How are intersections computed?
The intersection between two n-dimensional simplices is calculated boundary triangulation. Intersections are computed as follows.
- Find minimal set of points generating the intersection volume. These points form a convex polytope Pᵢ.
- Triangulate the faces of Pᵢ into simplices.
- Then combine each resulting boundary simplex with an interior point in Pᵢ. The set of all such combinations now form a triangulation of Pᵢ.
- Calculate the volume of each simplex in the resulting triangulation. Summing over these volumes given the volume of the intersection.