reactphysics3d/src/collision/EPA/EPAAlgorithm.h

/********************************************************************************
* ReactPhysics3D physics library, http://code.google.com/p/reactphysics3d/      *
* Copyright (c) 2011 Daniel Chappuis                                            *
*********************************************************************************
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#ifndef EPAAlgorithm_H
#define EPAAlgorithm_H

// Libraries
#include "../GJK/Simplex.h"
#include "../../body/NarrowBoundingVolume.h"
#include "../ContactInfo.h"
#include "../../mathematics/mathematics.h"
#include "TriangleEPA.h"
#include <algorithm>

// ReactPhysics3D namespace
namespace reactphysics3d {

// Constants
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).
        The EPA algorithm computes the penetration depth and contact points between
        two enlarged objects (with margin) where the original objects (without margin)
        intersect. The penetration depth of a pair of intersecting objects A and B is
        the length of a point on the boundary of the Minkowski sum (A-B) closest to the
        origin. The goal of the EPA algorithm is to start with an initial simplex polytope
        that contains the origin and expend it in order to find the point on the boundary
        of (A-B) that is closest to the origin. An initial simplex that contains origin
        has been computed wit GJK algorithm. The EPA Algorithm will extend this simplex
        polytope to find the correct penetration depth.
    -------------------------------------------------------------------
*/
class EPAAlgorithm {
    private:
        TriangleComparison triangleComparison;           // Triangle comparison operator

        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
        ~EPAAlgorithm();        // Destructor

        bool computePenetrationDepthAndContactPoints(Simplex simplex, const NarrowBoundingVolume* const boundingVolume1,
                                                     const NarrowBoundingVolume* const boundingVolume2,
                                                     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