implementation of GJK and EPA collision detection algorithm continued

git-svn-id: https://reactphysics3d.googlecode.com/svn/trunk@420 92aac97c-a6ce-11dd-a772-7fcde58d38e6

src/collision/EPA/EPAAlgorithm.cpp

@@ -24,6 +24,8 @@
 
 // Libraries
 #include "EPAAlgorithm.h"
+#include "../GJK/GJKAlgorithm.h"
+#include "TrianglesStore.h"
 
 // We want to use the ReactPhysics3D namespace
 using namespace reactphysics3d;
@@ -38,6 +40,39 @@ EPAAlgorithm::~EPAAlgorithm() {
     
 }
 
+// Decide if the origin is in the tetrahedron
+// Return 0 if the origin is in the tetrahedron and return the number (1,2,3 or 4) of
+// the vertex that is wrong if the origin is not in the tetrahedron
+int EPAAlgorithm::isOriginInTetrahedron(const Vector3D& p1, const Vector3D& p2, const Vector3D& p3, const Vector3D& p4) const {
+
+    // Check vertex 1
+    Vector3D normal1 = (p2-p1).cross(p3-p1);
+    if (normal1.dot(p1) > 0.0 == normal1.dot(p4) > 0.0) {
+        return 4;
+    }
+
+    // Check vertex 2
+    Vector3D normal2 = (p4-p2).cross(p3-p2);
+    if (normal2.dot(p2) > 0.0 == normal2.dot(p1) > 0.0) {
+        return 1;
+    }
+
+    // Check vertex 3
+    Vector3D normal3 = (p4-p3).cross(p1-p3);
+    if (normal3.dot(p3) > 0.0 == normal3.dot(p2) > 0.0) {
+        return 2;
+    }
+
+    // Check vertex 4
+    Vector3D normal4 = (p2-p4).cross(p1-p4);
+    if (normal4.dot(p4) > 0.0 == normal4.dot(p3) > 0.0) {
+        return 3;
+    }
+
+    // The origin is in the tetrahedron, we return 0
+    return 0;
+}
+
 // Compute the penetration depth with the EPA algorithms
 // This method computes the penetration depth and contact points between two
 // enlarged objects (with margin) where the original objects (without margin)
@@ -50,6 +85,8 @@ bool EPAAlgorithm::computePenetrationDepthAndContactPoints(Simplex simplex, cons
     Vector3D suppPointsA[MAX_SUPPORT_POINTS];       // Support points of object A in local coordinates
     Vector3D suppPointsB[MAX_SUPPORT_POINTS];       // Support points of object B in local coordinates
     Vector3D points[MAX_SUPPORT_POINTS];            // Current points
+    TrianglesStore triangleStore;                   // Store the triangles
+    TriangleEPA* triangleHeap[MAX_FACETS];          // Heap that contains the face candidate of the EPA algorithm
     
     // TODO : Check that we call all the supportPoint() function with a margin
 
@@ -62,7 +99,12 @@ bool EPAAlgorithm::computePenetrationDepthAndContactPoints(Simplex simplex, cons
     // Number of triangles in the polytope
     unsigned int nbTriangles = 0;
 
-    // Select an action according to the number of points in the simplex computed with GJK algorithm
+    // Clear the storing of triangles
+    triangleStore.clear();
+
+    // Select an action according to the number of points in the simplex
+    // computed with GJK algorithm in order to obtain an initial polytope for
+    // The EPA algorithm.
     switch(nbVertices) {
         case 1:
             // Only one point in the simplex (which should be the origin). We have a touching contact
@@ -70,7 +112,270 @@ bool EPAAlgorithm::computePenetrationDepthAndContactPoints(Simplex simplex, cons
             return false;
 
         case 2: {
+            // The simplex returned by GJK is a line segment d containing the origin.
+            // We add two additional support points to construct a hexahedron (two tetrahedron
+            // glued together with triangle faces. The idea is to compute three different vectors
+            // v1, v2 and v3 that are orthogonal to the segment d. The three vectors are relatively
+            // rotated of 120 degree around the d segment. The the three new points to
+            // construct the polytope are the three support points in those three directions
+            // v1, v2 and v3.
 
