Volume Cost Based Mesh Simplification

We develop a polygonal mesh simplification algorithm using a vertex decimation approach. The novelty in our method lies in (a) a characterization of mesh vertices as hyperbolic or nonhyperbolic based upon their discrete local geometry, (b) the cost function used to select a vertex for decimation, and (c) the heuristics applied to re-triangulate the resulting hole. The algorithm begins by classifying the input mesh vertices as hyperbolic or non-hyperbolic, and then computes a volume cost for each nonhyperbolic vertex, in analogy with spherical volume, to capture the loss of fidelity if that vertex is decimated. Vertices of least volume cost are successively deleted and the resulting hole re-triangulated. Preliminary experiments indicate a performance comparable to that of the best known mesh simplification algorithms.