411 lines
20 KiB
C++
411 lines
20 KiB
C++
/********************************************************************************
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* ReactPhysics3D physics library, http://code.google.com/p/reactphysics3d/ *
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* Copyright (c) 2010-2012 Daniel Chappuis *
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*********************************************************************************
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* *
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* This software is provided 'as-is', without any express or implied warranty. *
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* In no event will the authors be held liable for any damages arising from the *
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* use of this software. *
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* *
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* Permission is granted to anyone to use this software for any purpose, *
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* including commercial applications, and to alter it and redistribute it *
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* freely, subject to the following restrictions: *
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* *
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* 1. The origin of this software must not be misrepresented; you must not claim *
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* that you wrote the original software. If you use this software in a *
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* product, an acknowledgment in the product documentation would be *
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* appreciated but is not required. *
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* *
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* 2. Altered source versions must be plainly marked as such, and must not be *
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* misrepresented as being the original software. *
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* *
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* 3. This notice may not be removed or altered from any source distribution. *
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* *
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********************************************************************************/
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// Libraries
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#include "EPAAlgorithm.h"
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#include "../GJK/GJKAlgorithm.h"
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#include "TrianglesStore.h"
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// We want to use the ReactPhysics3D namespace
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using namespace reactphysics3d;
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// Constructor
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EPAAlgorithm::EPAAlgorithm(MemoryPool<ContactInfo>& memoryPoolContactInfos)
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: mMemoryPoolContactInfos(memoryPoolContactInfos) {
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}
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// Destructor
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EPAAlgorithm::~EPAAlgorithm() {
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}
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// Decide if the origin is in the tetrahedron
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// Return 0 if the origin is in the tetrahedron and return the number (1,2,3 or 4) of
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// the vertex that is wrong if the origin is not in the tetrahedron
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int EPAAlgorithm::isOriginInTetrahedron(const Vector3& p1, const Vector3& p2,
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const Vector3& p3, const Vector3& p4) const {
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// Check vertex 1
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Vector3 normal1 = (p2-p1).cross(p3-p1);
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if (normal1.dot(p1) > 0.0 == normal1.dot(p4) > 0.0) {
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return 4;
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}
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// Check vertex 2
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Vector3 normal2 = (p4-p2).cross(p3-p2);
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if (normal2.dot(p2) > 0.0 == normal2.dot(p1) > 0.0) {
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return 1;
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}
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// Check vertex 3
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Vector3 normal3 = (p4-p3).cross(p1-p3);
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if (normal3.dot(p3) > 0.0 == normal3.dot(p2) > 0.0) {
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return 2;
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}
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// Check vertex 4
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Vector3 normal4 = (p2-p4).cross(p1-p4);
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if (normal4.dot(p4) > 0.0 == normal4.dot(p3) > 0.0) {
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return 3;
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}
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// The origin is in the tetrahedron, we return 0
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return 0;
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}
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// Compute the penetration depth with the EPA algorithms
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// This method computes the penetration depth and contact points between two
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// enlarged objects (with margin) where the original objects (without margin)
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// intersect. An initial simplex that contains origin has been computed with
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// GJK algorithm. The EPA Algorithm will extend this simplex polytope to find
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// the correct penetration depth
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bool EPAAlgorithm::computePenetrationDepthAndContactPoints(const Simplex& simplex,
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const CollisionShape* collisionShape1,
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const Transform& transform1,
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const CollisionShape* collisionShape2,
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const Transform& transform2,
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Vector3& v, ContactInfo*& contactInfo) {
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Vector3 suppPointsA[MAX_SUPPORT_POINTS]; // Support points of object A in local coordinates
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Vector3 suppPointsB[MAX_SUPPORT_POINTS]; // Support points of object B in local coordinates
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Vector3 points[MAX_SUPPORT_POINTS]; // Current points
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TrianglesStore triangleStore; // Store the triangles
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TriangleEPA* triangleHeap[MAX_FACETS]; // Heap that contains the face
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// candidate of the EPA algorithm
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// Transform a point from local space of body 2 to local
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// space of body 1 (the GJK algorithm is done in local space of body 1)
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Transform body2Tobody1 = transform1.inverse() * transform2;
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// Matrix that transform a direction from local
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// space of body 1 into local space of body 2
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Matrix3x3 rotateToBody2 = transform2.getOrientation().getMatrix().getTranspose() *
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transform1.getOrientation().getMatrix();
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// Get the simplex computed previously by the GJK algorithm
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unsigned int nbVertices = simplex.getSimplex(suppPointsA, suppPointsB, points);
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// Compute the tolerance
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decimal tolerance = MACHINE_EPSILON * simplex.getMaxLengthSquareOfAPoint();
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// Number of triangles in the polytope
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unsigned int nbTriangles = 0;
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// Clear the storing of triangles
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triangleStore.clear();
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// Select an action according to the number of points in the simplex
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// computed with GJK algorithm in order to obtain an initial polytope for
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// The EPA algorithm.
