On the convergence of metric and geometric properties of polyhedral surfaces
Please always quote using this URN:urn:nbn:de:0296-matheon-2733
- We provide conditions for convergence of polyhedral surfaces and their discrete geometric properties to smooth surfaces embedded in R^3. 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 show that totally normal convergence implies convergence results for shortest geodesics, mean curvature, and solutions to the Dirichlet problem. This work provides the justifi- cation for a discrete theory of differential geometric operators defined on polyhedral surfaces based on a variational formulation.
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| Author: | Klaus A. Hildebrandt, Konrad Polthier, Max Wardetzky |
|---|---|
| URN: | urn:nbn:de:0296-matheon-2733 |
| Referee: | Konrad Polthier |
| Document Type: | Preprint, Research Center Matheon |
| Language: | English |
| Date of first Publication: | 2005/06/11 |
| Release Date: | 2005/10/26 |
| Institute: | Freie Universität Berlin |
| Preprint Number: | 282 |
