A divide and conquer algorithm for medial surface calculation of planar polyhedra

Abstract

The Medial Axis Transform surface, (or MAT or MS) is proving to be a useful tool for several applications and geometric reasoning tasks. However, calculation of the MAT is a time-consuming task and the benefits of the mathematical-based tool are offset by the cost of the calculation. This paper presents a method for medial surface calculation which uses subdivision to simplify the problem and hence speed up the calculation, a so-called ‘divide-and-conquer’ approach. The basis for this is a modification of the dual structure of the original object. As the calculation proceeds this structure is broken up into sub-pieces each representing a simpler sub-part of the MAT. Perhaps more importantly, this method creates a correct node decomposition of the dual structure. The paper goes on to demonstrate some applications of the results for geometric tasks, specifically offsetting and model subdivision, which are normally expensive but are simpler based on the MAT calculation results.