+            // Direction of the segment
+            Vector3D d = (points[1] - points[0]).getUnit();
+
+            // Choose the coordinate axis from the minimal absolute component of the vector d
+            int minAxis = d.getAbsoluteVector().getMinAxis();
+
+            // Compute sin(60)
+            const double sin60 = sqrt(3.0) * 0.5;
+
+            // Create a rotation quaternion to rotate the vector v1 to get the vectors
+            // v2 and v3
+            Quaternion rotationQuat(d.getX() * sin60, d.getY() * sin60, d.getZ() * sin60, 0.5);
+
+            // Construct the corresponding rotation matrix
+            Matrix3x3 rotationMat = rotationQuat.getMatrix();
+
+            // Compute the vector v1, v2, v3
+            Vector3D v1 = d.cross(Vector3D(minAxis == 0, minAxis == 1, minAxis == 2));
+            Vector3D v2 = rotationMat * v1;
+            Vector3D v3 = rotationMat * v2;
+
+            // Compute the support point in the direction of v1
+            suppPointsA[2] = boundingVolume1->getSupportPoint(v1, OBJECT_MARGIN);
+            suppPointsB[2] = boundingVolume2->getSupportPoint(v1.getOpposite(), OBJECT_MARGIN);
+            points[2] = suppPointsA[2] - suppPointsB[2];
+
+            // Compute the support point in the direction of v2
+            suppPointsA[3] = boundingVolume1->getSupportPoint(v2, OBJECT_MARGIN);
+            suppPointsB[3] = boundingVolume2->getSupportPoint(v2.getOpposite(), OBJECT_MARGIN);
+            points[3] = suppPointsA[3] - suppPointsB[3];
+
+            // Compute the support point in the direction of v3
+            suppPointsA[4] = boundingVolume1->getSupportPoint(v3, OBJECT_MARGIN);
+            suppPointsB[4] = boundingVolume2->getSupportPoint(v3.getOpposite(), OBJECT_MARGIN);
+            points[4] = suppPointsA[4] - suppPointsB[4];
+
+            // Now we have an hexahedron (two tetrahedron glued together). We can simply keep the
+            // tetrahedron that contains the origin in order that the initial polytope of the
+            // EPA algorithm is a tetrahedron, which is simpler to deal with.
+
+            // If the origin is in the tetrahedron of points 0, 2, 3, 4
+            if (isOriginInTetrahedron(points[0], points[2], points[3], points[4]) == 0) {
+                // We use the point 4 instead of point 1 for the initial tetrahedron
+                suppPointsA[1] = suppPointsA[4];
+                suppPointsB[1] = suppPointsB[4];
+                points[1] = points[4];
+            }
+            else if (isOriginInTetrahedron(points[1], points[2], points[3], points[4]) == 0) {  // If the origin is in the tetrahedron of points 1, 2, 3, 4
+                // We use the point 4 instead of point 0 for the initial tetrahedron
+                suppPointsA[0] = suppPointsA[0];
+                suppPointsB[0] = suppPointsB[0];
+                points[0] = points[0];
+            }
+            else {
+                // The origin is not in the initial polytope
+                return false;
+            }
+
+            // The polytope contains now 4 vertices
+            nbVertices = 4;
         }
+        case 4: {
+            // The simplex computed by the GJK algorithm is a tetrahedron. Here we check
+            // if this tetrahedron contains the origin. If it is the case, we keep it and
+            // otherwise we remove the wrong vertex of the tetrahedron and go in the case
+            // where the GJK algorithm compute a simplex of three vertices.
+
+            // Check if the tetrahedron contains the origin (or wich is the wrong vertex otherwise)
+            int badVertex = isOriginInTetrahedron(points[0], points[1], points[2], points[3]);
+
+            // If the origin is in the tetrahedron
+            if (badVertex == 0) {
+                // The tetrahedron is a correct initial polytope for the EPA algorithm.
+                // Therefore, we construct the tetrahedron.
+
+                // Comstruct the 4 triangle faces of the tetrahedron
+                TriangleEPA* face0 = triangleStore.newTriangle(points, 0, 1, 2);
+                TriangleEPA* face1 = triangleStore.newTriangle(points, 0, 3, 1);
+                TriangleEPA* face2 = triangleStore.newTriangle(points, 0, 2, 3);
