Discrete schemes for Gaussian curvature and their convergence
Abstract
In this paper, several discrete schemes for Gaussian curvature are surveyed. The convergence property of a modified discrete scheme for the Gaussian curvature is considered. Furthermore, a new discrete scheme for Gaussian curvature is resented. We prove that the new scheme converges at the regular vertex with valence not less than 5. By constructing a counterexample, we also show that it is impossible for building a discrete scheme for Gaussian curvature which converges over the regular vertex with valence 4. Finally, asymptotic errors of several discrete scheme for Gaussian curvature are compared.
- Publication:
-
arXiv e-prints
- Pub Date:
- April 2008
- DOI:
- 10.48550/arXiv.0804.1046
- arXiv:
- arXiv:0804.1046
- Bibcode:
- 2008arXiv0804.1046X
- Keywords:
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- Computer Science - Computer Vision and Pattern Recognition;
- Computer Science - Computational Geometry;
- Computer Science - Graphics;
- Computer Science - Numerical Analysis