Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
441400 | Computer Aided Geometric Design | 2006 | 15 Pages |
Abstract
In this paper, we study the convergence property of a well known discretized scheme for approximating 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 approximation has quadratic convergence rate if the surface sampling satisfies the so-called parallelogram criterion. Numerical results which justify the theoretical analysis are also presented.
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