bool IntersectsSegment(ref Plane3d plane, ref Triangle3d triangle, Vector3d end0, Vector3d end1)
{
// Compute the 2D representations of the triangle vertices and the
// segment endpoints relative to the plane of the triangle. Then
// compute the intersection in the 2D space.
// Project the triangle and segment onto the coordinate plane most
// aligned with the plane normal.
int maxNormal = 0;
double fmax = Math.Abs(plane.Normal.x);
double absMax = Math.Abs(plane.Normal.y);
if (absMax > fmax)
{
maxNormal = 1;
fmax = absMax;
}
absMax = Math.Abs(plane.Normal.z);
if (absMax > fmax)
{
maxNormal = 2;
}
Triangle2d projTri = new Triangle2d();
Vector2d projEnd0 = Vector2d.Zero, projEnd1 = Vector2d.Zero;
int i;
if (maxNormal == 0)
{
// Project onto yz-plane.
for (i = 0; i < 3; ++i)
{
projTri[i] = triangle[i].yz;
projEnd0.x = end0.y;
projEnd0.y = end0.z;
projEnd1.x = end1.y;
projEnd1.y = end1.z;
}
}
else if (maxNormal == 1)
{
// Project onto xz-plane.
for (i = 0; i < 3; ++i)
{
projTri[i] = triangle[i].xz;
projEnd0.x = end0.x;
projEnd0.y = end0.z;
projEnd1.x = end1.x;
projEnd1.y = end1.z;
}
}
else
{
// Project onto xy-plane.
for (i = 0; i < 3; ++i)
{
projTri[i] = triangle[i].xy;
projEnd0.x = end0.x;
projEnd0.y = end0.y;
projEnd1.x = end1.x;
projEnd1.y = end1.y;
}
}
Segment2d projSeg = new Segment2d(projEnd0, projEnd1);
IntrSegment2Triangle2 calc = new IntrSegment2Triangle2(projSeg, projTri);
if (!calc.Find())
{
return(false);
}
Vector2dTuple2 intr = new Vector2dTuple2();
if (calc.Type == IntersectionType.Segment)
{
Result = IntersectionResult.Intersects;
Type = IntersectionType.Segment;
Quantity = 2;
intr.V0 = calc.Point0;
intr.V1 = calc.Point1;
}
else
{
Debug.Assert(calc.Type == IntersectionType.Point);
//"Intersection must be a point\n";
Result = IntersectionResult.Intersects;
Type = IntersectionType.Point;
Quantity = 1;
intr.V0 = calc.Point0;
}
// Unproject the segment of intersection.
if (maxNormal == 0)
{
double invNX = ((double)1) / plane.Normal.x;
for (i = 0; i < Quantity; ++i)
{
double y = intr[i].x;
double z = intr[i].y;
double x = invNX * (plane.Constant - plane.Normal.y * y - plane.Normal.z * z);
Points[i] = new Vector3d(x, y, z);
}
}
else if (maxNormal == 1)
{
double invNY = ((double)1) / plane.Normal.y;
for (i = 0; i < Quantity; ++i)
{
double x = intr[i].x;
double z = intr[i].y;
double y = invNY * (plane.Constant - plane.Normal.x * x - plane.Normal.z * z);
Points[i] = new Vector3d(x, y, z);
}
}
else
{
double invNZ = ((double)1) / plane.Normal.z;
for (i = 0; i < Quantity; ++i)
{
double x = intr[i].x;
double y = intr[i].y;
double z = invNZ * (plane.Constant - plane.Normal.x * x - plane.Normal.y * y);
Points[i] = new Vector3d(x, y, z);
}
}
return(true);
}
Circle UpdateSupport2(int i, int[] permutation, Support support)
{
var point = new Vector2dTuple2(
Points[permutation[support.Index[0]]], // P0
Points[permutation[support.Index[1]]] // P1
);
Vector2d P2 = Points[permutation[i]];
// Permutations of type 2, used for calling ExactCircle2(..).
int numType2 = 2;
// Permutations of type 3, used for calling ExactCircle3(..).
//int numType3 = 1; // {0, 1, 2}
Circle[] circle = circle_buf;
int indexCircle = 0;
double minRSqr = double.MaxValue;
int indexMinRSqr = -1;
double distDiff = 0, minDistDiff = double.MaxValue;
int indexMinDistDiff = -1;
// Permutations of type 2.
int j;
for (j = 0; j < numType2; ++j, ++indexCircle)
{
circle[indexCircle] = ExactCircle2(point[type2_2[j, 0]], ref P2);
if (circle[indexCircle].Radius < minRSqr)
{
if (Contains(point[type2_2[j, 1]], ref circle[indexCircle], ref distDiff))
{
minRSqr = circle[indexCircle].Radius;
indexMinRSqr = indexCircle;
}
else if (distDiff < minDistDiff)
{
minDistDiff = distDiff;
indexMinDistDiff = indexCircle;
}
}
}
// Permutations of type 3.
circle[indexCircle] = ExactCircle3(point[0], point[1], ref P2);
if (circle[indexCircle].Radius < minRSqr)
{
minRSqr = circle[indexCircle].Radius;
indexMinRSqr = indexCircle;
}
// Theoreticaly, indexMinRSqr >= 0, but floating-point round-off errors
// can lead to indexMinRSqr == -1. When this happens, the minimal sphere
// is chosen to be the one that has the minimum absolute errors between
// the sphere and points (barely) outside the sphere.
if (indexMinRSqr == -1)
{
indexMinRSqr = indexMinDistDiff;
}
Circle minimal = circle[indexMinRSqr];
switch (indexMinRSqr)
{
case 0:
support.Index[1] = i;
break;
case 1:
support.Index[0] = i;
break;
case 2:
support.Quantity = 3;
support.Index[2] = i;
break;
}
return(minimal);
}