reactphysics3d/src/collision/SATAlgorithm.cpp

/********************************************************************************
* ReactPhysics3D physics library, http://code.google.com/p/reactphysics3d/      *
* Copyright (c) 2010 Daniel Chappuis                                            *
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// Libraries
#include "SATAlgorithm.h"
#include "../shapes/BoxShape.h"
#include "../body/RigidBody.h"
#include "../constraint/Contact.h"
#include "../mathematics/Transform.h"
#include <algorithm>
#include <cfloat>
#include <cmath>
#include <cassert>

// TODO : SAT Algorithm for box-box collision does not work anymore since the use of
//        transform. Maybe a problem with the computation of the normal vector
//        Anyway, the GJK algorithm should be used instead

// We want to use the ReactPhysics3D namespace
using namespace reactphysics3d;

// Constructor
SATAlgorithm::SATAlgorithm() {

}

// Destructor
SATAlgorithm::~SATAlgorithm() {

}

// Return true and compute a contact info if the two bounding volume collide.
// The method returns false if there is no collision between the two bounding volumes.
bool SATAlgorithm::testCollision(const Body* body1, const Body* body2, ContactInfo*& contactInfo) {
    
    assert(body1 != body2);

    const Transform& transform1 = body1->getTransform();
    const Transform& transform2 = body2->getTransform();
    const RigidBody* rigidBody1 = dynamic_cast<const RigidBody*>(body1);
    const RigidBody* rigidBody2 = dynamic_cast<const RigidBody*>(body2);
    const BoxShape* obb1 = dynamic_cast<const BoxShape*>(rigidBody1->getShape());
    const BoxShape* obb2 = dynamic_cast<const BoxShape*>(rigidBody2->getShape());

    // If the two bounding volumes are OBB
    if (obb1 && obb2) {
        // Compute the collision test between two OBB
        return computeCollisionTest(obb1, transform1, obb2, transform2, contactInfo);
    }
    else {
        return false;
    }
}


// This method returns true and computes a contact info if the two OBB intersect.
// This method implements the separating algorithm between two OBBs. The goal of this method is to test if the
// two OBBs intersect or not. If they intersect we report a contact info and the method returns true. If
// they don't intersect, the method returns false. The separation axis that have to be tested for two
// OBB are the six face normals (3 for each OBB) and the nine vectors V = Ai x Bj where Ai is the ith face normal
// vector of OBB 1 and Bj is the jth face normal vector of OBB 2. We will use the notation Ai for the ith face
// normal of OBB 1 and Bj for the jth face normal of OBB 2.
bool SATAlgorithm::computeCollisionTest(const BoxShape* obb1, const Transform& transform1,
                                        const BoxShape* obb2, const Transform& transform2, ContactInfo*& contactInfo) const {


    double center;                              // Center of a projection interval
    double radius1;                             // Radius of projection interval [min1, max1]
    double radius2;                             // Radius of projection interval [min2, max2]
    double min1;                                // Minimum of interval 1
    double max1;                                // Maximum of interval 1
    double min2;                                // Minimm of interval 2
    double max2;                                // Maximum of interval 2
    Vector3D normal;                            // Contact normal (correspond to the separation axis with the smallest positive penetration depth)
                                                // The contact normal point out of OBB1 toward OBB2
    double minPenetrationDepth = DBL_MAX;       // Minimum penetration depth detected among all separated axis
    const double cutoff = 0.99;                 // Cutoff for cosine of angles between box axes
    bool existsParallelPair = false;            // True if there exists two face normals that are parallel.
                                                // This is used because if a parallel pair exists, it is sufficient
                                                // to test only the face normals of the OBBs for separation. Two nearly
                                                // parallel faces can lead to all face normal tests reporting no separation
                                                // along those directions. The cross product directions are tested next, but
                                                // Ai x Bj is nearly the zero vector and can cause a report that the two OBBs
                                                // are not intersecting when in fact they are.
    double c[3][3];                             // c[i][j] = DotProduct(obb1.Ai, obb2.Bj)
    double absC[3][3];                          // absC[i][j] = abs(DotProduct(obb1.Ai, obb2.Bj))
    double udc1[3];                             // DotProduct(obb1.Ai, obb2.center - obb1.center)
    double udc2[3];                             // DotProduct(obb2.Ai, obb2.center - obb1.center)
    
    //Vector3D boxDistance = obb2->getCenter() - obb1->getCenter();   // Vector between the centers of the OBBs
    Vector3D boxDistance = transform2.getPosition() - transform1.getPosition();   // Vector between the centers of the OBBs

