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

Authors:
Oswin Aichholzer;Wolfgang Aigner;Franz Aurenhammer;Bert Jüttler
Affiliations:
Institute for Software Technology, Graz University of Technology, Austria;Institute for Software Technology, Graz University of Technology, Austria;Institute for Theoretical Computer Science, Graz University of Technology, Austria;Institute of Applied Geometry, Johannes Kepler University Linz, Austria
Venue:
Proceedings of the 7th international conference on Curves and Surfaces
Year:
2010

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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 $\mbox{\rm MA}(\Omega)$ of a triangulated solid Ω with respect to a piecewise linear (quasi-) metric dB. The obtained representation of Ω by the medial axis transform $\mbox{\rm MAT}(\Omega)$ allows for a convenient computation of the trimmed offset of Ω with respect to dB. 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.