Working on SAT algorithm between two polyhedra

This commit is contained in:
Daniel Chappuis 2017-05-16 07:10:44 +02:00
parent 7fb6f49149
commit 0ec21e36b9
6 changed files with 349 additions and 30 deletions

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@ -66,7 +66,7 @@ bool CapsuleVsCapsuleAlgorithm::testCollision(const NarrowPhaseInfo* narrowPhase
if (areParallelVectors(seg1, seg2)) {
// If the distance between the two segments is larger than the sum of the capsules radius (we do not have overlapping)
const decimal segmentsDistance = computeDistancePointToLineDistance(capsule1SegA, capsule1SegB, capsule2SegA);
const decimal segmentsDistance = computePointToLineDistance(capsule1SegA, capsule1SegB, capsule2SegA);
if (segmentsDistance >= sumRadius) {
// The capsule are parallel but their inner segment distance is larger than the sum of the capsules radius.

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@ -169,8 +169,7 @@ bool SATAlgorithm::testCollisionCapsuleVsConvexPolyhedron(const NarrowPhaseInfo*
const Vector3 capsuleSegB(0, capsuleShape->getHeight() * decimal(0.5), 0);
const Vector3 capsuleSegmentAxis = capsuleSegB - capsuleSegA;
// For each direction that is the cross product of the capsule inner segment and
// an edge of the polyhedron
// For each direction that is the cross product of the capsule inner segment and an edge of the polyhedron
for (uint e = 0; e < polyhedron->getNbHalfEdges(); e += 2) {
// Get an edge from the polyhedron (convert it into the capsule local-space)
@ -326,18 +325,327 @@ bool SATAlgorithm::isMinkowskiFaceCapsuleVsEdge(const Vector3& capsuleSegment, c
return capsuleSegment.dot(edgeAdjacentFace1Normal) * capsuleSegment.dot(edgeAdjacentFace2Normal) < decimal(0.0);
}
// Test collision between a triangle and a convex mesh
bool SATAlgorithm::testCollisionTriangleVsConvexMesh(const NarrowPhaseInfo* narrowPhaseInfo, ContactManifoldInfo& contactManifoldInfo) const {
assert(narrowPhaseInfo->collisionShape1->getType() == CollisionShapeType::TRIANGLE);
assert(narrowPhaseInfo->collisionShape2->getType() == CollisionShapeType::CONVEX_POLYHEDRON);
}
// Test collision between two convex meshes
bool SATAlgorithm::testCollisionConvexMeshVsConvexMesh(const NarrowPhaseInfo* narrowPhaseInfo, ContactManifoldInfo& contactManifoldInfo) const {
// Test collision between two convex polyhedrons
bool SATAlgorithm::testCollisionConvexPolyhedronVsConvexPolyhedron(const NarrowPhaseInfo* narrowPhaseInfo, ContactManifoldInfo& contactManifoldInfo) const {
assert(narrowPhaseInfo->collisionShape1->getType() == CollisionShapeType::CONVEX_POLYHEDRON);
assert(narrowPhaseInfo->collisionShape2->getType() == CollisionShapeType::CONVEX_POLYHEDRON);
const ConvexPolyhedronShape* polyhedron1 = static_cast<const ConvexPolyhedronShape*>(narrowPhaseInfo->collisionShape1);
const ConvexPolyhedronShape* polyhedron2 = static_cast<const ConvexPolyhedronShape*>(narrowPhaseInfo->collisionShape2);
const Transform polyhedron1ToPolyhedron2 = narrowPhaseInfo->shape2ToWorldTransform.getInverse() * narrowPhaseInfo->shape1ToWorldTransform;
const Transform polyhedron2ToPolyhedron1 = polyhedron1ToPolyhedron2.getInverse();
decimal minPenetrationDepth = DECIMAL_LARGEST;
uint minFaceIndex = 0;
bool isMinPenetrationFaceNormal = false;
bool isMinPenetrationFaceNormalPolyhedron1 = false;
Vector3 separatingEdge1A, separatingEdge1B;
Vector3 separatingEdge2A, separatingEdge2B;
Vector3 minEdgeVsEdgeSeparatingAxisPolyhedron2Space;
// Test all the face normals of the polyhedron 1 for separating axis
uint faceIndex;
decimal penetrationDepth = testFaceDirectionPolyhedronVsPolyhedron(polyhedron1, polyhedron2, polyhedron1ToPolyhedron2, faceIndex);
if (penetrationDepth <= decimal(0.0)) {
// We have found a separating axis
