Experimental Comparison of Methods for Differential Geometric Properties Evaluation in Triangular Meshes

Abstract

This paper deals with the investigation of the stability and the accuracy of the most important methods to estimate the parameters that are involved in the shape recognition process of tessellated surfaces. For this purpose, four approaches to estimate the differential geometric properties of tessellated surfaces are systematically examined (namely, simple and extended quadric fitting methods, Rusinkiewicz’s method and Meyer discrete method). A set of test cases has been designed in order to investigate the sensitivity of those methods to factors such as noise in point location, surface typology (chosen between those types that usually define the boundary of mechanical parts such as: planes, cylinders, spheres, cones and tori), mesh resolution and mesh regularity. Based on the results obtained, some criticism of the analyzed methods is made and some guidelines are provided in order to choose the most robust and reliable method in relation to the surface typology, quality of the mesh and noise in point location.

Keywords:

• triangular meshes
• curvature estimation
• shape recognition