Medial Axis Based Solid Representation

By Daniel Cohen-Or, Ariel Shamir and Amir Shaham.


The medial axis (MA) of an object and medial axis transform (MAT) have many applications in solid modeling, computer graphics and other areas. In this paper we present a novel representation of solids which we call a {\em pair-mesh}. The pair-mesh is a deformable manifold surface triangulation where each node deforms between a pair of vertices one on the MA and one on the boundary. Consequently, it provides a continuous map between the MA approximation and the boundary of the shape, encompassing the topological structures of them both. This representation can also be seen as a tetrahedral partitioning of the volume between the two, where each tetrahedron includes vertices from both the MA approximation and the reconstructed boundary. Given an object represented as a polyhedron or a point set, the pair-mesh creation is based on Voronoi based MA approximation algorithm. The MA approximation is constrained using a volume scaffolding to preserve the path-connectivity characteristic of the object, maintain the link between opposite sides of the MA, and prevent self intersections. We demonstrate the powerful properties of the pair-mesh by defining an effective local topological classification operator for elements in the medial axis.