+                TriangleEPA* face3 = triangleStore.newTriangle(points, 1, 3, 2);
+
+                // If the constructed tetrahedron is not correct
+                if (!(face0 && face1 && face2 && face3 && face0->getDistSquare() > 0.0 &&
+                      face1->getDistSquare() > 0.0 && face2->getDistSquare() > 0.0 && face3->getDistSquare() > 0.0)) {
+                    return false;
+                }
+
+                // Associate the edges of neighbouring triangle faces
+                EdgeEPA(face0, 0).link(EdgeEPA(face1, 2));
+                EdgeEPA(face0, 1).link(EdgeEPA(face3, 2));
+                EdgeEPA(face0, 2).link(EdgeEPA(face2, 0));
+                EdgeEPA(face1, 0).link(EdgeEPA(face2, 2));
+                EdgeEPA(face1, 1).link(EdgeEPA(face3, 0));
+                EdgeEPA(face2, 1).link(EdgeEPA(face3, 1));
+
+                // Add the triangle faces in the candidate heap
+                addFaceCandidate(face0, triangleHeap, nbTriangles, DBL_MAX);
+                addFaceCandidate(face1, triangleHeap, nbTriangles, DBL_MAX);
+                addFaceCandidate(face2, triangleHeap, nbTriangles, DBL_MAX);
+                addFaceCandidate(face3, triangleHeap, nbTriangles, DBL_MAX);
+
+                break;
+            }
+
+            // If the tetrahedron contains a wrong vertex (the origin is not inside the tetrahedron)
+            if (badVertex < 4) {
+                // Replace the wrong vertex with the point 5 (if it exists)
+                suppPointsA[badVertex-1] = suppPointsA[4];
+                suppPointsB[badVertex-1] = suppPointsB[4];
+                points[badVertex-1] = points[4];
+            }
+
+            // We have removed the wrong vertex
+            nbVertices = 3;
+        }
+        case 3: {
+            // The GJK algorithm returned a triangle that contains the origin.
+            // We need two new vertices to obtain a hexahedron. The two new vertices
+            // are the support points in the "n" and "-n" direction where "n" is the
+            // normal of the triangle.
+
+            // Compute the normal of the triangle
+            Vector3D v1 = points[1] - points[0];
+            Vector3D v2 = points[2] - points[0];
+            Vector3D n = v1.cross(v2);
+
+            // Compute the two new vertices to obtain a hexahedron
+            suppPointsA[3] = boundingVolume1->getSupportPoint(n, OBJECT_MARGIN);
+            suppPointsB[3] = boundingVolume2->getSupportPoint(n.getOpposite(), OBJECT_MARGIN);
+            points[3] = suppPointsA[3] - suppPointsB[3];
+            suppPointsA[4] = boundingVolume1->getSupportPoint(n.getOpposite(), OBJECT_MARGIN);
+            suppPointsB[4] = boundingVolume2->getSupportPoint(n, OBJECT_MARGIN);
+            points[4] = suppPointsA[4] - suppPointsB[4];
+
+            // Construct the triangle faces
+            TriangleEPA* face0 = triangleStore.newTriangle(points, 0, 1, 3);
+            TriangleEPA* face1 = triangleStore.newTriangle(points, 1, 2, 3);
+            TriangleEPA* face2 = triangleStore.newTriangle(points, 2, 0, 3);
+            TriangleEPA* face3 = triangleStore.newTriangle(points, 0, 2, 4);
+            TriangleEPA* face4 = triangleStore.newTriangle(points, 2, 1, 4);
+            TriangleEPA* face5 = triangleStore.newTriangle(points, 1, 0, 4);
+
+            // If the polytope hasn't been correctly constructed
+            if (!(face0 && face1 && face2 && face3 && face4 && face5 &&
+                  face0->getDistSquare() > 0.0 && face1->getDistSquare() > 0.0 &&
+                  face2->getDistSquare() > 0.0 && face3->getDistSquare() > 0.0 &&
+                  face4->getDistSquare() > 0.0 && face5->getDistSquare() > 0.0)) {
+                return false;
+            }
+
+            // Associate the edges of neighbouring faces
+            EdgeEPA(face0, 1).link(EdgeEPA(face1, 2));
+            EdgeEPA(face1, 1).link(EdgeEPA(face2, 2));
+            EdgeEPA(face2, 1).link(EdgeEPA(face0, 2));
+            EdgeEPA(face0, 0).link(EdgeEPA(face5, 0));
+            EdgeEPA(face1, 0).link(EdgeEPA(face4, 0));
+            EdgeEPA(face2, 0).link(EdgeEPA(face3, 0));
+            EdgeEPA(face3, 1).link(EdgeEPA(face4, 2));
+            EdgeEPA(face4, 1).link(EdgeEPA(face5, 2));
+            EdgeEPA(face5, 1).link(EdgeEPA(face3, 2));
