3307 Estimation of Principal Curvatures and Principal Directions for Triangular Meshes

Abstract

3D Objects in computer graphics are often represented by triangular meshes. Even surfaces are represented by piecewise planar meshes, we are often required to evaluate differential geometry properties such as normal vectors, principal curvatures, principal directions, locations of umbilics of the underlying smooth surface. However, there is no standard method for estimating differential geometry properties of the unknown smooth surface from polygonal meshes. In this paper, we introduce a new method to calculate principal curvatures and theirs directions. We demonstrate the effectiveness of our method by comparing with other conventional methods.