Estimating principal properties on triangular meshes

Abstract

In this paper, we estimate the principal curvatures of surfaces represented as triangular meshes using a generic model constructed from Euler Formula. Normal curvatures are sampled in the vertices on the direction of a 1-ring neighborhood of a target vertex. Our model is then fitted to a normal curvature graph that connects the pairs of sampled directions and normal curvatures. The principal properties of the surface at the target vertex are estimated from the parameters of the fitted model. We have tested our algorithm on triangular meshes generated from analytic surfaces and show that the errors in our technique are acceptable. We also apply the method to mesh models and discuss degenerate cases. © 2011 Springer-Verlag.