Discrete Curvature and Torsion from Cross-Ratios
Differential Geometry
2020-09-01 v1 Graphics
Numerical Analysis
Numerical Analysis
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.
Keywords
Cite
@article{arxiv.2008.13236,
title = {Discrete Curvature and Torsion from Cross-Ratios},
author = {Christian Müller and Amir Vaxman},
journal= {arXiv preprint arXiv:2008.13236},
year = {2020}
}