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

Voronoi diagrams for closed shapes have many practical applications, rangin g from numerical control machining to mesh generation. Curve offsetting bas ed on Voronoi diagrams avoids the topological problems encountered in tradi tional offsetting algorithms. In this paper, we present a new procedure for generating tool paths using z-buffer-based Voronoi diagrams specially to d eal with free-form shaped pockets. Using a z-buffer, a proposed algorithm e ffectively extracts the topological information on the Voronoi diagram, and generates the geometric information on the Voronoi edges approximately. Th ese Voronoi edges are refined using a numerical algorithm This method is in dependent of curve type and is applicable to any pockets with parametric cu rve boundaries that are twice differentiable.