Johan W.H. Tangelder, Delft University of Technology, Delft, The Netherlands

Joris S.M. Vergeest, Delft University of Technology, Delft, The Netherlands

Mark H. Overmars, Utrecht University, Utrecht, The Netherlands

In this paper we use Minkowski operations to describe freeform shape machining algorithms. Given a cutting tool, a toolholder and a stock-in-progress, that encloses the model to be machined, the computation of a tool path, for which the tool does not interfere the model and the toolholder does not interfere the stock-in-progress is described using the Minkowski addition. The computation of the stock-in-progress that is left, if the tool has followed the tool path, is described using the Minkowski subtraction. Grids of height values are described by real-valued functions on finite subsets of , called numerical functions. We use Minkowski operations on these numerical functions to describe the well-know "remove as much material as possible" machining strategy and the well-know "slicing" machining strategy. As far as we know these strategies have not been described using Minkowski operations. Since the "slicing strategy" generates tool paths that are machined faster, an efficient implementation of the "slicing strategy" is described using Z-pyramids.