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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