return false;
}
if (penetrationDepth < minPenetrationDepth) {
isMinPenetrationFaceNormal = true;
minPenetrationDepth = penetrationDepth;
minFaceIndex = faceIndex;
isMinPenetrationFaceNormalPolyhedron1 = true;
}
// Test all the face normals of the polyhedron 2 for separating axis
penetrationDepth = testFaceDirectionPolyhedronVsPolyhedron(polyhedron2, polyhedron1, polyhedron2ToPolyhedron1, faceIndex);
if (penetrationDepth <= decimal(0.0)) {
// We have found a separating axis
return false;
}
if (penetrationDepth < minPenetrationDepth) {
isMinPenetrationFaceNormal = true;
minPenetrationDepth = penetrationDepth;
minFaceIndex = faceIndex;
isMinPenetrationFaceNormalPolyhedron1 = false;
}
// Test the cross products of edges of polyhedron 1 with edges of polyhedron 2 for separating axis
for (uint i=0; i < polyhedron1->getNbHalfEdges(); i += 2) {
// Get an edge of polyhedron 1
HalfEdgeStructure::Edge edge1 = polyhedron1->getHalfEdge(i);
const Vector3 edge1A = polyhedron1ToPolyhedron2 * polyhedron1->getVertexPosition(edge1.vertexIndex);
const Vector3 edge1B = polyhedron1ToPolyhedron2 * polyhedron1->getVertexPosition(polyhedron1->getHalfEdge(edge1.nextEdgeIndex).vertexIndex);
const Vector3 edge1Direction = edge1B - edge1A;
for (uint j=0; j < polyhedron2->getNbHalfEdges(); j += 2) {
// Get an edge of polyhedron 2
HalfEdgeStructure::Edge edge2 = polyhedron2->getHalfEdge(j);
const Vector3 edge2A = polyhedron2->getVertexPosition(edge2.vertexIndex);
const Vector3 edge2B = polyhedron2->getVertexPosition(polyhedron2->getHalfEdge(edge2.nextEdgeIndex).vertexIndex);
const Vector3 edge2Direction = edge2B - edge2A;
// If the two edges build a minkowski face (and the cross product is
// therefore a candidate for separating axis
if (testEdgesBuildMinkowskiFace(polyhedron1, edge1, polyhedron2, edge2, polyhedron1ToPolyhedron2)) {
Vector3 separatingAxisPolyhedron2Space;
// Compute the penetration depth
decimal penetrationDepth = computeDistanceBetweenEdges(edge1A, edge2A, polyhedron2->getCentroid(),
edge1Direction, edge2Direction, separatingAxisPolyhedron2Space);
if (penetrationDepth <= decimal(0.0)) {
// We have found a separating axis
return false;
}
if (penetrationDepth < minPenetrationDepth) {
minPenetrationDepth = penetrationDepth;
isMinPenetrationFaceNormalPolyhedron1 = false;
isMinPenetrationFaceNormal = false;
separatingEdge1A = edge1A;
separatingEdge1B = edge1B;
separatingEdge2A = edge2A;
separatingEdge2B = edge2B;
minEdgeVsEdgeSeparatingAxisPolyhedron2Space = separatingAxisPolyhedron2Space;
}
}
}
}
assert(minPenetrationDepth > decimal(0.0));
assert((isMinPenetrationFaceNormal && minFaceIndex >= 0) || !isMinPenetrationFaceNormal);
// If the separation axis is a face normal
if (isMinPenetrationFaceNormal) {
const ConvexPolyhedronShape* referencePolyhedron = isMinPenetrationFaceNormalPolyhedron1 ? polyhedron1 : polyhedron2;
const ConvexPolyhedronShape* incidentPolyhedron = isMinPenetrationFaceNormalPolyhedron1 ? polyhedron2 : polyhedron1;
const Transform& referenceToIncidentTransform = isMinPenetrationFaceNormalPolyhedron1 ? polyhedron1ToPolyhedron2 : polyhedron2ToPolyhedron1;
const Transform& incidentToReferenceTransform = isMinPenetrationFaceNormalPolyhedron1 ? polyhedron2ToPolyhedron1 : polyhedron1ToPolyhedron2;
const Vector3 axisReferenceSpace = referencePolyhedron->getFaceNormal(minFaceIndex);
const Vector3 axisIncidentSpace = referenceToIncidentTransform.getOrientation() * axisReferenceSpace;
// Compute the world normal
const Vector3 normalWorld = isMinPenetrationFaceNormalPolyhedron1 ? narrowPhaseInfo->shape1ToWorldTransform.getOrientation() * axisReferenceSpace :
-(narrowPhaseInfo->shape2ToWorldTransform.getOrientation() * axisReferenceSpace);
// Get the reference face
