Convergence analysis of a discretization scheme for Gaussian curvature over triangular surfaces

In this paper, we study the convergent property of a well known discretized scheme of Gaussian curvature, derived from Gauss-Bonnet theorem, over triangulated surface. Suppose the triangulation is obtained from a sampling of a smooth parametric surface, we show theoretically that the discretized approximation has quadratic convergence rate for a special triangulation scenario of the surface. Numerical results which justify the theoretical analysis are also presented. Key words: Gaussian Curvature; Surface triangulation; Convergence.

• Type: Journal
• Year: 2006
• Where: CAGD
• Authors: Guoliang Xu
• Keywords: CAGD 2006, Gaussian Curvature, Smooth Parametric Surface, Triangulation