Placing the Largest Similar Copy of a Convex Polygon Among Polygonal Obstacles
| dc.contributor.author | Chew, L. Paul | en_US |
| dc.contributor.author | Kedem, Klara | en_US |
| dc.date.accessioned | 2007-04-23T17:41:29Z | |
| dc.date.available | 2007-04-23T17:41:29Z | |
| dc.date.issued | 1989-01 | en_US |
| dc.description.abstract | Given a convex polygon $P$ and an environment consisting of polygonal obstacles, we find the largest similar copy of $P$ that does not intersect any of the obstacles. Allowing translation, rotation, and change-of-size, our method combines a new notion of Delaunay triangulation for points and edges with the well-known functions based on Davenport-Schinzel sequences producing an almost quadratic algorithm for the problem. Namely, if $P$ is a convex $k$-gon and if $Q$ has $n$ corners and edges then we can find the placement of the largest similar copy of $P$ in the environment $Q$ in time $O (k^{4}n \lambda_{4}(kn)$ log$n$), where \lambda_{4} is one of the almost-linear functions related to Davenport-Schinzel sequences. If the environment consists only of points then we can find the placement of the largest similar copy of $P$ in time $O (k^{2}n \lambda_{3}(kn)$ log $n$). | en_US |
| dc.format.extent | 1509077 bytes | |
| dc.format.extent | 464857 bytes | |
| dc.format.mimetype | application/pdf | |
| dc.format.mimetype | application/postscript | |
| dc.identifier.citation | http://techreports.library.cornell.edu:8081/Dienst/UI/1.0/Display/cul.cs/TR89-964 | en_US |
| dc.identifier.uri | https://hdl.handle.net/1813/6880 | |
| dc.language.iso | en_US | en_US |
| dc.publisher | Cornell University | en_US |
| dc.subject | computer science | en_US |
| dc.subject | technical report | en_US |
| dc.title | Placing the Largest Similar Copy of a Convex Polygon Among Polygonal Obstacles | en_US |
| dc.type | technical report | en_US |