The graphic command called "hollow drawing" is a primitive of graphic operations, which renders the boundary of a given polygon. When drawing a hollow on a simple polygon, it is hard for a hollow pattern neither to self-intersect nor to be drawn outside of the polygon. These difficulties are characterized by formulating the notion of a bottleneck in a simple polygon. Using the Voronoi diagram of a simple polygon, we present an Ο(n long n) time algorithm for finding all bottlenecks of the simple polygon with n vertices. This leads to an efficient algorithm for drawing a hollow. It also gives a fast method for generating NC milling tool paths.
