Multivariate analysis of curvature estimators

ABSTRACTPrincipal curvature is one of the defining features of surfaces studied in differential geometry. While well-defined and easy to evaluate for smooth surfaces, it cannot be evaluated exactly if the surface is represented by a polygon mesh, unless some special conditions apply. Nevertheless, estimating the curvature of a surface mesh is a crucial step in common mesh processing algorithms, such as mesh segmentation, mesh smoothing, remeshing and others. While a wealth of approaches for estimating the curvature has been proposed in the literature, aiming at the best possible precision of the estimation, an objective study identifying the strengths and weaknesses of the different methods was usually lacking. We present results of a comprehensive study focused on different aspects of curvature estimation. We extend some of the estimators in order to match properties of others and thus provide comparable results. The results of the study indicate that currently there is no one universally optimal method ...