Mesh Simplification With Curvature Error Metric

Abstract

Progressive meshes algorithms aim at computing levels of detail from a highly detailed mesh. Many of these algorithms are based on a mesh decimation technique, generating coarse triangulation while optimizing for a particular metric which minimizes the distance to the original shape. However these metrics do not robustly handle high curvature regions, sharp features, boundaries or noise. We propose a novel error metric, based on algebraic spheres as a measure of the curvature of the mesh, to preserve curvature along the simplification process. This metric is compact, does not require extra input from the user, and is as simple to implement as a conventional quadric error metric.