Medial axis based solid representation

The medial axis (MA) of an object and medial axis transform (MAT) have many applications in solid modeling, computer graphics and other areas. Exact computation of MA is complex and various medial axis approximation algorithms were studied. One of the most successful is based on the computation of the Voronoi diagram of a set of sample points on the boundary of the object. Based on this method we present a novel representation of solids, which we call a pair-mesh. The pair-mesh is a deformable manifold surface triangulation where each node deforms between a pair of vertices one on the MA approximation and one on the boundary. Consequently, it provides a continuous map between the inner Voronoi based structure and the boundary of the shape, encompassing the topological structures of them both. This representation can also be seen as a partitioning of the volume between the two, where each element in the partition is either a tetrahedron or a pyramid and includes vertices from both the MA approximation and the reconstructed boundary.