Discrete schemes for Gaussian curvature and their convergence

Details Discrete schemes for Gaussian curvature and their convergence Discrete schemes for Gaussian curvature and their convergence

2008-04-07

arxiv.org/abs/0804.1046v1

Computer Science

Computer Vision and Pattern Recognition

Scientific paper

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.

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