reactphysics3d/sources/collision/SATAlgorithm.cpp
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/********************************************************************************
* ReactPhysics3D physics library, http://code.google.com/p/reactphysics3d/ *
* Copyright (c) 2010 Daniel Chappuis *
*********************************************************************************
* *
* Permission is hereby granted, free of charge, to any person obtaining a copy *
* of this software and associated documentation files (the "Software"), to deal *
* in the Software without restriction, including without limitation the rights *
* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell *
* copies of the Software, and to permit persons to whom the Software is *
* furnished to do so, subject to the following conditions: *
* *
* The above copyright notice and this permission notice shall be included in *
* all copies or substantial portions of the Software. *
* *
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR *
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, *
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE *
* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER *
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, *
* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN *
* THE SOFTWARE. *
********************************************************************************/
// Libraries
#include "SATAlgorithm.h"
#include "../body/OBB.h"
#include "../body/RigidBody.h"
#include "../constraint/Contact.h"
#include <algorithm>
#include <cfloat>
#include <cmath>
#include <cassert>
// 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 BoundingVolume* const boundingVolume1, const BoundingVolume* const boundingVolume2, ContactInfo*& contactInfo) {
assert(boundingVolume1 != boundingVolume2);
// If the two bounding volumes are OBB
//const OBB* const obb1 = dynamic_cast<const OBB* const>(boundingVolume1);
//const OBB* const obb2 = dynamic_cast<const OBB* const>(boundingVolume2);
const OBB* const obb1 = dynamic_cast<const OBB* const>(boundingVolume1);
const OBB* const obb2 = dynamic_cast<const OBB* const>(boundingVolume2);
// If the two bounding volumes are OBB
if (obb1 && obb2) {
// Compute the collision test between two OBB
return computeCollisionTest(obb1, obb2, 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 OBB* const obb1, const OBB* const obb2, 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
// Axis A0
for (int i=0; i<3; ++i) {
c[0][i] = obb1->getAxis(0).scalarProduct(obb2->getAxis(i));
absC[0][i] = fabs(c[0][i]);
if (absC[0][i] > cutoff) {
existsParallelPair = true;
}
}
udc1[0] = obb1->getAxis(0).scalarProduct(boxDistance);
center = udc1[0];
radius1 = obb1->getExtent(0);
radius2 = obb2->getExtent(0)*absC[0][0] + obb2->getExtent(1)*absC[0][1] + obb2->getExtent(2) * 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(obb1->getAxis(0), boxDistance); // Compute the contact normal with the correct sign
}
// Axis A1
for (int i=0; i<3; ++i) {
c[1][i] = obb1->getAxis(1).scalarProduct(obb2->getAxis(i));
absC[1][i] = fabs(c[1][i]);
if (absC[1][i] > cutoff) {
existsParallelPair = true;
}
}
udc1[1] = obb1->getAxis(1).scalarProduct(boxDistance);
center = udc1[1];
radius1 = obb1->getExtent(1);
radius2 = obb2->getExtent(0)*absC[1][0] + obb2->getExtent(1)*absC[1][1] + obb2->getExtent(2) * 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(obb1->getAxis(1), boxDistance); // Compute the contact normal with the correct sign
}
// Axis A2
for (int i=0; i<3; ++i) {
c[2][i] = obb1->getAxis(2).scalarProduct(obb2->getAxis(i));
absC[2][i] = fabs(c[2][i]);
if (absC[2][i] > cutoff) {
existsParallelPair = true;
}
}
udc1[2] = obb1->getAxis(2).scalarProduct(boxDistance);
center = udc1[2];
radius1 = obb1->getExtent(2);
radius2 = obb2->getExtent(0)*absC[2][0] + obb2->getExtent(1)*absC[2][1] + obb2->getExtent(2)*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
}
// Axis B0
udc2[0] = obb2->getAxis(0).scalarProduct(boxDistance);
center = udc2[0];
radius1 = obb1->getExtent(0)*absC[0][0] + obb1->getExtent(1)*absC[1][0] + obb1->getExtent(2) * absC[2][0];
radius2 = obb2->getExtent(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(obb2->getAxis(0), boxDistance); // Compute the contact normal with the correct sign
}
// Axis B1
udc2[1] = obb2->getAxis(1).scalarProduct(boxDistance);
center = udc2[1];
radius1 = obb1->getExtent(0)*absC[0][1] + obb1->getExtent(1)*absC[1][1] + obb1->getExtent(2) * absC[2][1];
radius2 = obb2->getExtent(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(obb2->getAxis(1), boxDistance); // Compute the contact normal with the correct sign
}
// Axis B2
udc2[2] = obb2->getAxis(2).scalarProduct(boxDistance);
center = udc2[2];
radius1 = obb1->getExtent(0)*absC[0][2] + obb1->getExtent(1)*absC[1][2] + obb1->getExtent(2)*absC[2][2];
radius2 = obb2->getExtent(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(obb2->getAxis(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, obb2, normal.getUnit(), minPenetrationDepth);
return true;
}
// Axis A0 x B0
center = udc1[2] * c[1][0] - udc1[1] * c[2][0];
radius1 = obb1->getExtent(1) * absC[2][0] + obb1->getExtent(2) * absC[1][0];
radius2 = obb2->getExtent(1) * absC[0][2] + obb2->getExtent(2) * 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(obb1->getAxis(0).crossProduct(obb2->getAxis(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(1) * absC[2][1] + obb1->getExtent(2) * absC[1][1];
radius2 = obb2->getExtent(0) * absC[0][2] + obb2->getExtent(2) * 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(obb1->getAxis(0).crossProduct(obb2->getAxis(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(1) * absC[2][2] + obb1->getExtent(2) * absC[1][2];
radius2 = obb2->getExtent(0) * absC[0][1] + obb2->getExtent(1) * 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(obb1->getAxis(0).crossProduct(obb2->getAxis(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(0) * absC[2][0] + obb1->getExtent(2) * absC[0][0];
radius2 = obb2->getExtent(1) * absC[1][2] + obb2->getExtent(2) * 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(obb1->getAxis(1).crossProduct(obb2->getAxis(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(0) * absC[2][1] + obb1->getExtent(2) * absC[0][1];
radius2 = obb2->getExtent(0) * absC[1][2] + obb2->getExtent(2) * 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(obb1->getAxis(1).crossProduct(obb2->getAxis(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(0) * absC[2][2] + obb1->getExtent(2) * absC[0][2];
radius2 = obb2->getExtent(0) * absC[1][1] + obb2->getExtent(1) * 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(obb1->getAxis(1).crossProduct(obb2->getAxis(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(0) * absC[1][0] + obb1->getExtent(1) * absC[0][0];
radius2 = obb2->getExtent(1) * absC[2][2] + obb2->getExtent(2) * 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(obb1->getAxis(2).crossProduct(obb2->getAxis(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(0) * absC[1][1] + obb1->getExtent(1) * absC[0][1];
radius2 = obb2->getExtent(0) * absC[2][2] + obb2->getExtent(2) * 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(obb1->getAxis(2).crossProduct(obb2->getAxis(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(0) * absC[1][2] + obb1->getExtent(1) * absC[0][2];
radius2 = obb2->getExtent(0) * absC[2][1] + obb2->getExtent(1) * 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(obb1->getAxis(2).crossProduct(obb2->getAxis(2)), boxDistance); // Compute the contact normal with the correct sign
}
// Compute the contact info
contactInfo = new ContactInfo(obb1, obb2, 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;
}