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implementation of GJK and EPA collision detection algorithm continued

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git-svn-id: https://reactphysics3d.googlecode.com/svn/trunk@420 92aac97c-a6ce-11dd-a772-7fcde58d38e6
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chappuis.daniel 2011-02-11 14:51:09 +00:00
parent 3fd0610925
commit cd5fda4396
3 changed files with 345 additions and 8 deletions
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311
src/collision/EPA/EPAAlgorithm.cpp
View File

@ -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)
@ -50,7 +85,9 @@ 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
// Get the simplex computed previously by the GJK algorithm
@ -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;
}

38
src/collision/EPA/EPAAlgorithm.h
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@ -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
bool isOrigininInTetrahedron(const Vector3D& p1, const Vector3D& p2,
const Vector3D& p3, const Vector3D& p4) const; // Return true if the origin is in the tetrahedron
void addFaceCandidate(TriangleEPA* triangle, TriangleEPA** heap,
uint& nbTriangles, double upperBoundSquarePenDepth); // Add a triangle face in the candidate triangle heap
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

4
src/collision/EPA/TriangleEPA.h
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@ -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) +
lambda2 * 1.0/det * (supportPointsOfObject[indicesVertices[2]] - p0));
return p0 + 1.0/det * (lambda1 * (supportPointsOfObject[indicesVertices[1]] - p0) +
lambda2 * (supportPointsOfObject[indicesVertices[2]] - p0));
}
// Access operator