Generating tool paths for free-form pocket machining using z-buffer-based Voronoi diagrams

Abstract

Voronoi diagrams for closed shapes have many practical applications, ranging from numerical control machining to mesh generation. Curve offsetting based on Voronoi diagrams avoids the topological problems encountered in traditional offsetting algorithms. In this paper, we present a new procedure for generating tool paths using z-buffer-based Voronoi diagrams specially to deal with free-form shaped pockets. Using a z-buffer, a proposed algorithm effectively extracts the topological information on the Voronoi diagram, and generates the geometric information on the Voronoi edges approximately. These Voronoi edges are refined using a numerical algorithm This method is independent of curve type and is applicable to any pockets with parametric curve boundaries that are twice differentiable.