HalfEdgeStructure::Face referenceFace = referencePolyhedron->getFace(minFaceIndex);
// Find the incident face on the other polyhedron (most anti-parallel face)
uint incidentFaceIndex = findMostAntiParallelFaceOnPolyhedron(incidentPolyhedron, axisIncidentSpace);
// Get the incident face
HalfEdgeStructure::Face incidentFace = incidentPolyhedron->getFace(incidentFaceIndex);
std::vector<Vector3> polygonVertices; // Vertices to clip of the incident face
std::vector<Vector3> planesNormals; // Normals of the clipping planes
std::vector<Vector3> planesPoints; // Points on the clipping planes
// Get all the vertices of the incident face (in the reference local-space)
std::vector<uint>::const_iterator it;
for (it = incidentFace.faceVertices.begin(); it != incidentFace.faceVertices.end(); ++it) {
const Vector3 faceVertexIncidentSpace = incidentPolyhedron->getVertexPosition(*it);
polygonVertices.push_back(incidentToReferenceTransform * faceVertexIncidentSpace);
}
// Get the reference face clipping planes
uint currentEdgeIndex = referenceFace.edgeIndex;
uint firstEdgeIndex = currentEdgeIndex;
do {
// Get the adjacent edge
HalfEdgeStructure::Edge edge = referencePolyhedron->getHalfEdge(currentEdgeIndex);
// Get the twin edge
HalfEdgeStructure::Edge twinEdge = referencePolyhedron->getHalfEdge(edge.twinEdgeIndex);
// Get the adjacent face normal (and negate it to have a clipping plane)
Vector3 faceNormal = -referencePolyhedron->getFaceNormal(twinEdge.faceIndex);
// Get a vertex of the clipping plane (vertex of the adjacent edge)
Vector3 faceVertex = referencePolyhedron->getVertexPosition(edge.vertexIndex);
planesNormals.push_back(faceNormal);
planesPoints.push_back(faceVertex);
// Go to the next adjacent edge of the reference face
currentEdgeIndex = edge.nextEdgeIndex;
} while (currentEdgeIndex != firstEdgeIndex);
// Clip the reference faces with the adjacent planes of the reference face
std::vector<Vector3> clipPolygonVertices = clipPolygonWithPlanes(polygonVertices, planesPoints, planesNormals);
// We only keep the clipped points that are below the reference face
const Vector3 referenceFaceVertex = referencePolyhedron->getVertexPosition(firstEdgeIndex);
std::vector<Vector3>::const_iterator itPoints;
for (itPoints = clipPolygonVertices.begin(); itPoints != clipPolygonVertices.end(); ++itPoints) {
// If the clip point is bellow the reference face
if (((*itPoints) - referenceFaceVertex).dot(axisReferenceSpace) < decimal(0.0)) {
// Convert the clip incident polyhedron vertex into the incident polyhedron local-space
const Vector3 contactPointIncidentPolyhedron = referenceToIncidentTransform * (*itPoints);
// Project the contact point onto the reference face
Vector3 contactPointReferencePolyhedron = (*itPoints) + axisReferenceSpace * minPenetrationDepth;
// Create a new contact point
contactManifoldInfo.addContactPoint(normalWorld, minPenetrationDepth,
isMinPenetrationFaceNormalPolyhedron1 ? contactPointReferencePolyhedron : contactPointIncidentPolyhedron,
isMinPenetrationFaceNormalPolyhedron1 ? contactPointIncidentPolyhedron : contactPointReferencePolyhedron);
}
}
}
else { // If we have an edge vs edge contact
// Compute the closest points between the two edges (in the local-space of poylhedron 2)
Vector3 closestPointPolyhedron1Edge, closestPointPolyhedron2Edge;
computeClosestPointBetweenTwoSegments(separatingEdge1A, separatingEdge1B, separatingEdge2A, separatingEdge2B,
closestPointPolyhedron1Edge, closestPointPolyhedron2Edge);
// Compute the contact point on polyhedron 1 edge in the local-space of polyhedron 1
const Vector3 closestPointPolyhedron1EdgeLocalSpace = polyhedron2ToPolyhedron1 * closestPointPolyhedron1Edge;
// Compute the world normal
const Vector3 normalWorld = narrowPhaseInfo->shape2ToWorldTransform.getOrientation() * minEdgeVsEdgeSeparatingAxisPolyhedron2Space;
