private PairSimplex(ref RigidTransform localTransformB)
{
//This isn't a very good approach since the transform position is not guaranteed to be within the object. Would have to use the GetNewSimplexPoint to make it valid.
previousDistanceToClosest = float.MaxValue;
errorTolerance = 0;
LocalTransformB = localTransformB;
//Warm up the simplex using the centroids.
//Could also use the GetNewSimplexPoint if it had a Empty case, but test before choosing.
State = SimplexState.Point;
SimplexA = new ContributingShapeSimplex();
SimplexB = new ContributingShapeSimplex {
A = localTransformB.Position
};
//minkowski space support = shapeA-shapeB = 0,0,0 - positionB
Vector3.Negate(ref localTransformB.Position, out A);
B = new Vector3();
C = new Vector3();
D = new Vector3();
U = 0;
V = 0;
W = 0;
}
///<summary>
/// Constructs a new pair simplex.
///</summary>
///<param name="cachedSimplex">Cached simplex to use to warmstart the simplex.</param>
///<param name="localTransformB">Transform of shape B in the local space of A.</param>
public PairSimplex(ref CachedSimplex cachedSimplex, ref RigidTransform localTransformB)
{
//NOTE:
//USING A CACHED SIMPLEX INVALIDATES ASSUMPTIONS THAT ALLOW SIMPLEX CASES TO BE IGNORED!
//To get those assumptions back, either DO NOT USE CACHED SIMPLEXES, or
//VERIFY THE SIMPLEXES.
//-A point requires no verification.
//-A segment needs verification that the origin is in front of A in the direction of B.
//-A triangle needs verification that the origin is within the edge planes and in the direction of C.
//-A tetrahedron needs verification that the origin is within the edge planes of triangle ABC and is in the direction of D.
//This simplex implementation will not ignore any cases, so we can warm start safely with one problem.
//Due to relative movement, the simplex may become degenerate. Edges could become points, etc.
//Some protections are built into the simplex cases, but keep an eye out for issues.
//Most dangerous degeneracy seen so far is tetrahedron. It fails to find any points on opposing sides due to numerical problems and returns intersection.
previousDistanceToClosest = float.MaxValue;
errorTolerance = 0;
LocalTransformB = localTransformB;
//Transform the SimplexB into the working space of the simplex and compute the working space simplex.
State = cachedSimplex.State;
SimplexA = cachedSimplex.LocalSimplexA;
SimplexB = new ContributingShapeSimplex();
U = 0;
V = 0;
W = 0;
switch (State)
{
case SimplexState.Point:
Quaternion.Transform(ref cachedSimplex.LocalSimplexB.A, ref LocalTransformB.Orientation, out SimplexB.A);
Vector3.Add(ref SimplexB.A, ref LocalTransformB.Position, out SimplexB.A);
Vector3.Subtract(ref SimplexA.A, ref SimplexB.A, out A);
B = new Vector3();
C = new Vector3();
D = new Vector3();
break;
case SimplexState.Segment:
Matrix3x3 transform;
Matrix3x3.CreateFromQuaternion(ref localTransformB.Orientation, out transform);
Matrix3x3.Transform(ref cachedSimplex.LocalSimplexB.A, ref transform, out SimplexB.A);
Matrix3x3.Transform(ref cachedSimplex.LocalSimplexB.B, ref transform, out SimplexB.B);
Vector3.Add(ref SimplexB.A, ref LocalTransformB.Position, out SimplexB.A);
Vector3.Add(ref SimplexB.B, ref LocalTransformB.Position, out SimplexB.B);
Vector3.Subtract(ref SimplexA.A, ref SimplexB.A, out A);
Vector3.Subtract(ref SimplexA.B, ref SimplexB.B, out B);
C = new Vector3();
D = new Vector3();
////Test for degeneracy.
//float edgeLengthAB;
//Vector3.DistanceSquared(ref A, ref B, out edgeLengthAB);
//if (edgeLengthAB < Toolbox.Epsilon)
// State = SimplexState.Point;
break;
case SimplexState.Triangle:
Matrix3x3.CreateFromQuaternion(ref localTransformB.Orientation, out transform);
Matrix3x3.Transform(ref cachedSimplex.LocalSimplexB.A, ref transform, out SimplexB.A);
Matrix3x3.Transform(ref cachedSimplex.LocalSimplexB.B, ref transform, out SimplexB.B);
Matrix3x3.Transform(ref cachedSimplex.LocalSimplexB.C, ref transform, out SimplexB.C);
Vector3.Add(ref SimplexB.A, ref LocalTransformB.Position, out SimplexB.A);
Vector3.Add(ref SimplexB.B, ref LocalTransformB.Position, out SimplexB.B);
Vector3.Add(ref SimplexB.C, ref LocalTransformB.Position, out SimplexB.C);
Vector3.Subtract(ref SimplexA.A, ref SimplexB.A, out A);
Vector3.Subtract(ref SimplexA.B, ref SimplexB.B, out B);
Vector3.Subtract(ref SimplexA.C, ref SimplexB.C, out C);
D = new Vector3();
////Test for degeneracy.
//Vector3 AB, AC;
//Vector3.Subtract(ref B, ref A, out AB);
//Vector3.Subtract(ref C, ref A, out AC);
//Vector3 cross;
//Vector3.Cross(ref AB, ref AC, out cross);
////If the area is small compared to a tolerance (adjusted by the partial perimeter), it's degenerate.
//if (cross.LengthSquared < Toolbox.BigEpsilon * (AB.LengthSquared + AC.LengthSquared))
// State = SimplexState.Point;
break;
case SimplexState.Tetrahedron:
Matrix3x3.CreateFromQuaternion(ref localTransformB.Orientation, out transform);
Matrix3x3.Transform(ref cachedSimplex.LocalSimplexB.A, ref transform, out SimplexB.A);
Matrix3x3.Transform(ref cachedSimplex.LocalSimplexB.B, ref transform, out SimplexB.B);
Matrix3x3.Transform(ref cachedSimplex.LocalSimplexB.C, ref transform, out SimplexB.C);
Matrix3x3.Transform(ref cachedSimplex.LocalSimplexB.D, ref transform, out SimplexB.D);
Vector3.Add(ref SimplexB.A, ref LocalTransformB.Position, out SimplexB.A);
Vector3.Add(ref SimplexB.B, ref LocalTransformB.Position, out SimplexB.B);
Vector3.Add(ref SimplexB.C, ref LocalTransformB.Position, out SimplexB.C);
Vector3.Add(ref SimplexB.D, ref LocalTransformB.Position, out SimplexB.D);
Vector3.Subtract(ref SimplexA.A, ref SimplexB.A, out A);
Vector3.Subtract(ref SimplexA.B, ref SimplexB.B, out B);
Vector3.Subtract(ref SimplexA.C, ref SimplexB.C, out C);
Vector3.Subtract(ref SimplexA.D, ref SimplexB.D, out D);
////Test for degeneracy.
//Vector3 AD;
//Vector3.Subtract(ref B, ref A, out AB);
//Vector3.Subtract(ref C, ref A, out AC);
//Vector3.Subtract(ref D, ref A, out AD);
//Vector3.Cross(ref AB, ref AC, out cross);
//float volume;
//Vector3.Dot(ref cross, ref AD, out volume);
////Volume is small compared to partial 'perimeter.'
//if (volume < Toolbox.BigEpsilon * (AB.LengthSquared + AC.LengthSquared + AD.LengthSquared))
// State = SimplexState.Point;
break;
default:
A = new Vector3();
B = new Vector3();
C = new Vector3();
D = new Vector3();
break;
}
}