public bool ClosestPtPointTetrahedron(Vector3 p, Vector3 a, Vector3 b, Vector3 c, Vector3 d, ref SubSimplexClosestResult finalResult) { SubSimplexClosestResult tempResult = new SubSimplexClosestResult(); // Start out assuming point inside all halfspaces, so closest to itself finalResult.ClosestPointOnSimplex = p; finalResult.UsedVertices.Reset(); finalResult.UsedVertices.UsedVertexA = true; finalResult.UsedVertices.UsedVertexB = true; finalResult.UsedVertices.UsedVertexC = true; finalResult.UsedVertices.UsedVertexD = true; int pointOutsideABC = PointOutsideOfPlane(p, a, b, c, d); int pointOutsideACD = PointOutsideOfPlane(p, a, c, d, b); int pointOutsideADB = PointOutsideOfPlane(p, a, d, b, c); int pointOutsideBDC = PointOutsideOfPlane(p, b, d, c, a); if (pointOutsideABC < 0 || pointOutsideACD < 0 || pointOutsideADB < 0 || pointOutsideBDC < 0) { finalResult.Degenerate = true; return false; } if (pointOutsideABC == 0 && pointOutsideACD == 0 && pointOutsideADB == 0 && pointOutsideBDC == 0) return false; float bestSqDist = float.MaxValue; // If point outside face abc then compute closest point on abc if (pointOutsideABC != 0) { ClosestPtPointTriangle(p, a, b, c, ref tempResult); Vector3 q = tempResult.ClosestPointOnSimplex; float sqDist = ((Vector3)(q - p)).LengthSquared(); // Update best closest point if (squared) distance is less than current best if (sqDist < bestSqDist) { bestSqDist = sqDist; finalResult.ClosestPointOnSimplex = q; //convert result bitmask! finalResult.UsedVertices.Reset(); finalResult.UsedVertices.UsedVertexA = tempResult.UsedVertices.UsedVertexA; finalResult.UsedVertices.UsedVertexB = tempResult.UsedVertices.UsedVertexB; finalResult.UsedVertices.UsedVertexC = tempResult.UsedVertices.UsedVertexC; finalResult.SetBarycentricCoordinates( tempResult.BarycentricCoords[VertexA], tempResult.BarycentricCoords[VertexB], tempResult.BarycentricCoords[VertexC], 0); } } // Repeat test for face acd if (pointOutsideACD != 0) { ClosestPtPointTriangle(p, a, c, d, ref tempResult); Vector3 q = tempResult.ClosestPointOnSimplex; //convert result bitmask! float sqDist = ((Vector3)(q - p)).LengthSquared(); if (sqDist < bestSqDist) { bestSqDist = sqDist; finalResult.ClosestPointOnSimplex = q; finalResult.UsedVertices.Reset(); finalResult.UsedVertices.UsedVertexA = tempResult.UsedVertices.UsedVertexA; finalResult.UsedVertices.UsedVertexC = tempResult.UsedVertices.UsedVertexB; finalResult.UsedVertices.UsedVertexD = tempResult.UsedVertices.UsedVertexC; finalResult.SetBarycentricCoordinates( tempResult.BarycentricCoords[VertexA], 0, tempResult.BarycentricCoords[VertexB], tempResult.BarycentricCoords[VertexC]); } } // Repeat test for face adb if (pointOutsideADB != 0) { ClosestPtPointTriangle(p, a, d, b, ref tempResult); Vector3 q = tempResult.ClosestPointOnSimplex; //convert result bitmask! float sqDist = ((Vector3)(q - p)).LengthSquared(); if (sqDist < bestSqDist) { bestSqDist = sqDist; finalResult.ClosestPointOnSimplex = q; finalResult.UsedVertices.Reset(); finalResult.UsedVertices.UsedVertexA = tempResult.UsedVertices.UsedVertexA; finalResult.UsedVertices.UsedVertexD = tempResult.UsedVertices.UsedVertexB; finalResult.UsedVertices.UsedVertexB = tempResult.UsedVertices.UsedVertexC; finalResult.SetBarycentricCoordinates( tempResult.BarycentricCoords[VertexA], tempResult.BarycentricCoords[VertexC], 0, tempResult.BarycentricCoords[VertexB]); } } // Repeat test for face bdc if (pointOutsideBDC != 0) { ClosestPtPointTriangle(p, b, d, c, ref tempResult); Vector3 q = tempResult.ClosestPointOnSimplex; //convert result bitmask! float sqDist = ((Vector3)(q - p)).LengthSquared(); if (sqDist < bestSqDist) { bestSqDist = sqDist; finalResult.ClosestPointOnSimplex = q; finalResult.UsedVertices.Reset(); finalResult.UsedVertices.UsedVertexB = tempResult.UsedVertices.UsedVertexA; finalResult.UsedVertices.UsedVertexD = tempResult.UsedVertices.UsedVertexB; finalResult.UsedVertices.UsedVertexC = tempResult.UsedVertices.UsedVertexC; finalResult.SetBarycentricCoordinates( 0, tempResult.BarycentricCoords[VertexA], tempResult.BarycentricCoords[VertexC], tempResult.BarycentricCoords[VertexB]); } } //help! we ended up full ! if (finalResult.UsedVertices.UsedVertexA && finalResult.UsedVertices.UsedVertexB && finalResult.UsedVertices.UsedVertexC && finalResult.UsedVertices.UsedVertexD) { return true; } return true; }
public bool ClosestPtPointTetrahedron(Vector3 p, Vector3 a, Vector3 b, Vector3 c, Vector3 d, ref SubSimplexClosestResult finalResult) { SubSimplexClosestResult tempResult = new SubSimplexClosestResult(); // Start out assuming point inside all halfspaces, so closest to itself finalResult.ClosestPointOnSimplex = p; finalResult.UsedVertices.Reset(); finalResult.UsedVertices.UsedVertexA = true; finalResult.UsedVertices.UsedVertexB = true; finalResult.UsedVertices.UsedVertexC = true; finalResult.UsedVertices.UsedVertexD = true; int pointOutsideABC = PointOutsideOfPlane(p, a, b, c, d); int pointOutsideACD = PointOutsideOfPlane(p, a, c, d, b); int pointOutsideADB = PointOutsideOfPlane(p, a, d, b, c); int pointOutsideBDC = PointOutsideOfPlane(p, b, d, c, a); if (pointOutsideABC < 0 || pointOutsideACD < 0 || pointOutsideADB < 0 || pointOutsideBDC < 0) { finalResult.Degenerate = true; return(false); } if (pointOutsideABC == 0 && pointOutsideACD == 0 && pointOutsideADB == 0 && pointOutsideBDC == 0) { return(false); } float bestSqDist = float.MaxValue; // If point outside face abc then compute closest point on abc if (pointOutsideABC != 0) { ClosestPtPointTriangle(p, a, b, c, ref tempResult); Vector3 q = tempResult.ClosestPointOnSimplex; float sqDist = ((Vector3)(q - p)).LengthSquared(); // Update best closest point if (squared) distance is less than current best if (sqDist < bestSqDist) { bestSqDist = sqDist; finalResult.ClosestPointOnSimplex = q; //convert result bitmask! finalResult.UsedVertices.Reset(); finalResult.UsedVertices.UsedVertexA = tempResult.UsedVertices.UsedVertexA; finalResult.UsedVertices.UsedVertexB = tempResult.UsedVertices.UsedVertexB; finalResult.UsedVertices.UsedVertexC = tempResult.UsedVertices.UsedVertexC; finalResult.SetBarycentricCoordinates( tempResult.BarycentricCoords[VertexA], tempResult.BarycentricCoords[VertexB], tempResult.BarycentricCoords[VertexC], 0); } } // Repeat test for face acd if (pointOutsideACD != 0) { ClosestPtPointTriangle(p, a, c, d, ref tempResult); Vector3 q = tempResult.ClosestPointOnSimplex; //convert result bitmask! float sqDist = ((Vector3)(q - p)).LengthSquared(); if (sqDist < bestSqDist) { bestSqDist = sqDist; finalResult.ClosestPointOnSimplex = q; finalResult.UsedVertices.Reset(); finalResult.UsedVertices.UsedVertexA = tempResult.UsedVertices.UsedVertexA; finalResult.UsedVertices.UsedVertexC = tempResult.UsedVertices.UsedVertexB; finalResult.UsedVertices.UsedVertexD = tempResult.UsedVertices.UsedVertexC; finalResult.SetBarycentricCoordinates( tempResult.BarycentricCoords[VertexA], 0, tempResult.BarycentricCoords[VertexB], tempResult.BarycentricCoords[VertexC]); } } // Repeat test for face adb if (pointOutsideADB != 0) { ClosestPtPointTriangle(p, a, d, b, ref tempResult); Vector3 q = tempResult.ClosestPointOnSimplex; //convert result bitmask! float sqDist = ((Vector3)(q - p)).LengthSquared(); if (sqDist < bestSqDist) { bestSqDist = sqDist; finalResult.ClosestPointOnSimplex = q; finalResult.UsedVertices.Reset(); finalResult.UsedVertices.UsedVertexA = tempResult.UsedVertices.UsedVertexA; finalResult.UsedVertices.UsedVertexD = tempResult.UsedVertices.UsedVertexB; finalResult.UsedVertices.UsedVertexB = tempResult.UsedVertices.UsedVertexC; finalResult.SetBarycentricCoordinates( tempResult.BarycentricCoords[VertexA], tempResult.BarycentricCoords[VertexC], 0, tempResult.BarycentricCoords[VertexB]); } } // Repeat test for face bdc if (pointOutsideBDC != 0) { ClosestPtPointTriangle(p, b, d, c, ref tempResult); Vector3 q = tempResult.ClosestPointOnSimplex; //convert result bitmask! float sqDist = ((Vector3)(q - p)).LengthSquared(); if (sqDist < bestSqDist) { bestSqDist = sqDist; finalResult.ClosestPointOnSimplex = q; finalResult.UsedVertices.Reset(); finalResult.UsedVertices.UsedVertexB = tempResult.UsedVertices.UsedVertexA; finalResult.UsedVertices.UsedVertexD = tempResult.UsedVertices.UsedVertexB; finalResult.UsedVertices.UsedVertexC = tempResult.UsedVertices.UsedVertexC; finalResult.SetBarycentricCoordinates( 0, tempResult.BarycentricCoords[VertexA], tempResult.BarycentricCoords[VertexC], tempResult.BarycentricCoords[VertexB]); } } //help! we ended up full ! if (finalResult.UsedVertices.UsedVertexA && finalResult.UsedVertices.UsedVertexB && finalResult.UsedVertices.UsedVertexC && finalResult.UsedVertices.UsedVertexD) { return(true); } return(true); }
public bool ClosestPtPointTriangle(Vector3 p, Vector3 a, Vector3 b, Vector3 c, ref SubSimplexClosestResult result) { result.UsedVertices.Reset(); float v, w; // Check if P in vertex region outside A Vector3 ab = b - a; Vector3 ac = c - a; Vector3 ap = p - a; float d1 = Vector3.Dot(ab, ap); float d2 = Vector3.Dot(ac, ap); if (d1 <= 0f && d2 <= 0f) { result.ClosestPointOnSimplex = a; result.UsedVertices.UsedVertexA = true; result.SetBarycentricCoordinates(1, 0, 0, 0); return true; // a; // barycentric coordinates (1,0,0) } // Check if P in vertex region outside B Vector3 bp = p - b; float d3 = Vector3.Dot(ab, bp); float d4 = Vector3.Dot(ac, bp); if (d3 >= 0f && d4 <= d3) { result.ClosestPointOnSimplex = b; result.UsedVertices.UsedVertexB = true; result.SetBarycentricCoordinates(0, 1, 0, 0); return true; // b; // barycentric coordinates (0,1,0) } // Check if P in edge region of AB, if so return projection of P onto AB float vc = d1 * d4 - d3 * d2; if (vc <= 0f && d1 >= 0f && d3 <= 0f) { v = d1 / (d1 - d3); result.ClosestPointOnSimplex = a + v * ab; result.UsedVertices.UsedVertexA = true; result.UsedVertices.UsedVertexB = true; result.SetBarycentricCoordinates(1 - v, v, 0, 0); return true; //return a + v * ab; // barycentric coordinates (1-v,v,0) } // Check if P in vertex region outside C Vector3 cp = p - c; float d5 = Vector3.Dot(ab, cp); float d6 = Vector3.Dot(ac, cp); if (d6 >= 0f && d5 <= d6) { result.ClosestPointOnSimplex = c; result.UsedVertices.UsedVertexC = true; result.SetBarycentricCoordinates(0, 0, 1, 0); return true;//c; // barycentric coordinates (0,0,1) } // Check if P in edge region of AC, if so return projection of P onto AC float vb = d5 * d2 - d1 * d6; if (vb <= 0f && d2 >= 0f && d6 <= 0f) { w = d2 / (d2 - d6); result.ClosestPointOnSimplex = a + w * ac; result.UsedVertices.UsedVertexA = true; result.UsedVertices.UsedVertexC = true; result.SetBarycentricCoordinates(1 - w, 0, w, 0); return true; //return a + w * ac; // barycentric coordinates (1-w,0,w) } // Check if P in edge region of BC, if so return projection of P onto BC float va = d3 * d6 - d5 * d4; if (va <= 0f && (d4 - d3) >= 0f && (d5 - d6) >= 0f) { w = (d4 - d3) / ((d4 - d3) + (d5 - d6)); result.ClosestPointOnSimplex = b + w * (c - b); result.UsedVertices.UsedVertexB = true; result.UsedVertices.UsedVertexC = true; result.SetBarycentricCoordinates(0, 1 - w, w, 0); return true; // return b + w * (c - b); // barycentric coordinates (0,1-w,w) } // P inside face region. Compute Q through its barycentric coordinates (u,v,w) float denom = 1.0f / (va + vb + vc); v = vb * denom; w = vc * denom; result.ClosestPointOnSimplex = a + ab * v + ac * w; result.UsedVertices.UsedVertexA = true; result.UsedVertices.UsedVertexB = true; result.UsedVertices.UsedVertexC = true; result.SetBarycentricCoordinates(1 - v - w, v, w, 0); return true; }
public bool ClosestPtPointTriangle(Vector3 p, Vector3 a, Vector3 b, Vector3 c, ref SubSimplexClosestResult result) { result.UsedVertices.Reset(); float v, w; // Check if P in vertex region outside A Vector3 ab = b - a; Vector3 ac = c - a; Vector3 ap = p - a; float d1 = Vector3.Dot(ab, ap); float d2 = Vector3.Dot(ac, ap); if (d1 <= 0f && d2 <= 0f) { result.ClosestPointOnSimplex = a; result.UsedVertices.UsedVertexA = true; result.SetBarycentricCoordinates(1, 0, 0, 0); return(true); // a; // barycentric coordinates (1,0,0) } // Check if P in vertex region outside B Vector3 bp = p - b; float d3 = Vector3.Dot(ab, bp); float d4 = Vector3.Dot(ac, bp); if (d3 >= 0f && d4 <= d3) { result.ClosestPointOnSimplex = b; result.UsedVertices.UsedVertexB = true; result.SetBarycentricCoordinates(0, 1, 0, 0); return(true); // b; // barycentric coordinates (0,1,0) } // Check if P in edge region of AB, if so return projection of P onto AB float vc = d1 * d4 - d3 * d2; if (vc <= 0f && d1 >= 0f && d3 <= 0f) { v = d1 / (d1 - d3); result.ClosestPointOnSimplex = a + v * ab; result.UsedVertices.UsedVertexA = true; result.UsedVertices.UsedVertexB = true; result.SetBarycentricCoordinates(1 - v, v, 0, 0); return(true); //return a + v * ab; // barycentric coordinates (1-v,v,0) } // Check if P in vertex region outside C Vector3 cp = p - c; float d5 = Vector3.Dot(ab, cp); float d6 = Vector3.Dot(ac, cp); if (d6 >= 0f && d5 <= d6) { result.ClosestPointOnSimplex = c; result.UsedVertices.UsedVertexC = true; result.SetBarycentricCoordinates(0, 0, 1, 0); return(true); //c; // barycentric coordinates (0,0,1) } // Check if P in edge region of AC, if so return projection of P onto AC float vb = d5 * d2 - d1 * d6; if (vb <= 0f && d2 >= 0f && d6 <= 0f) { w = d2 / (d2 - d6); result.ClosestPointOnSimplex = a + w * ac; result.UsedVertices.UsedVertexA = true; result.UsedVertices.UsedVertexC = true; result.SetBarycentricCoordinates(1 - w, 0, w, 0); return(true); //return a + w * ac; // barycentric coordinates (1-w,0,w) } // Check if P in edge region of BC, if so return projection of P onto BC float va = d3 * d6 - d5 * d4; if (va <= 0f && (d4 - d3) >= 0f && (d5 - d6) >= 0f) { w = (d4 - d3) / ((d4 - d3) + (d5 - d6)); result.ClosestPointOnSimplex = b + w * (c - b); result.UsedVertices.UsedVertexB = true; result.UsedVertices.UsedVertexC = true; result.SetBarycentricCoordinates(0, 1 - w, w, 0); return(true); // return b + w * (c - b); // barycentric coordinates (0,1-w,w) } // P inside face region. Compute Q through its barycentric coordinates (u,v,w) float denom = 1.0f / (va + vb + vc); v = vb * denom; w = vc * denom; result.ClosestPointOnSimplex = a + ab * v + ac * w; result.UsedVertices.UsedVertexA = true; result.UsedVertices.UsedVertexB = true; result.UsedVertices.UsedVertexC = true; result.SetBarycentricCoordinates(1 - v - w, v, w, 0); return(true); }