Overview

Mid-surface or medial surface ( medial axis in two dimensions) construction for a given domain is a very promising field of research that has multiple applications such as domain simplification, spatial dimension reduction and also as a first step to designing an algorithm for quad mesh generation. Similarly, the mid-surface associated with a three dimensional domain can serve the same purposes.

Several methods can be advocated to construct the medial entity of a domain, also referred to as the domain skeleton or neutral fiber. A brief survey of the possible methods can be found in [Turkiyyah et al. 1997]. In this respect, quadtree-octree based methods, tracing algorithms, adequate PDE solutions as well as Vorono -based methods can be considered. Among these methods, we focus here on the last approach. Since this method considers the Vorono cells of a given domain, it can be based on Delaunay triangulation of the domain. This opens up the discussion as to what is termed a Delaunay admissible boundary discretization (a polygon in two dimensions, a polyhedral simplicial surface in three dimensions).

Based on such a boundary discretization, it is possible to complete an "empty" Delaunay triangulation ^[1] of the domain of interest. From that, algorithms can be develope, resulting in the construction of the corresponding medial entity (actually, a discrete approximation of the entity). Thus, before considering medial entity construction and the various applications that can be derived from it, the first sections focus on Delaunay...