// Create the contact point
contactManifoldInfo.addContactPoint(normalWorld, minPenetrationDepth,
closestPointPolyhedron1EdgeLocalSpace, closestPointPolyhedron2Edge);
}
return true;
}
// Find and return the index of the polyhedron face with the most anti-parallel face normal given a direction vector
// This is used to find the incident face on a polyhedron of a given reference face of another polyhedron
uint SATAlgorithm::findMostAntiParallelFaceOnPolyhedron(const ConvexPolyhedronShape* polyhedron, const Vector3& direction) const {
decimal minDotProduct = DECIMAL_LARGEST;
uint mostAntiParallelFace = 0;
// For each face of the polyhedron
for (uint i=0; i < polyhedron->getNbFaces(); i++) {
// Get the face normal
decimal dotProduct = polyhedron->getFaceNormal(i).dot(direction);
if (dotProduct < minDotProduct) {
minDotProduct = dotProduct;
mostAntiParallelFace = i;
}
}
return mostAntiParallelFace;
}
// Compute and return the distance between the two edges in the direction of the candidate separating axis
decimal SATAlgorithm::computeDistanceBetweenEdges(const Vector3& edge1A, const Vector3& edge2A, const Vector3& polyhedron2Centroid,
const Vector3& edge1Direction, const Vector3& edge2Direction,
Vector3& outSeparatingAxisPolyhedron2Space) const {
// If the two edges are parallel
if (areParallelVectors(edge1Direction, edge2Direction)) {
// Return a large penetration depth to skip those edges
return DECIMAL_LARGEST;
}
// Compute the candidate separating axis (cross product between two polyhedrons edges)
Vector3 axis = edge1Direction.cross(edge2Direction).getUnit();
// Make sure the axis direction is going from first to second polyhedron
if (axis.dot(edge2A - polyhedron2Centroid) > decimal(0.0)) {
axis = -axis;
}
outSeparatingAxisPolyhedron2Space = axis;
// Compute and return the distance between the edges
return -axis.dot(edge2A - edge1A);
}
// Test all the normals of a polyhedron for separating axis in the polyhedron vs polyhedron case
decimal SATAlgorithm::testFaceDirectionPolyhedronVsPolyhedron(const ConvexPolyhedronShape* polyhedron1,
const ConvexPolyhedronShape* polyhedron2,
const Transform& polyhedron1ToPolyhedron2,
uint& minFaceIndex) const {
decimal minPenetrationDepth = DECIMAL_LARGEST;
// For each face of the first polyhedron
for (uint f = 0; f < polyhedron1->getNbFaces(); f++) {
HalfEdgeStructure::Face face = polyhedron1->getFace(f);
// Get the face normal
const Vector3 faceNormal = polyhedron1->getFaceNormal(f);
// Convert the face normal into the local-space of polyhedron 2
const Vector3 faceNormalPolyhedron2Space = polyhedron1ToPolyhedron2.getOrientation() * faceNormal;
// Get the support point of polyhedron 2 in the inverse direction of face normal
const Vector3 supportPoint = polyhedron2->getLocalSupportPointWithoutMargin(-faceNormalPolyhedron2Space, nullptr);
// Compute the penetration depth
const Vector3 faceVertex = polyhedron1ToPolyhedron2 * polyhedron1->getVertexPosition(face.faceVertices[0]);
decimal penetrationDepth = (faceVertex - supportPoint).dot(faceNormalPolyhedron2Space);
// If the penetration depth is negative, we have found a separating axis
if (penetrationDepth <= decimal(0.0)) {
return penetrationDepth;
}
// Check if we have found a new minimum penetration axis
if (penetrationDepth < minPenetrationDepth) {
minPenetrationDepth = penetrationDepth;
minFaceIndex = f;
}
}
return minPenetrationDepth;
}
// Return true if two edges of two polyhedrons build a minkowski face (and can therefore be a separating axis)
bool SATAlgorithm::testEdgesBuildMinkowskiFace(const ConvexPolyhedronShape* polyhedron1, const HalfEdgeStructure::Edge& edge1,
const ConvexPolyhedronShape* polyhedron2, const HalfEdgeStructure::Edge& edge2,
