Exact Medial Axis Computation for Triangulated Solids with Respect to Piecewise Linear Metrics

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(Ω) of a triangulated solid Ω with respect to a piecewise linear (quasi-) metric dB . The obtained representation of Ω by the medial axis transform MAT(Ω) 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.