public IntrPlane3Plane3(Plane3d p0, Plane3d p1)
{
plane0 = p0;
plane1 = p1;
}
public IntrLine3Plane3(Line3d l, Plane3d p)
{
line = l;
plane = p;
}
public bool Find()
{
if (Result != IntersectionResult.NotComputed)
{
return(Result != g3.IntersectionResult.NoIntersection);
}
// in this code the results get initialized in subroutines, so we
// set the defautl value here...
Result = IntersectionResult.NoIntersection;
int i, iM, iP;
// Get the plane of triangle0.
Plane3d plane0 = new Plane3d(triangle0.V0, triangle0.V1, triangle0.V2);
// Compute the signed distances of triangle1 vertices to plane0. Use
// an epsilon-thick plane test.
int pos1, neg1, zero1;
Index3i sign1;
Vector3d dist1;
TrianglePlaneRelations(ref triangle1, ref plane0, out dist1, out sign1, out pos1, out neg1, out zero1);
if (pos1 == 3 || neg1 == 3)
{
// Triangle1 is fully on one side of plane0.
return(false);
}
if (zero1 == 3)
{
// Triangle1 is contained by plane0.
if (ReportCoplanarIntersection)
{
return(GetCoplanarIntersection(ref plane0, ref triangle0, ref triangle1));
}
return(false);
}
// Check for grazing contact between triangle1 and plane0.
if (pos1 == 0 || neg1 == 0)
{
if (zero1 == 2)
{
// An edge of triangle1 is in plane0.
for (i = 0; i < 3; ++i)
{
if (sign1[i] != 0)
{
iM = (i + 2) % 3;
iP = (i + 1) % 3;
return(IntersectsSegment(ref plane0, ref triangle0, triangle1[iM], triangle1[iP]));
}
}
}
else // zero1 == 1
// A vertex of triangle1 is in plane0.
{
for (i = 0; i < 3; ++i)
{
if (sign1[i] == 0)
{
return(ContainsPoint(ref triangle0, ref plane0, triangle1[i]));
}
}
}
}
// At this point, triangle1 tranversely intersects plane 0. Compute the
// line segment of intersection. Then test for intersection between this
// segment and triangle 0.
double t;
Vector3d intr0, intr1;
if (zero1 == 0)
{
int iSign = (pos1 == 1 ? +1 : -1);
for (i = 0; i < 3; ++i)
{
if (sign1[i] == iSign)
{
iM = (i + 2) % 3;
iP = (i + 1) % 3;
t = dist1[i] / (dist1[i] - dist1[iM]);
intr0 = triangle1[i] + t * (triangle1[iM] - triangle1[i]);
t = dist1[i] / (dist1[i] - dist1[iP]);
intr1 = triangle1[i] + t * (triangle1[iP] - triangle1[i]);
return(IntersectsSegment(ref plane0, ref triangle0, intr0, intr1));
}
}
}
// zero1 == 1
for (i = 0; i < 3; ++i)
{
if (sign1[i] == 0)
{
iM = (i + 2) % 3;
iP = (i + 1) % 3;
t = dist1[iM] / (dist1[iM] - dist1[iP]);
intr0 = triangle1[iM] + t * (triangle1[iP] - triangle1[iM]);
return(IntersectsSegment(ref plane0, ref triangle0, triangle1[i], intr0));
}
}
// should never get here...
Debug.Assert(false);
return(false);
}
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 IntrRay3Plane3(Ray3d r, Plane3d p)
{
ray = r;
plane = p;
}