const Transform& polyhedron1ToPolyhedron2) const {
const Vector3 a = polyhedron1ToPolyhedron2 * polyhedron1->getFaceNormal(edge1.faceIndex);
const Vector3 b = polyhedron1ToPolyhedron2 * polyhedron1->getFaceNormal(polyhedron1->getHalfEdge(edge1.twinEdgeIndex).faceIndex);
const Vector3 c = polyhedron2->getFaceNormal(edge2.faceIndex);
const Vector3 d = polyhedron2->getFaceNormal(polyhedron2->getHalfEdge(edge2.twinEdgeIndex).faceIndex);
// Compute b.cross(a) using the edge direction
const Vector3 edge1Vertex1 = polyhedron1->getVertexPosition(edge1.vertexIndex);
const Vector3 edge1Vertex2 = polyhedron1->getVertexPosition(polyhedron1->getHalfEdge(edge1.twinEdgeIndex).vertexIndex);
const Vector3 bCrossA = polyhedron1ToPolyhedron2.getOrientation() * (edge1Vertex2 - edge1Vertex1);
// Compute d.cross(c) using the edge direction
const Vector3 edge2Vertex1 = polyhedron2->getVertexPosition(edge2.vertexIndex);
const Vector3 edge2Vertex2 = polyhedron2->getVertexPosition(polyhedron2->getHalfEdge(edge2.twinEdgeIndex).vertexIndex);
const Vector3 dCrossC = edge2Vertex2 - edge2Vertex1;
// Test if the two arcs of the Gauss Map intersect (therefore forming a minkowski face)
// Note that we negate the normals of the second polyhedron because we are looking at the
// Gauss map of the minkowski difference of the polyhedrons
return testGaussMapArcsIntersect(a, b, -c, -d, bCrossA, dCrossC);
}
@ -346,10 +654,8 @@ bool SATAlgorithm::testCollisionConvexMeshVsConvexMesh(const NarrowPhaseInfo* na
/// and edge between faces with normal C and D on second polygon create a face on the Minkowski
/// sum of both polygons. If this is the case, it means that the cross product of both edges
/// might be a separating axis.
bool SATAlgorithm::testGaussMapArcsIntersect(const Vector3& a, const Vector3& b,
const Vector3& c, const Vector3& d) const {
const Vector3 bCrossA = b.cross(a);
const Vector3 dCrossC = d.cross(c);
bool SATAlgorithm::testGaussMapArcsIntersect(const Vector3& a, const Vector3& b, const Vector3& c, const Vector3& d,
const Vector3& bCrossA, const Vector3& dCrossC) const {
const decimal cba = c.dot(bCrossA);
const decimal dba = d.dot(bCrossA);

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@ -43,9 +43,23 @@ class SATAlgorithm {
// -------------------- Methods -------------------- //
/// Return true if two edges of two polyhedrons build a minkowski face (and can therefore be a separating axis)
bool testEdgesBuildMinkowskiFace(const ConvexPolyhedronShape* polyhedron1, const HalfEdgeStructure::Edge& edge1,
const ConvexPolyhedronShape* polyhedron2, const HalfEdgeStructure::Edge& edge2,
const Transform& polyhedron1ToPolyhedron2) const;
/// Return true if the arcs AB and CD on the Gauss Map intersect
bool testGaussMapArcsIntersect(const Vector3& a, const Vector3& b,
const Vector3& c, const Vector3& d) const;
const Vector3& c, const Vector3& d,
const Vector3& bCrossA, const Vector3& dCrossC) const;
// Find and return the index of the polyhedron face with the most anti-parallel face normal given a direction vector
uint findMostAntiParallelFaceOnPolyhedron(const ConvexPolyhedronShape* polyhedron, const Vector3& direction) const;
/// Compute and return the distance between the two edges in the direction of the candidate separating axis
decimal computeDistanceBetweenEdges(const Vector3& edge1A, const Vector3& edge2A, const Vector3& polyhedron2Centroid,
const Vector3& edge1Direction, const Vector3& edge2Direction,
Vector3& outSeparatingAxis) const;
public :
@ -80,12 +94,12 @@ class SATAlgorithm {
bool isMinkowskiFaceCapsuleVsEdge(const Vector3& capsuleSegment, const Vector3& edgeAdjacentFace1Normal,
const Vector3& edgeAdjacentFace2Normal) const;
/// Test collision between a triangle and a convex mesh
