Computing the medial surface of a 3-D boundary representation model

Medial surface, the skeletal abstraction of a solid shape, can be used in applications such as shell (solid) mesh generation, robot path planning, and feature recognition. Unfortunately, computing the medical surface is very difficult. Those few algorithms proposed invariably need to solve systems of non-linear polynomial equations, which requires complicated numerical techniques. Recently, an algorithm has been proposed by the authors that is applicable to a polyhedral model. It uses voxel-bisector intersection relationships to calculate the intersection points and, from these, constructs the boundaries of the medical surface patches. Unfortunately, it does not handle the degenerate cases. This paper extends the scope of the voxel-bisector intersection algorithm by proposing a supplementary algorithm to detect the existence of the degenerate intersection curve in a specified region (voxel). An enhancement to the voxel-bisector intersection algorithm by using the Voronoi territory, which needs no polynomial root-finding scheme, is also proposed.