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switch(nbVertices) {
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case 1:
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// Only one point in the simplex (which should be the origin).
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// We have a touching contact with zero penetration depth.
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// We drop that kind of contact. Therefore, we return false
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return false;
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case 2: {
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// The simplex returned by GJK is a line segment d containing the origin.
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// We add two additional support points to construct a hexahedron (two tetrahedron
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// glued together with triangle faces. The idea is to compute three different vectors
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// v1, v2 and v3 that are orthogonal to the segment d. The three vectors are relatively
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// rotated of 120 degree around the d segment. The the three new points to
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// construct the polytope are the three support points in those three directions
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// v1, v2 and v3.
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// Direction of the segment
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Vector3 d = (points[1] - points[0]).getUnit();
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// Choose the coordinate axis from the minimal absolute component of the vector d
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int minAxis = d.getAbsoluteVector().getMinAxis();
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// Compute sin(60)
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const decimal sin60 = sqrt(3.0) * 0.5;
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// Create a rotation quaternion to rotate the vector v1 to get the vectors
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// v2 and v3
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Quaternion rotationQuat(d.x * sin60, d.y * sin60, d.z * sin60, 0.5);
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// Construct the corresponding rotation matrix
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Matrix3x3 rotationMat = rotationQuat.getMatrix();
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// Compute the vector v1, v2, v3
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Vector3 v1 = d.cross(Vector3(minAxis == 0, minAxis == 1, minAxis == 2));
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Vector3 v2 = rotationMat * v1;
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Vector3 v3 = rotationMat * v2;
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// Compute the support point in the direction of v1
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suppPointsA[2] = collisionShape1->getLocalSupportPoint(v1, OBJECT_MARGIN);
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suppPointsB[2] = body2Tobody1 * collisionShape2->getLocalSupportPoint(rotateToBody2 *
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(-v1),
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OBJECT_MARGIN);
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points[2] = suppPointsA[2] - suppPointsB[2];
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// Compute the support point in the direction of v2
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suppPointsA[3] = collisionShape1->getLocalSupportPoint(v2, OBJECT_MARGIN);
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suppPointsB[3] = body2Tobody1 * collisionShape2->getLocalSupportPoint(rotateToBody2 *
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(-v2),
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OBJECT_MARGIN);
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points[3] = suppPointsA[3] - suppPointsB[3];
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// Compute the support point in the direction of v3
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suppPointsA[4] = collisionShape1->getLocalSupportPoint(v3, OBJECT_MARGIN);
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suppPointsB[4] = body2Tobody1 * collisionShape2->getLocalSupportPoint(rotateToBody2 *
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(-v3),
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OBJECT_MARGIN);
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points[4] = suppPointsA[4] - suppPointsB[4];
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// Now we have an hexahedron (two tetrahedron glued together). We can simply keep the
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// tetrahedron that contains the origin in order that the initial polytope of the
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// EPA algorithm is a tetrahedron, which is simpler to deal with.
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// If the origin is in the tetrahedron of points 0, 2, 3, 4
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if (isOriginInTetrahedron(points[0], points[2], points[3], points[4]) == 0) {
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// We use the point 4 instead of point 1 for the initial tetrahedron
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suppPointsA[1] = suppPointsA[4];
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suppPointsB[1] = suppPointsB[4];
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points[1] = points[4];
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}
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// If the origin is in the tetrahedron of points 1, 2, 3, 4
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else if (isOriginInTetrahedron(points[1], points[2], points[3], points[4]) == 0) {
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// We use the point 4 instead of point 0 for the initial tetrahedron
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suppPointsA[0] = suppPointsA[4];
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suppPointsB[0] = suppPointsB[4];
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points[0] = points[4];
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}
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else {
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// The origin is not in the initial polytope
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return false;
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}
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// The polytope contains now 4 vertices
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nbVertices = 4;
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}
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case 4: {
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// The simplex computed by the GJK algorithm is a tetrahedron. Here we check
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// if this tetrahedron contains the origin. If it is the case, we keep it and
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// otherwise we remove the wrong vertex of the tetrahedron and go in the case
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// where the GJK algorithm compute a simplex of three vertices.
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// Check if the tetrahedron contains the origin (or wich is the wrong vertex otherwise)
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int badVertex = isOriginInTetrahedron(points[0], points[1], points[2], points[3]);
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// If the origin is in the tetrahedron
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if (badVertex == 0) {
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// The tetrahedron is a correct initial polytope for the EPA algorithm.
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// Therefore, we construct the tetrahedron.
