Name
Abstract | ||
|---|---|---|
AbstractThis 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 2ź. Another example shows that the spiralling number of a shortest path on the boundary of a convex polyhedron can be arbitrarily large. |
Year | DOI | Venue |
|---|---|---|
2003 | 10.1007/s00454-003-0001-z | Periodicals |
Keywords | Field | DocType |
convex. i. barany's research was supported in part by hungarian national science foundation grants #t-032452 and #t-029255.,. total curvature,shortest path,spiralling number,3 dimensional,euclidean space | Topology,Combinatorics,Shortest path problem,Total curvature,Inscribed figure,Regular polygon,Convex polytope,Polytope,Mathematics,Arbitrarily large,Euclidean shortest path | Journal |
Volume | Issue | ISSN |
30 | 2 | 0179-5376 |
Citations | PageRank | References |
0 | 0.34 | 1 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Imre Bárány | 1 | 435 | 95.10 |
| Krystyna Kuperberg | 2 | 3 | 1.53 |
| Tudor Zamfirescu | 3 | 77 | 16.85 |