+
+            // Add the candidate faces in the heap
+            addFaceCandidate(face0, triangleHeap, nbTriangles, DBL_MAX);
+            addFaceCandidate(face1, triangleHeap, nbTriangles, DBL_MAX);
+            addFaceCandidate(face2, triangleHeap, nbTriangles, DBL_MAX);
+            addFaceCandidate(face3, triangleHeap, nbTriangles, DBL_MAX);
+            addFaceCandidate(face4, triangleHeap, nbTriangles, DBL_MAX);
+            addFaceCandidate(face5, triangleHeap, nbTriangles, DBL_MAX);
+
+            nbVertices = 5;
+        }
+        break;
     }
+
+    // At this point, we have a polytope that contains the origin. Therefore, we
+    // can run the EPA algorithm.
+
+    if (nbTriangles == 0) {
+        return false;
+    }
+
+    TriangleEPA* triangle = 0;
+    double upperBoundSquarePenDepth = DBL_MAX;
+
+    do {
+        triangle = triangleHeap[0];
+
+        // Get the next candidate face (the face closest to the origin)
+        std::pop_heap(&triangleHeap[0], &triangleHeap[nbTriangles], triangleComparison);
+        nbTriangles--;
+
+        // If the candidate face in the heap is not obsolete
+        if (!triangle->getIsObsolete()) {
+            // If we have reached the maximum number of support points
+            if (nbVertices == MAX_SUPPORT_POINTS) {
+                assert(false);
+                break;
+            }
+
+            // Compute the support point of the Minkowski difference (A-B) in the closest point direction
+            suppPointsA[nbVertices] = boundingVolume1->getSupportPoint(triangle->getClosestPoint(), OBJECT_MARGIN);
+            suppPointsB[nbVertices] = boundingVolume2->getSupportPoint(triangle->getClosestPoint().getOpposite());
+            points[nbVertices] = suppPointsA[nbVertices] - suppPointsB[nbVertices];
+
+            int indexNewVertex = nbVertices;
+            nbVertices++;
+
+            // Update the upper bound of the penetration depth
+            double wDotv = points[indexNewVertex].dot(triangle->getClosestPoint());
+            assert(wDotv > 0.0);
+            double wDotVSquare = wDotv * wDotv / triangle->getDistSquare();
+            if (wDotVSquare < upperBoundSquarePenDepth) {
+                upperBoundSquarePenDepth = wDotVSquare;
+            }
+
+            // Compute the error
+            double error = wDotv - triangle->getDistSquare();
+            if (error <= std::max(tolerance, REL_ERROR_SQUARE * wDotv) ||
+                points[indexNewVertex] == points[(*triangle)[0]] ||
+                points[indexNewVertex] == points[(*triangle)[1]] ||
+                points[indexNewVertex] == points[(*triangle)[2]]) {
+                break;
+            }
+
+            // Now, we compute the silhouette cast by the new vertex.
+            // The current triangle face will not be in the convex hull.
+            // We start the local recursive silhouette algorithm from
+            // the current triangle face.
+            int i = triangleStore.getNbTriangles();
+            if (!triangle->computeSilhouette(points, indexNewVertex, triangleStore)) {
+                break;
+            }
+
+            // Construct the new polytope by constructing triangle faces from the
+            // silhouette to the new vertex of the polytope in order that the new
+            // polytope is always convex
+            while(i != triangleStore.getNbTriangles()) {
+                TriangleEPA* newTriangle = &triangleStore[i];
+
+                addFaceCandidate(newTriangle, triangleHeap, nbTriangles, upperBoundSquarePenDepth);
+                i++;
+            }
+        }
+
+    } while(nbTriangles > 0 && triangleHeap[0]->getDistSquare() <= upperBoundSquarePenDepth);
+
+    // Compute the contact info
+    v = triangle->getClosestPoint();
+    Vector3D pA = triangle->computeClosestPointOfObject(suppPointsA);
+    Vector3D pB = triangle->computeClosestPointOfObject(suppPointsB);
+    Vector3D diff = pB - pA;
+    Vector3D normal = diff.getUnit();
+    double penetrationDepth = diff.length();
+    assert(penetrationDepth > 0.0);
+    contactInfo = new ContactInfo(boundingVolume1->getBodyPointer(), boundingVolume2->getBodyPointer(),
+                                  normal, penetrationDepth, pA, pB);
+    
+    return true;
 }