bool testCollisionTriangleVsConvexMesh(const NarrowPhaseInfo* narrowPhaseInfo, ContactManifoldInfo& contactManifoldInfo) const;
/// Test collision between two convex meshes
bool testCollisionConvexMeshVsConvexMesh(const NarrowPhaseInfo* narrowPhaseInfo, ContactManifoldInfo& contactManifoldInfo) const;
bool testCollisionConvexPolyhedronVsConvexPolyhedron(const NarrowPhaseInfo* narrowPhaseInfo, ContactManifoldInfo& contactManifoldInfo) const;
/// Test all the normals of a polyhedron for separating axis in the polyhedron vs polyhedron case
decimal testFaceDirectionPolyhedronVsPolyhedron(const ConvexPolyhedronShape* polyhedron1, const ConvexPolyhedronShape* polyhedron2,
const Transform& polyhedron1ToPolyhedron2, uint& minFaceIndex) const;
};
}

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@ -194,7 +194,7 @@ decimal reactphysics3d::computePlaneSegmentIntersection(const Vector3& segA, con
}
// Compute the distance between a point "point" and a line given by the points "linePointA" and "linePointB"
decimal reactphysics3d::computeDistancePointToLineDistance(const Vector3& linePointA, const Vector3& linePointB, const Vector3& point) {
decimal reactphysics3d::computePointToLineDistance(const Vector3& linePointA, const Vector3& linePointB, const Vector3& point) {
decimal distAB = (linePointB - linePointA).length();

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@ -98,7 +98,7 @@ void computeBarycentricCoordinatesInTriangle(const Vector3& a, const Vector3& b,
decimal computePlaneSegmentIntersection(const Vector3& segA, const Vector3& segB, const decimal planeD, const Vector3& planeNormal);
/// Compute the distance between a point and a line
decimal computeDistancePointToLineDistance(const Vector3& linePointA, const Vector3& linePointB, const Vector3& point);
decimal computePointToLineDistance(const Vector3& linePointA, const Vector3& linePointB, const Vector3& point);
/// Clip a segment against multiple planes and return the clipped segment vertices
std::vector<Vector3> clipSegmentWithPlanes(const Vector3& segA, const Vector3& segB,

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@ -162,13 +162,12 @@ class TestMathematicsFunctions : public Test {
decimal tIntersect = computePlaneSegmentIntersection(Vector3(5, 4, 0), Vector3(9, 4, 0), 4, Vector3(0, 1, 0));
test(tIntersect < 0.0 || tIntersect > 1.0);
// Test computeDistancePointToLineDistance()
test(approxEqual(computeDistancePointToLineDistance(Vector3(6, 0, 0), Vector3(14, 0, 0), Vector3(5, 3, 0)), 3.0, 0.000001));
test(approxEqual(computeDistancePointToLineDistance(Vector3(6, -5, 0), Vector3(10, -5, 0), Vector3(4, 3, 0)), 8.0, 0.000001));
test(approxEqual(computeDistancePointToLineDistance(Vector3(6, -5, 0), Vector3(10, -5, 0), Vector3(-43, 254, 0)), 259.0, 0.000001));
test(approxEqual(computeDistancePointToLineDistance(Vector3(6, -5, 8), Vector3(10, -5, -5), Vector3(6, -5, 8)), 0.0, 0.000001));
test(approxEqual(computeDistancePointToLineDistance(Vector3(6, -5, 8), Vector3(10, -5, -5), Vector3(10, -5, -5)), 0.0, 0.000001));
// Test computePointToLineDistance()
test(approxEqual(computePointToLineDistance(Vector3(6, 0, 0), Vector3(14, 0, 0), Vector3(5, 3, 0)), 3.0, 0.000001));
test(approxEqual(computePointToLineDistance(Vector3(6, -5, 0), Vector3(10, -5, 0), Vector3(4, 3, 0)), 8.0, 0.000001));
test(approxEqual(computePointToLineDistance(Vector3(6, -5, 0), Vector3(10, -5, 0), Vector3(-43, 254, 0)), 259.0, 0.000001));
test(approxEqual(computePointToLineDistance(Vector3(6, -5, 8), Vector3(10, -5, -5), Vector3(6, -5, 8)), 0.0, 0.000001));
test(approxEqual(computePointToLineDistance(Vector3(6, -5, 8), Vector3(10, -5, -5), Vector3(10, -5, -5)), 0.0, 0.000001));
// Test clipSegmentWithPlanes()
std::vector<Vector3> segmentVertices;