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arXiv · 2008.13236

Discrete Curvature and Torsion from Cross-Ratios

Christian Müller·Amir Vaxman
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Abstract

Motivated by a M\"obius 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 M\"obius 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 M\"obius invariant notion, using the cross-ratio and show its asymptotic behavior in analogy to the curvature.

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BibTeXRIS

Christian Müller, Amir Vaxman. 2020-08-30. Discrete Curvature and Torsion from Cross-Ratios. https://arxiv.org/abs/2008.13236

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