    // Axis A0
    for (int i=0; i<3; ++i) {
        c[0][i] = transform1.getOrientation().getColumn(0).dot(transform2.getOrientation().getColumn(i));
        absC[0][i] = fabs(c[0][i]);
        if (absC[0][i] > cutoff) {
            existsParallelPair = true;
        }
    }
    udc1[0] = transform1.getOrientation().getColumn(0).dot(boxDistance);
    center = udc1[0];
    radius1 = obb1->getExtent().getX();
    radius2 = obb2->getExtent().getX()*absC[0][0] + obb2->getExtent().getY()*absC[0][1] + obb2->getExtent().getZ() * absC[0][2];
    min1 = -radius1;
    max1 = radius1;
    min2 = center - radius2;
    max2 = center + radius2;
    double penetrationDepth = computePenetrationDepth(min1, max1, min2, max2);
    if (penetrationDepth < 0) { // We have found a separation axis, therefore the two OBBs don't collide
        return false;
    }
    else if (penetrationDepth < minPenetrationDepth) {  // Interval 1 and 2 overlap with a smaller penetration depth on this axis
        minPenetrationDepth = penetrationDepth;                         // Update the minimum penetration depth
        normal = computeContactNormal(transform1.getOrientation().getColumn(0), boxDistance);   // Compute the contact normal with the correct sign
    }

    // Axis A1
    for (int i=0; i<3; ++i) {
        c[1][i] = transform1.getOrientation().getColumn(1).dot(transform2.getOrientation().getColumn(i));
        absC[1][i] = fabs(c[1][i]);
        if (absC[1][i] > cutoff) {
            existsParallelPair = true;
        }
    }
    udc1[1] = transform1.getOrientation().getColumn(1).dot(boxDistance);
    center = udc1[1];
    radius1 = obb1->getExtent().getY();
    radius2 = obb2->getExtent().getX()*absC[1][0] + obb2->getExtent().getY()*absC[1][1] + obb2->getExtent().getZ() * absC[1][2];
    min1 = -radius1;
    max1 = radius1;
    min2 = center - radius2;
    max2 = center + radius2;
    penetrationDepth = computePenetrationDepth(min1, max1, min2, max2);
    if (penetrationDepth < 0) { // We have found a separation axis, therefore the two OBBs don't collide
        return false;
    }
    else if (penetrationDepth < minPenetrationDepth) {  // Interval 1 and 2 overlap with a smaller penetration depth on this axis
        minPenetrationDepth = penetrationDepth;                         // Update the minimum penetration depth
        normal = computeContactNormal(transform1.getOrientation().getColumn(1), boxDistance);   // Compute the contact normal with the correct sign
    }

    // Axis A2
    for (int i=0; i<3; ++i) {
        c[2][i] = transform1.getOrientation().getColumn(2).dot(transform2.getOrientation().getColumn(i));
        absC[2][i] = fabs(c[2][i]);
        if (absC[2][i] > cutoff) {
            existsParallelPair = true;
        }
    }
    udc1[2] = transform1.getOrientation().getColumn(2).dot(boxDistance);
    center = udc1[2];
    radius1 = obb1->getExtent().getZ();
    radius2 = obb2->getExtent().getX()*absC[2][0] + obb2->getExtent().getY()*absC[2][1] + obb2->getExtent().getZ()*absC[2][2];
    min1 = -radius1;
    max1 = radius1;
    min2 = center - radius2;
    max2 = center + radius2;
    penetrationDepth = computePenetrationDepth(min1, max1, min2, max2);
    if (penetrationDepth < 0) { // We have found a separation axis, therefore the two OBBs don't collide
        return false;
    }
    else if (penetrationDepth < minPenetrationDepth) {  // Interval 1 and 2 overlap with a smaller penetration depth on this axis
        minPenetrationDepth = penetrationDepth;                         // Update the minimum penetration depth
        normal = computeContactNormal(transform1.getOrientation().getColumn(2), boxDistance);   // Compute the contact normal with the correct sign
    }

