Total Curvature and Spiralling Shortest Paths
| Autor: | Tudor Zamfirescu, Krystyna Kuperberg, Imre Bárány |
|---|---|
| Rok vydání: | 2003 |
| Předmět: |
Regular polygon
Polytope Computer Science::Computational Geometry Theoretical Computer Science Combinatorics Euclidean shortest path Arbitrarily large Computational Theory and Mathematics Shortest path problem Convex polytope Mathematics::Metric Geometry Discrete Mathematics and Combinatorics Total curvature Geometry and Topology Ball (mathematics) Mathematics |
| Zdroj: | Discrete and Computational Geometry. 30:167-176 |
| ISSN: | 1432-0444 0179-5376 |
| DOI: | 10.1007/s00454-003-0001-z |
| Popis: | This paper gives a partial confirmation of a conjecture of Agarwal, Har-Peled, Sharir, and Varadarajan that the total curvature of a shortest path on the boundary of a convex polyhedron in R3 cannot be arbitrarily large. It is shown here that the conjecture holds for a class of polytopes for which the ratio of the radii of the circumscribed and inscribed ball is bounded. On the other hand, an example is constructed to show that the total curvature of a shortest path on the boundary of a convex polyhedron in R3 can exceed 2π. Another example shows that the spiralling number of a shortest path on the boundary of a convex polyhedron can be arbitrarily large. |
| Databáze: | OpenAIRE |
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