Convergent Discrete Laplace-Beltrami Operators over Triangular Surfaces

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GMP '04 Proceedings of the Geometric Modeling and Processing 2004
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2004

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Abstract

The convergence property of the discrete Laplace-Beltrami operators is the foundation of convergence analysis of the numerical simulation process of somegeometric partial differential equations which involvethe operator. In this paper we propose several simple discretization schemes of Laplace-Beltrami operators over triangulated surfaces. Convergence resultsfor these discrete Laplace-Beltrami operators are established under various conditions. Numerical results that support the theoretical analysis are given. Application examples of the proposed discrete Laplace-Beltrami operators in surface processing and modelling are also presented.