public static void TriangleLineRelations(
Vector2d origin, Vector2d direction,
Triangle2d tri, ref Vector3d dist, ref Vector3i sign,
ref int positive, ref int negative, ref int zero)
{
positive = 0;
negative = 0;
zero = 0;
for (int i = 0; i < 3; ++i)
{
Vector2d diff = tri[i] - origin;
dist[i] = diff.DotPerp(direction);
if (dist[i] > MathUtil.ZeroTolerance)
{
sign[i] = 1;
++positive;
}
else if (dist[i] < -MathUtil.ZeroTolerance)
{
sign[i] = -1;
++negative;
}
else
{
dist[i] = 0.0;
sign[i] = 0;
++zero;
}
}
}
public static int WhichSide(Triangle2d V, Vector2d P, Vector2d D)
{
// Vertices are projected to the form P+t*D. Return value is +1 if all
// t > 0, -1 if all t < 0, 0 otherwise, in which case the line splits the
// triangle.
int positive = 0, negative = 0, zero = 0;
for (int i = 0; i < 3; ++i)
{
double t = D.Dot(V[i] - P);
if (t > (double)0)
{
++positive;
}
else if (t < (double)0)
{
++negative;
}
else
{
++zero;
}
if (positive > 0 && negative > 0)
{
return(0);
}
}
return(zero == 0 ? (positive > 0 ? 1 : -1) : 0);
}
public IntrLine2Triangle2(Line2d l, Triangle2d t)
{
line = l; triangle = t;
}
public static void GetInterval(Vector2d origin, Vector2d direction, Triangle2d tri,
Vector3d dist, Vector3i sign, ref Vector2d param)
{
// Project triangle onto line.
Vector3d proj = Vector3d.Zero;
int i;
for (i = 0; i < 3; ++i)
{
Vector2d diff = tri[i] - origin;
proj[i] = direction.Dot(diff);
}
// Compute transverse intersections of triangle edges with line.
double numer, denom;
int i0, i1, i2;
int quantity = 0;
for (i0 = 2, i1 = 0; i1 < 3; i0 = i1++)
{
if (sign[i0] * sign[i1] < 0)
{
if (quantity >= 2)
{
throw new Exception("IntrLine2Triangle2.GetInterval: too many intersections!");
}
numer = dist[i0] * proj[i1] - dist[i1] * proj[i0];
denom = dist[i0] - dist[i1];
param[quantity++] = numer / denom;
}
}
// Check for grazing contact.
if (quantity < 2)
{
for (i0 = 1, i1 = 2, i2 = 0; i2 < 3; i0 = i1, i1 = i2++)
{
if (sign[i2] == 0)
{
if (quantity >= 2)
{
throw new Exception("IntrLine2Triangle2.GetInterval: too many intersections!");
}
param[quantity++] = proj[i2];
}
}
}
// Sort.
if (quantity < 1)
{
throw new Exception("IntrLine2Triangle2.GetInterval: need at least one intersection");
}
if (quantity == 2)
{
if (param[0] > param[1])
{
double save = param[0];
param[0] = param[1];
param[1] = save;
}
}
else
{
param[1] = param[0];
}
}
public IntrTriangle2Triangle2(Triangle2d t0, Triangle2d t1)
{
triangle0 = t0;
triangle1 = t1;
Points = null;
}
bool GetCoplanarIntersection(ref Plane3d plane, ref Triangle3d tri0, ref Triangle3d tri1)
{
// Project triangles onto coordinate plane most aligned with 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 projTri0 = new Triangle2d(), projTri1 = new Triangle2d();
int i;
if (maxNormal == 0)
{
// Project onto yz-plane.
for (i = 0; i < 3; ++i)
{
projTri0[i] = tri0[i].yz;
projTri1[i] = tri1[i].yz;
}
}
else if (maxNormal == 1)
{
// Project onto xz-plane.
for (i = 0; i < 3; ++i)
{
projTri0[i] = tri0[i].xz;
projTri1[i] = tri1[i].xz;
}
}
else
{
// Project onto xy-plane.
for (i = 0; i < 3; ++i)
{
projTri0[i] = tri0[i].xy;
projTri1[i] = tri1[i].xy;
}
}
// 2D triangle intersection routines require counterclockwise ordering.
Vector2d save;
Vector2d edge0 = projTri0[1] - projTri0[0];
Vector2d edge1 = projTri0[2] - projTri0[0];
if (edge0.DotPerp(edge1) < (double)0)
{
// Triangle is clockwise, reorder it.
save = projTri0[1];
projTri0[1] = projTri0[2];
projTri0[2] = save;
}
edge0 = projTri1[1] - projTri1[0];
edge1 = projTri1[2] - projTri1[0];
if (edge0.DotPerp(edge1) < (double)0)
{
// Triangle is clockwise, reorder it.
save = projTri1[1];
projTri1[1] = projTri1[2];
projTri1[2] = save;
}
IntrTriangle2Triangle2 intr = new IntrTriangle2Triangle2(projTri0, projTri1);
if (!intr.Find())
{
return(false);
}
PolygonPoints = new Vector3d[intr.Quantity];
// Map 2D intersections back to the 3D triangle space.
Quantity = intr.Quantity;
if (maxNormal == 0)
{
double invNX = ((double)1) / plane.Normal.x;
for (i = 0; i < Quantity; i++)
{
double y = intr.Points[i].x;
double z = intr.Points[i].y;
double x = invNX * (plane.Constant - plane.Normal.y * y - plane.Normal.z * z);
PolygonPoints[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.Points[i].x;
double z = intr.Points[i].y;
double y = invNY * (plane.Constant - plane.Normal.x * x - plane.Normal.z * z);
PolygonPoints[i] = new Vector3d(x, y, z);
}
}
else
{
double invNZ = ((double)1) / plane.Normal.z;
for (i = 0; i < Quantity; i++)
{
double x = intr.Points[i].x;
double y = intr.Points[i].y;
double z = invNZ * (plane.Constant - plane.Normal.x * x - plane.Normal.y * y);
PolygonPoints[i] = new Vector3d(x, y, z);
}
}
Result = IntersectionResult.Intersects;
Type = IntersectionType.Polygon;
return(true);
}
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);
}
public IntrSegment2Triangle2(Segment2d s, Triangle2d t)
{
segment = s; triangle = t;
}