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// Comstruct the 4 triangle faces of the tetrahedron
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TriangleEPA* face0 = triangleStore.newTriangle(points, 0, 1, 2);
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TriangleEPA* face1 = triangleStore.newTriangle(points, 0, 3, 1);
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TriangleEPA* face2 = triangleStore.newTriangle(points, 0, 2, 3);
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TriangleEPA* face3 = triangleStore.newTriangle(points, 1, 3, 2);
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// If the constructed tetrahedron is not correct
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if (!(face0 && face1 && face2 && face3 && face0->getDistSquare() > 0.0 &&
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face1->getDistSquare() > 0.0 && face2->getDistSquare() > 0.0 &&
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face3->getDistSquare() > 0.0)) {
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return false;
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}
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// Associate the edges of neighbouring triangle faces
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link(EdgeEPA(face0, 0), EdgeEPA(face1, 2));
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link(EdgeEPA(face0, 1), EdgeEPA(face3, 2));
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link(EdgeEPA(face0, 2), EdgeEPA(face2, 0));
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link(EdgeEPA(face1, 0), EdgeEPA(face2, 2));
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link(EdgeEPA(face1, 1), EdgeEPA(face3, 0));
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link(EdgeEPA(face2, 1), EdgeEPA(face3, 1));
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// Add the triangle faces in the candidate heap
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addFaceCandidate(face0, triangleHeap, nbTriangles, DECIMAL_LARGEST);
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addFaceCandidate(face1, triangleHeap, nbTriangles, DECIMAL_LARGEST);
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addFaceCandidate(face2, triangleHeap, nbTriangles, DECIMAL_LARGEST);
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addFaceCandidate(face3, triangleHeap, nbTriangles, DECIMAL_LARGEST);
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break;
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}
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// If the tetrahedron contains a wrong vertex (the origin is not inside the tetrahedron)
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if (badVertex < 4) {
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// Replace the wrong vertex with the point 5 (if it exists)
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suppPointsA[badVertex-1] = suppPointsA[4];
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suppPointsB[badVertex-1] = suppPointsB[4];
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points[badVertex-1] = points[4];
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}
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// We have removed the wrong vertex
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nbVertices = 3;
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}
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case 3: {
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// The GJK algorithm returned a triangle that contains the origin.
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// We need two new vertices to obtain a hexahedron. The two new vertices
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// are the support points in the "n" and "-n" direction where "n" is the
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// normal of the triangle.
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// Compute the normal of the triangle
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Vector3 v1 = points[1] - points[0];
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Vector3 v2 = points[2] - points[0];
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Vector3 n = v1.cross(v2);
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// Compute the two new vertices to obtain a hexahedron
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suppPointsA[3] = collisionShape1->getLocalSupportPoint(n, OBJECT_MARGIN);
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suppPointsB[3] = body2Tobody1 * collisionShape2->getLocalSupportPoint(rotateToBody2 *
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(-n),
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OBJECT_MARGIN);
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points[3] = suppPointsA[3] - suppPointsB[3];
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suppPointsA[4] = collisionShape1->getLocalSupportPoint(-n, OBJECT_MARGIN);
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suppPointsB[4] = body2Tobody1 * collisionShape2->getLocalSupportPoint(rotateToBody2 * n,
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OBJECT_MARGIN);
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points[4] = suppPointsA[4] - suppPointsB[4];
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// Construct the triangle faces
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TriangleEPA* face0 = triangleStore.newTriangle(points, 0, 1, 3);
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TriangleEPA* face1 = triangleStore.newTriangle(points, 1, 2, 3);
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TriangleEPA* face2 = triangleStore.newTriangle(points, 2, 0, 3);
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TriangleEPA* face3 = triangleStore.newTriangle(points, 0, 2, 4);
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TriangleEPA* face4 = triangleStore.newTriangle(points, 2, 1, 4);
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TriangleEPA* face5 = triangleStore.newTriangle(points, 1, 0, 4);
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// If the polytope hasn't been correctly constructed
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if (!(face0 && face1 && face2 && face3 && face4 && face5 &&
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face0->getDistSquare() > 0.0 && face1->getDistSquare() > 0.0 &&
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face2->getDistSquare() > 0.0 && face3->getDistSquare() > 0.0 &&
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face4->getDistSquare() > 0.0 && face5->getDistSquare() > 0.0)) {
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return false;
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}
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// Associate the edges of neighbouring faces
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link(EdgeEPA(face0, 1), EdgeEPA(face1, 2));
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link(EdgeEPA(face1, 1), EdgeEPA(face2, 2));
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link(EdgeEPA(face2, 1), EdgeEPA(face0, 2));
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link(EdgeEPA(face0, 0), EdgeEPA(face5, 0));
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link(EdgeEPA(face1, 0), EdgeEPA(face4, 0));
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link(EdgeEPA(face2, 0), EdgeEPA(face3, 0));
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link(EdgeEPA(face3, 1), EdgeEPA(face4, 2));
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link(EdgeEPA(face4, 1), EdgeEPA(face5, 2));
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link(EdgeEPA(face5, 1), EdgeEPA(face3, 2));
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// Add the candidate faces in the heap
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addFaceCandidate(face0, triangleHeap, nbTriangles, DECIMAL_LARGEST);
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addFaceCandidate(face1, triangleHeap, nbTriangles, DECIMAL_LARGEST);
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addFaceCandidate(face2, triangleHeap, nbTriangles, DECIMAL_LARGEST);
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addFaceCandidate(face3, triangleHeap, nbTriangles, DECIMAL_LARGEST);
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addFaceCandidate(face4, triangleHeap, nbTriangles, DECIMAL_LARGEST);
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addFaceCandidate(face5, triangleHeap, nbTriangles, DECIMAL_LARGEST);
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nbVertices = 5;
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}
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break;
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}
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// At this point, we have a polytope that contains the origin. Therefore, we
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// can run the EPA algorithm.
