bool ContainsPoint(ref Triangle3d triangle, ref Plane3d plane, Vector3D point)
{
// Generate a coordinate system for the plane. The incoming triangle has
// vertices <V0,V1,V2>. The incoming plane has unit-length normal N.
// The incoming point is P. V0 is chosen as the origin for the plane. The
// coordinate axis directions are two unit-length vectors, U0 and U1,
// constructed so that {U0,U1,N} is an orthonormal set. Any point Q
// in the plane may be written as Q = V0 + x0*U0 + x1*U1. The coordinates
// are computed as x0 = Dot(U0,Q-V0) and x1 = Dot(U1,Q-V0).
Vector3D U0 = Vector3D.Zero, U1 = Vector3D.Zero;
Vector3D.GenerateComplementBasis(ref U0, ref U1, plane.Normal);
// Compute the planar coordinates for the points P, V1, and V2. To
// simplify matters, the origin is subtracted from the points, in which
// case the planar coordinates are for P-V0, V1-V0, and V2-V0.
Vector3D PmV0 = point - triangle[0];
Vector3D V1mV0 = triangle[1] - triangle[0];
Vector3D V2mV0 = triangle[2] - triangle[0];
// The planar representation of P-V0.
Vector2D ProjP = new Vector2D(U0.Dot(PmV0), U1.Dot(PmV0));
// The planar representation of the triangle <V0-V0,V1-V0,V2-V0>.
Vector2dTuple3 ProjV = new Vector2dTuple3(
Vector2D.Zero,
new Vector2D(U0.Dot(V1mV0), U1.Dot(V1mV0)),
new Vector2D(U0.Dot(V2mV0), U1.Dot(V2mV0)));
// Test whether P-V0 is in the triangle <0,V1-V0,V2-V0>.
QueryTuple2d query = new QueryTuple2d(ProjV);
if (query.ToTriangle(ProjP, 0, 1, 2) <= 0)
{
Result = IntersectionResult.Intersects;
Type = IntersectionType.Point;
Quantity = 1;
Points[0] = point;
return(true);
}
return(false);
}
public QueryTuple2d(Vector2D v0, Vector2D v1, Vector2D v2)
{
mVertices = new Vector2dTuple3(v0, v1, v2);
}
public QueryTuple2d(Vector2dTuple3 tuple)
{
mVertices = tuple;
}
