/// <summary>
/// Reads the cache using the specified cache
/// </summary>
/// <param name="cache">The cache</param>
/// <param name="shapeA">The shape</param>
/// <param name="transformA">The transform</param>
/// <param name="shapeB">The shape</param>
/// <param name="transformB">The transform</param>
internal unsafe void ReadCache(SimplexCache *cache, Shape shapeA, XForm transformA, Shape shapeB,
XForm transformB)
{
Box2DxDebug.Assert(0 <= cache->Count && cache->Count <= 3);
// Copy data from cache.
Count = cache->Count;
SimplexVertex **vertices = stackalloc SimplexVertex *[3];
fixed(SimplexVertex *v1Ptr = &V1, v2Ptr = &V2, v3Ptr = &V3)
{
vertices[0] = v1Ptr;
vertices[1] = v2Ptr;
vertices[2] = v3Ptr;
for (int i = 0; i < Count; ++i)
{
SimplexVertex *v = vertices[i];
v->IndexA = cache->IndexA[i];
v->IndexB = cache->IndexB[i];
Vec2 wALocal = shapeA.GetVertex(v->IndexA);
Vec2 wBLocal = shapeB.GetVertex(v->IndexB);
v->Wa = Math.Mul(transformA, wALocal);
v->Wb = Math.Mul(transformB, wBLocal);
v->W = v->Wb - v->Wa;
v->A = 0.0f;
}
// Compute the new simplex metric, if it is substantially different than
// old metric then flush the simplex.
if (Count > 1)
{
float metric1 = cache->Metric;
float metric2 = GetMetric();
if (metric2 < 0.5f * metric1 || 2.0f * metric1 < metric2 || metric2 < Settings.FltEpsilon)
{
// Reset the simplex.
Count = 0;
}
}
// If the cache is empty or invalid ...
if (Count == 0)
{
SimplexVertex *v = vertices[0];
v->IndexA = 0;
v->IndexB = 0;
Vec2 wALocal = shapeA.GetVertex(0);
Vec2 wBLocal = shapeB.GetVertex(0);
v->Wa = Math.Mul(transformA, wALocal);
v->Wb = Math.Mul(transformB, wBLocal);
v->W = v->Wb - v->Wa;
Count = 1;
}
}
}
internal unsafe void ReadCache(SimplexCache *cache, Shape shapeA, Transform TransformA, Shape shapeB, Transform TransformB)
{
Box2DXDebug.Assert(0 <= cache->Count && cache->Count <= 3);
// Copy data from cache.
_count = cache->Count;
SimplexVertex **vertices = stackalloc SimplexVertex *[3];
fixed(SimplexVertex *v1Ptr = &_v1, v2Ptr = &_v2, v3Ptr = &_v3)
{
vertices[0] = v1Ptr;
vertices[1] = v2Ptr;
vertices[2] = v3Ptr;
for (int i = 0; i < _count; ++i)
{
SimplexVertex *v = vertices[i];
v->indexA = cache->IndexA[i];
v->indexB = cache->IndexB[i];
Vector2 wALocal = shapeA.GetVertex(v->indexA);
Vector2 wBLocal = shapeB.GetVertex(v->indexB);
v->wA = TransformA.TransformPoint(wALocal);
v->wB = TransformB.TransformPoint(wBLocal);
v->w = v->wB - v->wA;
v->a = 0.0f;
}
// Compute the new simplex metric, if it is substantially different than
// old metric then flush the simplex.
if (_count > 1)
{
float metric1 = cache->Metric;
float metric2 = GetMetric();
if (metric2 < 0.5f * metric1 || 2.0f * metric1 < metric2 || metric2 < Common.Settings.FLT_EPSILON)
{
// Reset the simplex.
_count = 0;
}
}
// If the cache is empty or invalid ...
if (_count == 0)
{
SimplexVertex *v = vertices[0];
v->indexA = 0;
v->indexB = 0;
Vector2 wALocal = shapeA.GetVertex(0);
Vector2 wBLocal = shapeB.GetVertex(0);
v->wA = TransformA.TransformPoint(wALocal);
v->wB = TransformB.TransformPoint(wBLocal);
v->w = v->wB - v->wA;
_count = 1;
}
}
}
static void Distance(out DistanceOutput output, ref SimplexCache cache, ref DistanceInput input, Shape shapeA, Shape shapeB)
{
output = new DistanceOutput();
Transform transformA = input.TransformA;
Transform transformB = input.TransformB;
// Initialize the simplex.