    // Axis B0
    udc2[0] = transform2.getOrientation().getColumn(0).dot(boxDistance);
    center = udc2[0];
    radius1 = obb1->getExtent().getX()*absC[0][0] + obb1->getExtent().getY()*absC[1][0] + obb1->getExtent().getZ() * absC[2][0];
    radius2 = obb2->getExtent().getX();
    min1 = -radius1;
    max1 = radius1;
    min2 = center - radius2;
    max2 = center + radius2;
    penetrationDepth = computePenetrationDepth(min1, max1, min2, max2);
    if (penetrationDepth < 0) { // We have found a separation axis, therefore the two OBBs don't collide
        return false;
    }
    else if (penetrationDepth < minPenetrationDepth) {  // Interval 1 and 2 overlap with a smaller penetration depth on this axis
        minPenetrationDepth = penetrationDepth;                         // Update the minimum penetration depth
        normal = computeContactNormal(transform2.getOrientation().getColumn(0), boxDistance);   // Compute the contact normal with the correct sign
    }

    // Axis B1
    udc2[1] = transform2.getOrientation().getColumn(1).dot(boxDistance);
    center = udc2[1];
    radius1 = obb1->getExtent().getX()*absC[0][1] + obb1->getExtent().getY()*absC[1][1] + obb1->getExtent().getZ() * absC[2][1];
    radius2 = obb2->getExtent().getY();
    min1 = - radius1;
    max1 = radius1;
    min2 = center - radius2;
    max2 = center + radius2;
    penetrationDepth = computePenetrationDepth(min1, max1, min2, max2);
    if (penetrationDepth < 0) { // We have found a separation axis, therefore the two OBBs don't collide
        return false;
    }
    else if (penetrationDepth < minPenetrationDepth) {  // Interval 1 and 2 overlap with a smaller penetration depth on this axis
        minPenetrationDepth = penetrationDepth;                         // Update the minimum penetration depth
        normal = computeContactNormal(transform2.getOrientation().getColumn(1), boxDistance);   // Compute the contact normal with the correct sign
    }

    // Axis B2
    udc2[2] = transform2.getOrientation().getColumn(2).dot(boxDistance);
    center = udc2[2];
    radius1 = obb1->getExtent().getX()*absC[0][2] + obb1->getExtent().getY()*absC[1][2] + obb1->getExtent().getZ()*absC[2][2];
    radius2 = obb2->getExtent().getZ();
    min1 = - radius1;
    max1 = radius1;
    min2 = center - radius2;
    max2 = center + radius2;
    penetrationDepth = computePenetrationDepth(min1, max1, min2, max2);
    if (penetrationDepth < 0) { // We have found a separation axis, therefore the two OBBs don't collide
        return false;
    }
    else if (penetrationDepth < minPenetrationDepth) {  // Interval 1 and 2 overlap with a smaller penetration depth on this axis
        minPenetrationDepth = penetrationDepth;                         // Update the minimum penetration depth
        normal = computeContactNormal(transform2.getOrientation().getColumn(2), boxDistance);   // Compute the contact normal with the correct sign
    }

    // If there exists a parallel pair of face normals
    if (existsParallelPair) {
        // There exists a parallel pair of face normals and we have already checked all the face
        // normals for separation. Therefore the OBBs must intersect

        // Compute the contact info
        contactInfo = new ContactInfo(obb1->getBodyPointer(), obb2->getBodyPointer(), normal.getUnit(), minPenetrationDepth);
        
        return true;
    }

    // Axis A0 x B0
    center = udc1[2] * c[1][0] - udc1[1] * c[2][0];
    radius1 = obb1->getExtent().getY() * absC[2][0] + obb1->getExtent().getZ() * absC[1][0];
    radius2 = obb2->getExtent().getY() * absC[0][2] + obb2->getExtent().getZ() * absC[0][1];
    min1 = -radius1;
    max1 = radius1;
    min2 = center - radius2;
    max2 = center + radius2;
    penetrationDepth = computePenetrationDepth(min1, max1, min2, max2);
    if (penetrationDepth < 0) { // We have found a separation axis, therefore the two OBBs don't collide
        return false;
    }
    else if (penetrationDepth < minPenetrationDepth) {  // Interval 1 and 2 overlap with a smaller penetration depth on this axis
        minPenetrationDepth = penetrationDepth;                                                         // Update the minimum penetration depth
        normal = computeContactNormal(transform1.getOrientation().getColumn(0).cross(transform2.getOrientation().getColumn(0)), boxDistance);    // Compute the contact normal with the correct sign
    }

