Curvature Estimation over Smooth Polygonal Meshes using The Half Tube Formula Ronen Lev 1 , Emil Saucan 2 , and Gershon Elber 3 1 OptiTex Ltd., Petach-Tikva 49221, Israel, ronen.lev@optitex.com 2 Electrical Engineering Department, Technion, Haifa 32000, Israel, semil@ee.technion.ac.il 3 Computer Science Department, Technion, Haifa 32000, Israel, gershon@cs.technion.ac.il Abstract 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 2 continuous surface, these methods attempt to estimate the curvature properties of the orig- inal 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. 1 Introduction Polygonal meshes are basic representations of geometry that are employed in a whole variety of fields from vision and image processing to computer graphics, geometric modeling and manufacturing. Analysis of such data sets is of great value in many applications such as reconstruction, segmentation and recognition or even non photorealistic rendering. In this context, curvature analysis plays a major role. As an example, curvature analysis of 3D scanned data sets were shown to be one of the best approaches to segmenting the data [32]. Though many algorithms attempt to estimate the total, or Gaussian cur- vature K, and mean curvature, H , of the original surface, given its polygonal approximation, we will discuss here only the most well known and accurate ones. For a more rigorous comparison of curvature estimation methods, see, for example, [28].