Simplex simplex = new Simplex();
#if ALLOWUNSAFE
fixed(SimplexCache *sPtr = &cache)
{
simplex.ReadCache(sPtr, shapeA, transformA, shapeB, transformB);
}
#else
simplex.ReadCache(cache, shapeA, transformA, shapeB, transformB);
#endif
// Get simplex vertices as an array.
#if ALLOWUNSAFE
SimplexVertex *vertices = &simplex._v1;
#else
SimplexVertex[] vertices = new SimplexVertex[] { simplex._v1, simplex._v2, simplex._v3 };
#endif
// These store the vertices of the last simplex so that we
// can check for duplicates and prevent cycling.
#if ALLOWUNSAFE
int *lastA = stackalloc int[4], lastB = stackalloc int[4];
#else
int[] lastA = new int[4];
int[] lastB = new int[4];
#endif // ALLOWUNSAFE
int lastCount;
// Main iteration loop.
int iter = 0;
const int k_maxIterationCount = 20;
while (iter < k_maxIterationCount)
{
// Copy simplex so we can identify duplicates.
lastCount = simplex._count;
int i;
for (i = 0; i < lastCount; ++i)
{
lastA[i] = vertices[i].indexA;
lastB[i] = vertices[i].indexB;
}
switch (simplex._count)
{
case 1:
break;
case 2:
simplex.Solve2();
break;
case 3:
simplex.Solve3();
break;
default:
break;
}
// If we have 3 points, then the origin is in the corresponding triangle.
if (simplex._count == 3)
{
break;
}
// Compute closest point.
Vector2 p = simplex.GetClosestPoint();
float distanceSqr = p.LengthSquared();
// Ensure the search direction is numerically fit.
if (distanceSqr < Common.Settings.FLT_EPSILON_SQUARED)
{
// 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.
#if ALLOWUNSAFE
SimplexVertex *vertex = vertices + simplex._count;
vertex->indexA = shapeA.GetSupport(transformA.InverseTransformDirection(p));
vertex->wA = transformA.TransformPoint(shapeA.GetVertex(vertex->indexA));
//Vec2 wBLocal;
vertex->indexB = shapeB.GetSupport(transformB.InverseTransformDirection(-p));
vertex->wB = transformB.TransformPoint(shapeB.GetVertex(vertex->indexB));
vertex->w = vertex->wB - vertex->wA;
#else
SimplexVertex vertex = vertices[simplex._count - 1];
vertex.indexA = shapeA.GetSupport(transformA.InverseTransformDirection(p));
vertex.wA = transformA.TransformPoint(shapeA.GetVertex(vertex.indexA));
//Vec2 wBLocal;
vertex.indexB = shapeB.GetSupport(transformB.InverseTransformDirection(-p));
vertex.wB = transformB.TransformPoint(shapeB.GetVertex(vertex.indexB));
vertex.w = vertex.wB - vertex.wA;
#endif // ALLOWUNSAFE
// Iteration count is equated to the number of support point calls.
++iter;
// Check for convergence.
#if ALLOWUNSAFE
float lowerBound = Vector2.Dot(p, vertex->w);
#else
float lowerBound = Vector2.Dot(p, vertex.w);
#endif
float upperBound = distanceSqr;
const float k_relativeTolSqr = 0.01f * 0.01f; // 1:100
if (upperBound - lowerBound <= k_relativeTolSqr * upperBound)
{
// Converged!
break;
}
// Check for duplicate support points.
bool duplicate = false;
for (i = 0; i < lastCount; ++i)
{
#if ALLOWUNSAFE
if (vertex->indexA == lastA[i] && vertex->indexB == lastB[i])
#else
if (vertex.indexA == lastA[i] && vertex.indexB == lastB[i])
#endif
{
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 ALLOWUNSAFE
fixed(DistanceOutput *doPtr = &output)
{
// Prepare output.
simplex.GetWitnessPoints(&doPtr->PointA, &doPtr->PointB);
doPtr->Distance = Vector2.Distance(doPtr->PointA, doPtr->PointB);
doPtr->Iterations = iter;
}
fixed(SimplexCache *sPtr = &cache)
{
// Cache the simplex.
simplex.WriteCache(sPtr);
}
#else
// Prepare output.
simplex.GetWitnessPoints(ref output.PointA, ref output.PointB);
output.Distance = Box2DNet.Common.Math.Distance(output.PointA, output.PointB);
output.Iterations = iter;
// Cache the simplex.
simplex.WriteCache(cache);
#endif
// Apply radii if requested.
if (input.UseRadii)
{
float rA = shapeA._radius;
float rB = shapeB._radius;
if (output.Distance > rA + rB && output.Distance > Common.Settings.FLT_EPSILON)
{
// Shapes are still no overlapped.
