On the Convergence of Metric and Geometric Properties of Polyhedral Surfaces
Please always quote using this URN: urn:nbn:de:0297-zib-8587
- 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.
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| Author: | Klaus Hildebrandt, Konrad Polthier, Max Wardetzky |
|---|---|
| Document Type: | ZIB-Report |
| Tag: | Differential Geometry; Discrete Geometry; Numerical Analysis |
| Date of first Publication: | 2005/04/08 |
| Series (Serial Number): | ZIB-Report (05-24) |
| ZIB-Reportnumber: | 05-24 |
| Published in: | Appeared in: Geometriae Dedicata 123 (2006) 89-112 |
