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- W1643287545 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." @default.
- W1643287545 created "2016-06-24" @default.
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- W1643287545 date "2006-01-18" @default.
- W1643287545 modified "2023-10-06" @default.
- W1643287545 title "Around Vogt's theorem" @default.
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