Around Vogt's theorem
Differential Geometry
2012-07-17 v2
Abstract
Vogt's theorem, concerning boundary angles of a convex arc with monotonic curvature (spiral arc), is taken as a starting point to establish basic properties of spirals. The theorem is expanded by removing requirements of convexity and curvature continuity; the cases of inflection and multiple windings are considered. Positional restrictions for a spiral arc with two given curvature elements at the endpoints are established, as well as the necessary and sufficient conditions for the existence of such spiral. Keywords: Vogt's theorem, spiral, inversive invariant, monotonic curvature, lense, biarc, bilense.
Cite
@article{arxiv.math/0601440,
title = {Around Vogt's theorem},
author = {Alexey Kurnosenko},
journal= {arXiv preprint arXiv:math/0601440},
year = {2012}
}
Comments
31+1 pages with 19 figures; typo & e-mail corrected