PolyCover: Shape Approximating With Discrete Surface Orientation

Abstract

We consider the problem of approximating given shapes so that the surface normals are restricted to a prescribed discrete set. Such shape approximations are commonly required in the context of manufacturing shapes. We provide an algorithm that first computes maximal interior polytopes and, then, selects a subset of offsets from the interior polytopes that cover the shape. This provides prescribed Hausdorff error approximations that use only a small number of primitives.