Discrete curvature and torsion from cross-ratios
Annali di Matematica Pura ed Applicata (1923 -)(2021)
摘要
Motivated by a Möbius invariant subdivision scheme for polygons, we study a curvature notion for discrete curves where the cross-ratio plays an important role in all our key definitions. Using a particular Möbius invariant point-insertion-rule, comparable to the classical four-point-scheme, we construct circles along discrete curves. Asymptotic analysis shows that these circles defined on a sampled curve converge to the smooth curvature circles as the sampling density increases. We express our discrete torsion for space curves, which is not a Möbius invariant notion, using the cross-ratio and show its asymptotic behavior in analogy to the curvature.
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关键词
Discrete curvature, Discrete torsion, Asymptotic analysis, 41A60, 52Cxx, 53A40
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