Exact medial axis computation for triangulated solids with respect to piecewise linear metrics

O. Aichholzer, W. Aigner, F. Aurenhammer, and B. Jüttler

Abstract:

We propose a novel approach for the medial axis approximation of triangulated solids by using a polyhedral unit ball $B$ instead of the standard Euclidean unit ball. By this means, we compute the exact medial axis $MA(\Omega)$ of a triangulated solid $\Omega$ with respect to a piecewise linear (quasi-)metric $d_B$. The obtained representation of $\Omega$ by the medial axis transform $MAT(\Omega)$ allows for a convenient computation of the trimmed offset of $\Omega$ with respect to $d_B$. All calculations are performed within the field of rational numbers, resulting in a robust and efficient implementation of our approach. Adapting the properties of $B$ provides an easy way to control the level of details captured by the medial axis, making use of the implicit pruning at flat boundary features.



Reference: O. Aichholzer, W. Aigner, F. Aurenhammer, and B. Jüttler. Exact medial axis computation for triangulated solids with respect to piecewise linear metrics. In Proc. Int. Conf. Curves and Surfaces, Springer LNCS, volume 6920, pages 1-27, Avignon, France, 2011.