Skeletal representations of orthogonal shapes

Abstract

In this paper we present two skeletal representations applied to orthogonal shapes of R^n : the cube axis and a family of skeletal representations provided by the scale cube axis. Orthogonal shapes are a subset of polytopes, where the hyperplanes of the bounding facets are restricted to be axis aligned. Both skeletal representations rely on the L∞ metric and are proven to be homotopically equivalent to its shape. The resulting skeleton is composed of n − 1 dimensional facets. We also provide an efficient and robust algorithm to compute the scale cube axis in the plane and compare the resulting skeleton with other skeletal representations.