E-cient and RobustComputationof an ApproximatedMedial Axis

The medial axis can be viewed as a compact represen- tation for an arbitrary model; it is an essential ge- ometric structure in many applications. A number of practical algorithms for its computation have been aimed at speeding up its computation and at address- ing its instabilities. In this paper we propose a new algorithm to compute the medial axis with arbitrary precision. It exhibits several desirable properties not previously combined in a practical and e-cient algo- rithm. First, it allows for a trade-ofi between com- putation time and accuracy, making it well-suited for applications in which an approximation of the medial axis su-ces, but computational e-ciency is of partic- ular concern. Second, it is output sensitive: the com- putation complexity of the algorithm does not depend on the size of the representation of a model, but on the size of the representation of the resulting medial axis. Third, the densities of the approximated medial axis points in difierent areas are adaptive to local free spacevolumes,basedontheassumptionthatacoarser approximationinwideopenareacanstillsu-cethere- quirements of the applications. We present theoretical results, bounding the error introduced by the approxi- mation process. The algorithm has been implemented and experimental results are presented that illustrate its computational e-ciency and robustness.