Abstract
We consider the problem of better approximating surfaces by triangular meshes. The approximating triangulations are regarded as finite metric spaces and the approximated smooth surfaces are viewed as their Haussdorff-Gromov limit. This allows us to define in a more natural way the relevant elements, constants and invariants, such as principal directions and Gauss curvature, etc. By a “natural way” we mean intrinsic, discrete, metric definitions as opposed to approximating or paraphrasing the differentiable notions. Here we consider the problem of determining the Gauss curvature of a polyhedral surface, by using the metric curvatures in the sense of Wald, Menger and Haantjes. We present three modalities of employing these definitions for the computation of Gauss curvature.
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Saucan, E., Appleboim, E. (2009). Metric Methods in Surface Triangulation. In: Hancock, E.R., Martin, R.R., Sabin, M.A. (eds) Mathematics of Surfaces XIII. Mathematics of Surfaces 2009. Lecture Notes in Computer Science, vol 5654. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03596-8_20
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DOI: https://doi.org/10.1007/978-3-642-03596-8_20
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