internal void Initialize(SimplexCache cache, Shape shapeA, Transform transformA, Shape shapeB, Transform transformB) { ShapeA = shapeA; ShapeB = shapeB; int count = cache.Count; if (count == 1) { FaceType = Type.Points; Vector2 localPointA = ShapeA.GetVertex(cache.IndexA[0]); Vector2 localPointB = ShapeB.GetVertex(cache.IndexB[0]); Vector2 pointA = transformA.TransformPoint(localPointA); Vector2 pointB = transformB.TransformPoint(localPointB); Axis = pointB - pointA; Axis.Normalize(); } else if (cache.IndexB[0] == cache.IndexB[1]) { // Two points on A and one on B FaceType = Type.FaceA; Vector2 localPointA1 = ShapeA.GetVertex(cache.IndexA[0]); Vector2 localPointA2 = ShapeA.GetVertex(cache.IndexA[1]); Vector2 localPointB = ShapeB.GetVertex(cache.IndexB[0]); LocalPoint = 0.5f * (localPointA1 + localPointA2); Axis = (localPointA2 - localPointA1).CrossScalarPostMultiply(1.0f); Axis.Normalize(); Vector2 normal = transformA.TransformDirection(Axis); Vector2 pointA = transformA.TransformPoint(LocalPoint); Vector2 pointB = transformB.TransformPoint(localPointB); float s = Vector2.Dot(pointB - pointA, normal); if (s < 0.0f) { Axis = -Axis; } } else { // Two points on B and one or two points on A. // We ignore the second point on A. FaceType = Type.FaceB; Vector2 localPointA = shapeA.GetVertex(cache.IndexA[0]); Vector2 localPointB1 = shapeB.GetVertex(cache.IndexB[0]); Vector2 localPointB2 = shapeB.GetVertex(cache.IndexB[1]); LocalPoint = 0.5f * (localPointB1 + localPointB2); Axis = (localPointB2 - localPointB1).CrossScalarPostMultiply(1.0f); Axis.Normalize(); Vector2 normal = transformB.TransformDirection(Axis); Vector2 pointB = transformB.TransformPoint(LocalPoint); Vector2 pointA = transformA.TransformPoint(localPointA); float s = Vector2.Dot(pointA - pointB, normal); if (s < 0.0f) { Axis = -Axis; } } }
internal void WriteCache(SimplexCache cache) { cache.Metric = GetMetric(); cache.Count = (UInt16)_count; SimplexVertex[] vertices = new SimplexVertex[] { _v1, _v2, _v3 }; for (int i = 0; i < _count; ++i) { cache.IndexA[i] = (Byte)(vertices[i].indexA); cache.IndexB[i] = (Byte)(vertices[i].indexB); } }
internal void ReadCache(SimplexCache cache, Shape shapeA, Transform transformA, Shape shapeB, Transform transformB) { Box2DNetDebug.Assert(0 <= cache.Count && cache.Count <= 3); // Copy data from cache. _count = cache.Count; SimplexVertex[] vertices = new SimplexVertex[] { _v1, _v2, _v3 }; 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; } }
void ReadCache(SimplexCache cache, DistanceProxy proxyA, XForm transformA, DistanceProxy proxyB, XForm transformB) { // Copy data from cache. m_count = cache.count; SimplexVertex[] vertices = m_v1; for (int i = 0; i < m_count; ++i) { SimplexVertex v = vertices[i]; v.indexA = cache.indexA[i]; v.indexB = cache.indexB[i]; Vec2 wALocal = proxyA.GetVertex(v.indexA); Vec2 wBLocal = proxyB.GetVertex(v.indexB); v.wA = MathB2.Mul(transformA, wALocal); v.wB = MathB2.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 (m_count > 1) { float metric1 = cache.metric; float metric2 = GetMetric(); if (metric2 < 0.5f * metric1 || 2.0f * metric1 < metric2 || metric2 < Settings.FLT_EPSILON) { // Reset the simplex. m_count = 0; } } // If the cache is empty or invalid ... if (m_count == 0) { SimplexVertex v = vertices[0]; v.indexA = 0; v.indexB = 0; Vec2 wALocal = proxyA.GetVertex(0); Vec2 wBLocal = proxyB.GetVertex(0); v.wA = MathB2.Mul(transformA, wALocal); v.wB = MathB2.Mul(transformB, wBLocal); v.w = v.wB - v.wA; v.a = 1.0f; m_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; } } }
// CCD via the secant method. /// <summary> /// Compute the time when two shapes begin to touch or touch at a closer distance. /// TOI considers the shape radii. It attempts to have the radii overlap by the tolerance. /// Iterations terminate with the overlap is within 0.5 * tolerance. The tolerance should be /// smaller than sum of the shape radii. /// Warning the sweeps must have the same time interval. /// </summary> /// <returns> /// The fraction between [0,1] in which the shapes first touch. /// fraction=0 means the shapes begin touching/overlapped, and fraction=1 means the shapes don't touch. /// </returns> public static float TimeOfImpact(TOIInput input, Shape shapeA, Shape shapeB) { Sweep sweepA = input.SweepA; Sweep sweepB = input.SweepB; Box2DNetDebug.Assert(sweepA.T0 == sweepB.T0); Box2DNetDebug.Assert(1.0f - sweepA.T0 > Common.Settings.FLT_EPSILON); float radius = shapeA._radius + shapeB._radius; float tolerance = input.Tolerance; float alpha = 0.0f; const int k_maxIterations = 1000; // TODO_ERIN b2Settings int iter = 0; float target = 0.0f; // Prepare input for distance query. SimplexCache cache = new SimplexCache { Count = 0 }; DistanceInput distanceInput; distanceInput.UseRadii = false; for (; ;) { XForm xfA, xfB; sweepA.GetTransform(out xfA, alpha); sweepB.GetTransform(out xfB, alpha); // Get the distance between shapes. distanceInput.TransformA = xfA; distanceInput.TransformB = xfB; DistanceOutput distanceOutput; Distance(out distanceOutput, ref cache, ref distanceInput, shapeA, shapeB); if (distanceOutput.Distance <= 0.0f) { alpha = 1.0f; break; } SeparationFunction fcn = new SeparationFunction(); unsafe { fcn.Initialize(&cache, shapeA, xfA, shapeB, xfB); } float separation = fcn.Evaluate(xfA, xfB); if (separation <= 0.0f) { alpha = 1.0f; break; } if (iter == 0) { // Compute a reasonable target distance to give some breathing room // for conservative advancement. We take advantage of the shape radii // to create additional clearance. target = separation > radius?Common.Math.Max(radius - tolerance, 0.75f *radius) : Common.Math.Max(separation - tolerance, 0.02f * radius); } if (separation - target < 0.5f * tolerance) { if (iter == 0) { alpha = 1.0f; break; } break; } #if _FALSE // Dump the curve seen by the root finder { const int32 N = 100; float32 dx = 1.0f / N; float32 xs[N + 1];