Mesh Simplification via a Volume Cost Measure

We develop a polygonal mesh simplification algorithm based on a novel analysis of the mesh geometry. Particularly, we propose first a characterization of vertices as hyperbolic or non-hyperbolic depend-ing upon their discrete local geometry. Subsequently, the simplification process computes a volume cost for each non-hyperbolic vertex, in anal-ogy with spherical volume, to capture the loss of fidelity if that vertex is decimated. Vertices of least volume cost are then successively deleted and the resulting holes retriangulated using a method based on a novel heuristic. Preliminary experiments indicate a performance comparable to that of the best known mesh simplification algorithms.