    // Axis A0 x B1
    center = udc1[2] * c[1][1] - udc1[1] * c[2][1];
    radius1 = obb1->getExtent().getY() * absC[2][1] + obb1->getExtent().getZ() * absC[1][1];
    radius2 = obb2->getExtent().getX() * absC[0][2] + obb2->getExtent().getZ() * absC[0][0];
    min1 = -radius1;
    max1 = radius1;
    min2 = center - radius2;
    max2 = center + radius2;
    penetrationDepth = computePenetrationDepth(min1, max1, min2, max2);
    if (penetrationDepth < 0) { // We have found a separation axis, therefore the two OBBs don't collide
        return false;
    }
    else if (penetrationDepth < minPenetrationDepth) {  // Interval 1 and 2 overlap with a smaller penetration depth on this axis
        minPenetrationDepth = penetrationDepth;                                                         // Update the minimum penetration depth
        normal = computeContactNormal(transform1.getOrientation().getColumn(0).cross(transform2.getOrientation().getColumn(1)), boxDistance);    // Compute the contact normal with the correct sign
    }

    // Axis A0 x B2
    center = udc1[2] * c[1][2] - udc1[1] * c[2][2];
    radius1 = obb1->getExtent().getY() * absC[2][2] + obb1->getExtent().getZ() * absC[1][2];
    radius2 = obb2->getExtent().getX() * absC[0][1] + obb2->getExtent().getY() * absC[0][0];
    min1 = -radius1;
    max1 = radius1;
    min2 = center - radius2;
    max2 = center + radius2;
    penetrationDepth = computePenetrationDepth(min1, max1, min2, max2);
    if (penetrationDepth < 0) { // We have found a separation axis, therefore the two OBBs don't collide
        return false;
    }
    else if (penetrationDepth < minPenetrationDepth) {  // Interval 1 and 2 overlap with a smaller penetration depth on this axis
        minPenetrationDepth = penetrationDepth;                                                         // Update the minimum penetration depth
        normal = computeContactNormal(transform1.getOrientation().getColumn(0).cross(transform2.getOrientation().getColumn(2)), boxDistance);    // Compute the contact normal with the correct sign
    }

    // Axis A1 x B0
    center = udc1[0] * c[2][0] - udc1[2] * c[0][0];
    radius1 = obb1->getExtent().getX() * absC[2][0] + obb1->getExtent().getZ() * absC[0][0];
    radius2 = obb2->getExtent().getY() * absC[1][2] + obb2->getExtent().getZ() * absC[1][1];
    min1 = -radius1;
    max1 = radius1;
    min2 = center - radius2;
    max2 = center + radius2;
    penetrationDepth = computePenetrationDepth(min1, max1, min2, max2);
    if (penetrationDepth < 0) { // We have found a separation axis, therefore the two OBBs don't collide
        return false;
    }
    else if (penetrationDepth < minPenetrationDepth) {  // Interval 1 and 2 overlap with a smaller penetration depth on this axis
        minPenetrationDepth = penetrationDepth;                                                         // Update the minimum penetration depth
        normal = computeContactNormal(transform1.getOrientation().getColumn(1).cross(transform2.getOrientation().getColumn(0)), boxDistance);    // Compute the contact normal with the correct sign
    }

    // Axis A1 x B1
    center = udc1[0] * c[2][1] - udc1[2] * c[0][1];
    radius1 = obb1->getExtent().getX() * absC[2][1] + obb1->getExtent().getZ() * absC[0][1];
    radius2 = obb2->getExtent().getX() * absC[1][2] + obb2->getExtent().getZ() * absC[1][0];
    min1 = -radius1;
    max1 = radius1;
    min2 = center - radius2;
    max2 = center + radius2;
    penetrationDepth = computePenetrationDepth(min1, max1, min2, max2);
    if (penetrationDepth < 0) { // We have found a separation axis, therefore the two OBBs don't collide
        return false;
    }
    else if (penetrationDepth < minPenetrationDepth) {  // Interval 1 and 2 overlap with a smaller penetration depth on this axis
        minPenetrationDepth = penetrationDepth;                                                         // Update the minimum penetration depth
        normal = computeContactNormal(transform1.getOrientation().getColumn(1).cross(transform2.getOrientation().getColumn(1)), boxDistance);    // Compute the contact normal with the correct sign
    }

    // Axis A1 x B2
    center = udc1[0] * c[2][2] - udc1[2] * c[0][2];
    radius1 = obb1->getExtent().getX() * absC[2][2] + obb1->getExtent().getZ() * absC[0][2];
    radius2 = obb2->getExtent().getX() * absC[1][1] + obb2->getExtent().getY() * absC[1][0];
    min1 = -radius1;
    max1 = radius1;
    min2 = center - radius2;
    max2 = center + radius2;
    penetrationDepth = computePenetrationDepth(min1, max1, min2, max2);
    if (penetrationDepth < 0) { // We have found a separation axis, therefore the two OBBs don't collide
        return false;
    }
    else if (penetrationDepth < minPenetrationDepth) {  // Interval 1 and 2 overlap with a smaller penetration depth on this axis
        minPenetrationDepth = penetrationDepth;                                                         // Update the minimum penetration depth
        normal = computeContactNormal(transform1.getOrientation().getColumn(1).cross(transform2.getOrientation().getColumn(2)), boxDistance);    // Compute the contact normal with the correct sign
    }