src/collision/EPA/EPAAlgorithm.h

@@ -30,6 +30,8 @@
 #include "../../body/NarrowBoundingVolume.h"
 #include "../ContactInfo.h"
 #include "../../mathematics/mathematics.h"
+#include "TriangleEPA.h"
+#include <algorithm>
 
 // ReactPhysics3D namespace
 namespace reactphysics3d {
@@ -38,6 +40,20 @@ namespace reactphysics3d {
 const unsigned int MAX_SUPPORT_POINTS = 100;    // Maximum number of support points of the polytope
 const unsigned int MAX_FACETS = 200;            // Maximum number of facets of the polytope
 
+
+// Class TriangleComparison that allow the comparison of two triangles in the heap
+// The comparison between two triangles is made using their square distance to the closest
+// point to the origin. The goal is that in the heap, the first triangle is the one with the
+// smallest square distance.
+class TriangleComparison {
+    public:
+        // Comparison operator
+        bool operator()(const TriangleEPA* face1, const TriangleEPA* face2) {
+            return (face1->getDistSquare() > face2->getDistSquare());
+        }
+};
+
+
 /*  -------------------------------------------------------------------
     Class EPAAlgorithm :
         This class is the implementation of the Expanding Polytope Algorithm (EPA).
@@ -54,10 +70,12 @@ const unsigned int MAX_FACETS = 200;            // Maximum number of facets of t
 */
 class EPAAlgorithm {
     private:
+        TriangleComparison triangleComparison;           // Triangle comparison operator
 
-
+        void addFaceCandidate(TriangleEPA* triangle, TriangleEPA** heap,
-        bool isOrigininInTetrahedron(const Vector3D& p1, const Vector3D& p2,
+                              uint& nbTriangles, double upperBoundSquarePenDepth);      // Add a triangle face in the candidate triangle heap
-                                     const Vector3D& p3, const Vector3D& p4) const; // Return true if the origin is in the tetrahedron
+        int isOriginInTetrahedron(const Vector3D& p1, const Vector3D& p2,
+                                  const Vector3D& p3, const Vector3D& p4) const;        // Decide if the origin is in the tetrahedron
 
     public:
         EPAAlgorithm();         // Constructor
@@ -68,6 +86,20 @@ class EPAAlgorithm {
                                                      Vector3D& v, ContactInfo*& contactInfo);                         // Compute the penetration depth with EPA algorithm
 };
 
+// Add a triangle face in the candidate triangle heap in the EPA algorithm
+inline void EPAAlgorithm::addFaceCandidate(TriangleEPA* triangle, TriangleEPA** heap,
+                                           uint& nbTriangles, double upperBoundSquarePenDepth) {
+    
+    // If the closest point of the affine hull of triangle points is internal to the triangle and
+    // if the distance of the closest point from the origin is at most the penetration depth upper bound
+    if (triangle->isClosestPointInternalToTriangle() && triangle->getDistSquare() <= upperBoundSquarePenDepth) {
+        // Add the triangle face to the list of candidates
+        heap[nbTriangles] = triangle;
+        nbTriangles++;
+        std::push_heap(&heap[0], &heap[nbTriangles], triangleComparison);
+    }
+}
+
 } // End of ReactPhysics3D namespace
 
 #endif

src/collision/EPA/TriangleEPA.h

@@ -118,8 +118,8 @@ inline bool TriangleEPA::isVisibleFromVertex(const Vector3D* vertices, uint inde
 // Compute the point of an object closest to the origin
 inline Vector3D TriangleEPA::computeClosestPointOfObject(const Vector3D* supportPointsOfObject) const {
     const Vector3D& p0 = supportPointsOfObject[indicesVertices[0]];
-    return p0 + (lambda1 * (supportPointsOfObject[indicesVertices[1]] - p0) +
+    return p0 + 1.0/det * (lambda1 * (supportPointsOfObject[indicesVertices[1]] - p0) +
-                 lambda2 * 1.0/det * (supportPointsOfObject[indicesVertices[2]] - p0));
+                           lambda2 * (supportPointsOfObject[indicesVertices[2]] - p0));
 }
 
 // Access operator