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On the Convergence of Metric and Geometric Properties of Polyhedral Surfaces (2005)

Hildebrandt, Klaus ; Polthier, Konrad ; Wardetzky, Max

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Publication Date: 2014-02-26

Description: We provide conditions for convergence of polyhedral surfaces and their discrete geometric properties to smooth surfaces embedded in Euclidian $3$-space. The notion of totally normal convergence is shown to be equivalent to the convergence of either one of the following: surface area, intrinsic metric, and Laplace-Beltrami operators. We further s how that totally normal convergence implies convergence results for shortest geodesics, mean curvature, and solutions to the Dirichlet problem. This work provides the justification for a discrete theory of differential geometric operators defined on polyhedral surfaces based on a variational formulation.

Keywords: ddc:000

Language: English

Type: reportzib , doc-type:preprint

Format: application/pdf

Format: application/postscript

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