Discrete extrinsic curvatures based on polar polyhedra concept - Mathematics > Differential GeometryReport as inadecuate




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Abstract: Duality principle for approximation of geometrical objects also known asEudoxus exhaustion method was extended and perfected by Archimedes in hisfamous tractate -Measurement of circle-. The main idea of the approximationmethod by Archimedes is to construct a sequence of pairs of inscribed andcircumscribed polygons polyhedra which approximate curvilinear convex body.This sequence allows to approximate length of curve, as well as area and volumeof the bodies and to obtain error estimates for approximation. In this work itis shown that a sequence of pairs of locally polar polyhedra allows toconstruct piecewise-affine approximation to scherical Gauss map, to constructconvergent point-wise approximations to mean and Gauss curvature, as well as toobtain natural discretizations of bending energies.



Author: V.A. Garanzha

Source: https://arxiv.org/







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