Curvature Estimation over Smooth Polygonal Meshes Using the Half Tube Formula

The interest, in recent years, in the geometric processing of polygonal meshes, has spawned a whole range of algorithms to estimate curvature properties over smooth polygonal meshes. Being a discrete approximation of a C continuous surface, these methods attempt to estimate the curvature properties of the original surface. The best known methods are quite effective in estimating the total or Gaussian curvature but less so in estimating the mean curvature. In this work, we present a scheme to accurately estimate the mean curvature of smooth polygonal meshes using a one sided tube formula [16] of the volume above the surface. In the presented comparison, the proposed scheme yielded results whose accuracy is amongst the highest compared to similar techniques for estimating the mean curvature.