, impulse);
}
data.velocities[_indexA].v = vA;
data.velocities[_indexA].w = wA;
data.velocities[_indexB].v = vB;
data.velocities[_indexB].w = wB;
}
//Extracted from Box2D
/// <summary>
/// Returns the convex hull from the given vertices.
/// </summary>
/// <param name="vertices">The vertices.</param>
public static Vertices GetConvexHull(Vertices vertices)
{
if (vertices.Count <= 3)
{
return(vertices);
}
// Find the right most point on the hull
int i0 = 0;
FP x0 = vertices[0].x;
for (int i = 1; i < vertices.Count; ++i)
{
FP x = vertices[i].x;
if (x > x0 || (x == x0 && vertices[i].y < vertices[i0].y))
{
i0 = i;
x0 = x;
}
}
int[] hull = new int[vertices.Count];
int m = 0;
int ih = i0;
for (; ;)
{
hull[m] = ih;
int ie = 0;
for (int j = 1; j < vertices.Count; ++j)
{
if (ie == ih)
{
ie = j;
continue;
}
FPVector2 r = vertices[ie] - vertices[hull[m]];
FPVector2 v = vertices[j] - vertices[hull[m]];
FP c = MathUtils.Cross(ref r, ref v);
if (c < 0.0f)
{
ie = j;
}
// Collinearity check
if (c == 0.0f && v.LengthSquared() > r.LengthSquared())
{
ie = j;
}
}
++m;
ih = ie;
if (ie == i0)
{
break;
}
}
Vertices result = new Vertices(m);
// Copy vertices.
for (int i = 0; i < m; ++i)
{
result.Add(vertices[hull[i]]);
}
return(result);
}
public override void Update(FP dt)
{
FPVector2 f = FPVector2.zero;
foreach (Body worldBody in World.BodyList)
{
if (!IsActiveOn(worldBody))
{
continue;
}
foreach (Body controllerBody in Bodies)
{
if (worldBody == controllerBody || (worldBody.IsStatic && controllerBody.IsStatic) || !controllerBody.Enabled)
{
continue;
}
FPVector2 d = controllerBody.Position - worldBody.Position;
FP r2 = d.LengthSquared();
if (r2 <= Settings.Epsilon || r2 > MaxRadius * MaxRadius || r2 < MinRadius * MinRadius)
{
continue;
}
switch (GravityType)
{
case GravityType.DistanceSquared:
f = Strength / r2 * worldBody.Mass * controllerBody.Mass * d;
break;
case GravityType.Linear:
f = Strength / FP.Sqrt(r2) * worldBody.Mass * controllerBody.Mass * d;
break;
}
worldBody.ApplyForce(ref f);
}
foreach (FPVector2 point in Points)
{
FPVector2 d = point - worldBody.Position;
FP r2 = d.LengthSquared();
if (r2 <= Settings.Epsilon || r2 > MaxRadius * MaxRadius || r2 < MinRadius * MinRadius)
{
continue;
}
switch (GravityType)
{
case GravityType.DistanceSquared:
f = Strength / r2 * worldBody.Mass * d;
break;
case GravityType.Linear:
f = Strength / FP.Sqrt(r2) * worldBody.Mass * d;
break;
}
worldBody.ApplyForce(ref f);
}
}
}
/// <summary>
/// Ray-cast against the proxies in the tree. This relies on the callback
/// to perform a exact ray-cast in the case were the proxy contains a Shape.
/// The callback also performs the any collision filtering. This has performance
/// roughly equal to k * log(n), where k is the number of collisions and n is the
/// number of proxies in the tree.
/// </summary>
/// <param name="callback">A callback class that is called for each proxy that is hit by the ray.</param>
/// <param name="input">The ray-cast input data. The ray extends from p1 to p1 + maxFraction * (p2 - p1).</param>
public void RayCast(Func<RayCastInput, int, FP> callback, ref RayCastInput input)
{
FPVector2 p1 = input.Point1;
FPVector2 p2 = input.Point2;
FPVector2 r = p2 - p1;
Debug.Assert(r.LengthSquared() > 0.0f);
r.Normalize();
// v is perpendicular to the segment.
FPVector2 absV = MathUtils.Abs(new FPVector2(-r.y, r.x)); //FPE: Inlined the 'v' variable
// Separating axis for segment (Gino, p80).
// |dot(v, p1 - c)| > dot(|v|, h)
FP maxFraction = input.MaxFraction;
// Build a bounding box for the segment.
AABB segmentAABB = new AABB();
{
FPVector2 t = p1 + maxFraction * (p2 - p1);
FPVector2.Min(ref p1, ref t, out segmentAABB.LowerBound);
FPVector2.Max(ref p1, ref t, out segmentAABB.UpperBound);
}
_raycastStack.Clear();
_raycastStack.Push(_root);
while (_raycastStack.Count > 0)
{
int nodeId = _raycastStack.Pop();
if (nodeId == NullNode)
{
continue;
}
TreeNode<T> node = _nodes[nodeId];
if (AABB.TestOverlap(ref node.AABB, ref segmentAABB) == false)
{
continue;
}
// Separating axis for segment (Gino, p80).
