Uniform Convergence of Discrete Curvatures from Nets of Curvature Lines
Copyright policy )Uniform Convergence of Discrete Curvatures from Nets of Curvature Lines
We study discrete curvatures computed from nets of curvature lines on a given smooth surface, and prove their uniform convergence to smooth principal curvatures. We provide explicit error bounds, with constants depending only on properties of the smooth limit surface and the shape regularity of the discrete net.
21 pages, 8 figures
- University of Göttingen Germany
- Freie Universität Berlin Germany
Mathematics - Differential Geometry, polyhedral surfaces, Polyhedral manifolds, curvature lines, Theoretical Computer Science, Surfaces in Euclidean and related spaces, Computer-aided design (modeling of curves and surfaces), Computational Theory and Mathematics, Differential Geometry (math.DG), FOS: Mathematics, Discrete Mathematics and Combinatorics, 53A05, 65D18, Geometry and Topology, discrete curvatures, cotangent formula
Mathematics - Differential Geometry, polyhedral surfaces, Polyhedral manifolds, curvature lines, Theoretical Computer Science, Surfaces in Euclidean and related spaces, Computer-aided design (modeling of curves and surfaces), Computational Theory and Mathematics, Differential Geometry (math.DG), FOS: Mathematics, Discrete Mathematics and Combinatorics, 53A05, 65D18, Geometry and Topology, discrete curvatures, cotangent formula
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