// Move the witness points to the outer surface.
output.Distance -= rA + rB;
Vector2 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.
Vector2 p = 0.5f * (output.PointA + output.PointB);
output.PointA = p;
output.PointB = p;
output.Distance = 0.0f;
}
}
}
/// <summary>
/// Compute the closest points between two shapes. Supports any combination of:
/// CircleShape, PolygonShape, EdgeShape. The simplex cache is input/output.
/// On the first call set SimplexCache.Count to zero.
/// </summary>
public static unsafe void Distance(out DistanceOutput output, ref SimplexCache cache, ref DistanceInput input,
Shape shapeA, Shape shapeB)
{
output = new DistanceOutput();
XForm transformA = input.TransformA;
XForm transformB = input.TransformB;
// Initialize the simplex.
Simplex simplex = new Simplex();
fixed(SimplexCache *sPtr = &cache)
{
simplex.ReadCache(sPtr, shapeA, transformA, shapeB, transformB);
}
// Get simplex vertices as an array.
SimplexVertex *vertices = &simplex.V1;
// These store the vertices of the last simplex so that we
// can check for duplicates and prevent cycling.
int *lastA = stackalloc int[4], lastB = stackalloc int[4];
int lastCount;
// Main iteration loop.
int iter = 0;
const int kMaxIterationCount = 20;
while (iter < kMaxIterationCount)
{
// Copy simplex so we can identify duplicates.
lastCount = simplex.Count;
int i;
for (i = 0; i < lastCount; ++i)
{
lastA[i] = vertices[i].IndexA;
lastB[i] = vertices[i].IndexB;
}
switch (simplex.Count)
{
case 1:
break;
case 2:
simplex.Solve2();
break;
case 3:
simplex.Solve3();
break;
default:
#if DEBUG
Box2DxDebug.Assert(false);
#endif
break;
}
// If we have 3 points, then the origin is in the corresponding triangle.
if (simplex.Count == 3)
{
break;
}
// Compute closest point.
Vec2 p = simplex.GetClosestPoint();
float distanceSqr = p.LengthSquared();
// Ensure the search direction is numerically fit.
if (distanceSqr < Settings.FltEpsilonSquared)
{
// 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 = vertices + simplex.Count;
vertex->IndexA = shapeA.GetSupport(Math.MulT(transformA.R, p));
vertex->Wa = Math.Mul(transformA, shapeA.GetVertex(vertex->IndexA));
//Vec2 wBLocal;
vertex->IndexB = shapeB.GetSupport(Math.MulT(transformB.R, -p));
vertex->Wb = Math.Mul(transformB, shapeB.GetVertex(vertex->IndexB));
vertex->W = vertex->Wb - vertex->Wa;
// Iteration count is equated to the number of support point calls.
++iter;
// Check for convergence.
float lowerBound = Vec2.Dot(p, vertex->W);
float upperBound = distanceSqr;
const float kRelativeTolSqr = 0.01f * 0.01f; // 1:100
if (upperBound - lowerBound <= kRelativeTolSqr * upperBound)
{
// Converged!
break;
}
// Check for duplicate support points.
bool duplicate = false;
for (i = 0; i < lastCount; ++i)
{
if (vertex->IndexA == lastA[i] && vertex->IndexB == lastB[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;
}
fixed(DistanceOutput *doPtr = &output)
{
// Prepare output.
simplex.GetWitnessPoints(&doPtr->PointA, &doPtr->PointB);
doPtr->Distance = Vec2.Distance(doPtr->PointA, doPtr->PointB);
doPtr->Iterations = iter;
}
fixed(SimplexCache *sPtr = &cache)
{
// Cache the simplex.
simplex.WriteCache(sPtr);
}
// Apply radii if requested.
if (input.UseRadii)
{
float rA = shapeA.Radius;
float rB = shapeB.Radius;
if (output.Distance > rA + rB && output.Distance > Settings.FltEpsilon)
{
// Shapes are still no overlapped.
// Move the witness points to the outer surface.
output.Distance -= rA + rB;
Vec2 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.
Vec2 p = 0.5f * (output.PointA + output.PointB);
output.PointA = p;
output.PointB = p;
output.Distance = 0.0f;
}
}
}
