ABSTRACT
In this paper we use Minkowski operations to describe freeform shape machining algorithms. Given a cut ting tool, a toolholder and a stock-in-progress, that en closes 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 stockin-progress is described using the Minkowski addition. The computation of the stock-in-progress that is left, i f the tool has followed the tool path, is described us ing the Minkowski subtraction. Grids of height values are described by real-valued functions on finite subsets of 2Z2, called numerical functions. We use Minkowski operations on these numerical functions to describe the well-know “remove as much material as possible” ma chining strategy and the well-know "slicingn machin ing strategy. As far as we know these strategies have not been described using Minkowski operations. Since the uslicing strategy ” generates tool paths that are ma chined faster, an efficient implementation of the “slic ing strategyn is described using Z-pyramids.
