FAST RAY – CONVEX POLYHEDRON INTERSECTION

Publisher Summary This chapter analyzes ray-convex polyhedron intersection. The standard solution to ray–polyhedron intersection is to test the ray against each polygon and find the closest intersection, if any. If the polyhedron is convex, the ray-polyhedron test can be accelerated by considering the polyhedron to be the space inside a set of planes. This definition also drastically reduces the memory requirements for such polyhedra, as none of the vertices and their connectivities need to be stored; only the plane equations for the faces are needed. The ray-polyhedron test outlined in this chapter avoids the problems that can occur when the shared edge of two polygons is intersected by a ray, because there no longer are any edges. There is no chance of a ray “slipping through the cracks” by having its intersection point on an edge not considered being inside either polygon. The algorithm presented in the chapter is based on the ideas of Roth (1981) and Kay and Kajiya (1986). The basic idea is that each plane of the polyhedron defines a half-space: All points to one side of this space are considered inside the plane. The logical intersection of the half-spaces of all the convex polyhedron's planes is the volume defined by the polyhedron.