// |dot(v, p1 - c)| > dot(|v|, h)
FPVector2 c = node.AABB.Center;
FPVector2 h = node.AABB.Extents;
FP separation = FP.Abs(FPVector2.Dot(new FPVector2(-r.y, r.x), p1 - c)) - FPVector2.Dot(absV, h);
if (separation > 0.0f)
{
continue;
}
if (node.IsLeaf())
{
RayCastInput subInput;
subInput.Point1 = input.Point1;
subInput.Point2 = input.Point2;
subInput.MaxFraction = maxFraction;
FP value = callback(subInput, nodeId);
if (value == 0.0f)
{
// the client has terminated the raycast.
return;
}
if (value > 0.0f)
{
// Update segment bounding box.
maxFraction = value;
FPVector2 t = p1 + maxFraction * (p2 - p1);
segmentAABB.LowerBound = FPVector2.Min(p1, t);
segmentAABB.UpperBound = FPVector2.Max(p1, t);
}
}
else
{
_raycastStack.Push(node.Child1);
_raycastStack.Push(node.Child2);
}
}
}
public static void ComputeDistance(out DistanceOutput output, out SimplexCache cache, DistanceInput input)
{
cache = new SimplexCache();
if (Settings.EnableDiagnostics) //FPE: We only gather diagnostics when enabled
{
++GJKCalls;
}
// Initialize the simplex.
Simplex simplex = new Simplex();
simplex.ReadCache(ref cache, input.ProxyA, ref input.TransformA, input.ProxyB, ref input.TransformB);
// These store the vertices of the last simplex so that we
// can check for duplicates and prevent cycling.
FixedArray3 <int> saveA = new FixedArray3 <int>();
FixedArray3 <int> saveB = new FixedArray3 <int>();
//FP distanceSqr1 = Settings.MaxFP;
// Main iteration loop.
int iter = 0;
while (iter < Settings.MaxGJKIterations)
{
// Copy simplex so we can identify duplicates.
int saveCount = simplex.Count;
for (int i = 0; i < saveCount; ++i)
{
saveA[i] = simplex.V[i].IndexA;
saveB[i] = simplex.V[i].IndexB;
}
switch (simplex.Count)
{
case 1:
break;
case 2:
simplex.Solve2();
break;
case 3:
simplex.Solve3();
break;
default:
Debug.Assert(false);
break;
}
// If we have 3 points, then the origin is in the corresponding triangle.
if (simplex.Count == 3)
{
break;
}
//FPE: This code was not used anyway.
// Compute closest point.
//Vector2 p = simplex.GetClosestPoint();
//FP distanceSqr2 = p.LengthSquared();
// Ensure progress
//if (distanceSqr2 >= distanceSqr1)
//{
//break;
//}
//distanceSqr1 = distanceSqr2;
// Get search direction.
FPVector2 d = simplex.GetSearchDirection();
// Ensure the search direction is numerically fit.
if (d.LengthSquared() < Settings.EpsilonSqr)
{
// The origin is probably contained by a line segment
// or triangle. Thus the shapes are overlapped.
// We can't return zero here even though there may be overlap.
// In case the simplex is a point, segment, or triangle it is difficult
// to determine if the origin is contained in the CSO or very close to it.
break;
}
// Compute a tentative new simplex vertex using support points.
SimplexVertex vertex = simplex.V[simplex.Count];
vertex.IndexA = input.ProxyA.GetSupport(MathUtils.MulT(input.TransformA.q, -d));
vertex.WA = MathUtils.Mul(ref input.TransformA, input.ProxyA.Vertices[vertex.IndexA]);
vertex.IndexB = input.ProxyB.GetSupport(MathUtils.MulT(input.TransformB.q, d));
vertex.WB = MathUtils.Mul(ref input.TransformB, input.ProxyB.Vertices[vertex.IndexB]);
vertex.W = vertex.WB - vertex.WA;
simplex.V[simplex.Count] = vertex;
// Iteration count is equated to the number of support point calls.
++iter;
if (Settings.EnableDiagnostics) //FPE: We only gather diagnostics when enabled
{
++GJKIters;
}
// Check for duplicate support points. This is the main termination criteria.
bool duplicate = false;
for (int i = 0; i < saveCount; ++i)
{
if (vertex.IndexA == saveA[i] && vertex.IndexB == saveB[i])
{
duplicate = true;
break;
}
}
// If we found a duplicate support point we must exit to avoid cycling.
if (duplicate)
{
break;
}
// New vertex is ok and needed.
++simplex.Count;
}
if (Settings.EnableDiagnostics) //FPE: We only gather diagnostics when enabled
{
GJKMaxIters = Math.Max(GJKMaxIters, iter);
}
// Prepare output.
simplex.GetWitnessPoints(out output.PointA, out output.PointB);
output.Distance = (output.PointA - output.PointB).magnitude;
output.Iterations = iter;
// Cache the simplex.
simplex.WriteCache(ref cache);
// Apply radii if requested.
if (input.UseRadii)
{
FP rA = input.ProxyA.Radius;
FP rB = input.ProxyB.Radius;
if (output.Distance > rA + rB && output.Distance > Settings.Epsilon)
{
// Shapes are still no overlapped.
// Move the witness points to the outer surface.
output.Distance -= rA + rB;
FPVector2 normal = output.PointB - output.PointA;
normal.Normalize();
output.PointA += rA * normal;
output.PointB -= rB * normal;
}
else
{
// Shapes are overlapped when radii are considered.
// Move the witness points to the middle.
FPVector2 p = 0.5f * (output.PointA + output.PointB);
output.PointA = p;
output.PointB = p;
output.Distance = 0.0f;
}
}
}
