Computing offsets and tool paths with Voronoi diagrams

In this paper we describe the use of Voronoi diagrams to generate offsets for planar regions bounded by circular arcs and line segments, and then use the generated offsets as tool paths for NC machining. Two methods are presented, each producing a different type of offset. One of them generates the offsets of the region; the other divides the region into subpockets first, then offsets of the subpockets boundaries are used for tool paths. We show that a set of m offsets can be computed in 0(c\n log n + C2mn) time , where n is the numberof sides of the region, using either method.