The convergence property of the discrete Laplace-Beltrami operators is the foundation of convergence analysis of the numerical simulation process of some geometric partial differential equations which involve the operator. In this paper we propose several simple discretization schemes of Laplace-Beltrami operators over triangulated surfaces. Convergence results for 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.
Discrete Laplace-Beltrami Operators for Shape Analysis and Segmentation
S Biasotti;D Giorgi;M Spagnuolo
2009
Abstract
The convergence property of the discrete Laplace-Beltrami operators is the foundation of convergence analysis of the numerical simulation process of some geometric partial differential equations which involve the operator. In this paper we propose several simple discretization schemes of Laplace-Beltrami operators over triangulated surfaces. Convergence results for 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