    // Axis A2 x B0
    center = udc1[1] * c[0][0] - udc1[0] * c[1][0];
    radius1 = obb1->getExtent().getX() * absC[1][0] + obb1->getExtent().getY() * absC[0][0];
    radius2 = obb2->getExtent().getY() * absC[2][2] + obb2->getExtent().getZ() * absC[2][1];
    min1 = -radius1;
    max1 = radius1;
    min2 = center - radius2;
    max2 = center + radius2;
    penetrationDepth = computePenetrationDepth(min1, max1, min2, max2);
    if (penetrationDepth < 0) { // We have found a separation axis, therefore the two OBBs don't collide
        return false;
    }
    else if (penetrationDepth < minPenetrationDepth) {  // Interval 1 and 2 overlap with a smaller penetration depth on this axis
        minPenetrationDepth = penetrationDepth;                                                         // Update the minimum penetration depth
        normal = computeContactNormal(transform1.getOrientation().getColumn(2).cross(transform2.getOrientation().getColumn(0)), boxDistance);    // Compute the contact normal with the correct sign
    }

    // Axis A2 x B1
    center = udc1[1] * c[0][1] - udc1[0] * c[1][1];
    radius1 = obb1->getExtent().getX() * absC[1][1] + obb1->getExtent().getY() * absC[0][1];
    radius2 = obb2->getExtent().getX() * absC[2][2] + obb2->getExtent().getZ() * absC[2][0];
    min1 = -radius1;
    max1 = radius1;
    min2 = center - radius2;
    max2 = center + radius2;
    penetrationDepth = computePenetrationDepth(min1, max1, min2, max2);
    if (penetrationDepth < 0) { // We have found a separation axis, therefore the two OBBs don't collide
        return false;
    }
    else if (penetrationDepth < minPenetrationDepth) {  // Interval 1 and 2 overlap with a smaller penetration depth on this axis
        minPenetrationDepth = penetrationDepth;                                                         // Update the minimum penetration depth
        normal = computeContactNormal(transform1.getOrientation().getColumn(2).cross(transform2.getOrientation().getColumn(1)), boxDistance);    // Compute the contact normal with the correct sign
    }

    // Axis A2 x B2
    center = udc1[1] * c[0][2] - udc1[0] * c[1][2];
    radius1 = obb1->getExtent().getX() * absC[1][2] + obb1->getExtent().getY() * absC[0][2];
    radius2 = obb2->getExtent().getX() * absC[2][1] + obb2->getExtent().getY() * absC[2][0];
    min1 = -radius1;
    max1 = radius1;
    min2 = center - radius2;
    max2 = center + radius2;
    penetrationDepth = computePenetrationDepth(min1, max1, min2, max2);
    if (penetrationDepth < 0) { // We have found a separation axis, therefore the two OBBs don't collide
        return false;
    }
    else if (penetrationDepth < minPenetrationDepth) {  // Interval 1 and 2 overlap with a smaller penetration depth on this axis
        minPenetrationDepth = penetrationDepth;                                                         // Update the minimum penetration depth
        normal = computeContactNormal(transform1.getOrientation().getColumn(2).cross(transform2.getOrientation().getColumn(2)), boxDistance);    // Compute the contact normal with the correct sign
    }

    // Compute the contact info
    contactInfo = new ContactInfo(obb1->getBodyPointer(), obb2->getBodyPointer(), normal.getUnit(), minPenetrationDepth);
    
    return true;
}

// This method computes and returns the penetration depth between two intervals. This method returns the computed
// penetration depth (note that it could return a negative penetration depth if the intervals are separated.
double SATAlgorithm::computePenetrationDepth(double min1, double max1, double min2, double max2) const {

    // Compute the length of both intervals
    double lengthInterval1 = max1 - min1;
    double lengthInterval2 = max2 - min2;

    // Compute the total length of both intervals
    double minExtreme = std::min(min1, min2);
    double maxExtreme = std::max(max1, max2);
    double lengthBothIntervals = maxExtreme - minExtreme;

    // Compute the current penetration depth
    return (lengthInterval1 + lengthInterval2) - lengthBothIntervals;
}