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if (nbTriangles == 0) {
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return false;
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}
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TriangleEPA* triangle = 0;
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decimal upperBoundSquarePenDepth = DECIMAL_LARGEST;
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do {
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triangle = triangleHeap[0];
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// Get the next candidate face (the face closest to the origin)
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std::pop_heap(&triangleHeap[0], &triangleHeap[nbTriangles], mTriangleComparison);
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nbTriangles--;
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// If the candidate face in the heap is not obsolete
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if (!triangle->getIsObsolete()) {
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// If we have reached the maximum number of support points
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if (nbVertices == MAX_SUPPORT_POINTS) {
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assert(false);
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break;
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}
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// Compute the support point of the Minkowski
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// difference (A-B) in the closest point direction
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suppPointsA[nbVertices] = collisionShape1->getLocalSupportPoint(
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triangle->getClosestPoint(), OBJECT_MARGIN);
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suppPointsB[nbVertices] = body2Tobody1 * collisionShape2->getLocalSupportPoint(
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rotateToBody2 * (-triangle->getClosestPoint()),
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OBJECT_MARGIN);
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points[nbVertices] = suppPointsA[nbVertices] - suppPointsB[nbVertices];
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int indexNewVertex = nbVertices;
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nbVertices++;
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// Update the upper bound of the penetration depth
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decimal wDotv = points[indexNewVertex].dot(triangle->getClosestPoint());
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assert(wDotv > 0.0);
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decimal wDotVSquare = wDotv * wDotv / triangle->getDistSquare();
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if (wDotVSquare < upperBoundSquarePenDepth) {
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upperBoundSquarePenDepth = wDotVSquare;
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}
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// Compute the error
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decimal error = wDotv - triangle->getDistSquare();
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if (error <= std::max(tolerance, REL_ERROR_SQUARE * wDotv) ||
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points[indexNewVertex] == points[(*triangle)[0]] ||
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points[indexNewVertex] == points[(*triangle)[1]] ||
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points[indexNewVertex] == points[(*triangle)[2]]) {
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break;
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}
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// Now, we compute the silhouette cast by the new vertex. The current triangle
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// face will not be in the convex hull. We start the local recursive silhouette
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// algorithm from the current triangle face.
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int i = triangleStore.getNbTriangles();
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if (!triangle->computeSilhouette(points, indexNewVertex, triangleStore)) {
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break;
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}
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// Add all the new triangle faces computed with the silhouette algorithm
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// to the candidates list of faces of the current polytope
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while(i != triangleStore.getNbTriangles()) {
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TriangleEPA* newTriangle = &triangleStore[i];
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addFaceCandidate(newTriangle, triangleHeap, nbTriangles, upperBoundSquarePenDepth);
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i++;
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}
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}
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} while(nbTriangles > 0 && triangleHeap[0]->getDistSquare() <= upperBoundSquarePenDepth);
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// Compute the contact info
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v = transform1.getOrientation().getMatrix() * triangle->getClosestPoint();
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Vector3 pALocal = triangle->computeClosestPointOfObject(suppPointsA);
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Vector3 pBLocal = body2Tobody1.inverse() * triangle->computeClosestPointOfObject(suppPointsB);
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Vector3 normal = v.getUnit();
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decimal penetrationDepth = v.length();
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assert(penetrationDepth > 0.0);
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// Create the contact info object
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contactInfo = new (mMemoryPoolContactInfos.allocateObject()) ContactInfo(normal,
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penetrationDepth,
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pALocal, pBLocal);
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return true;
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}
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