Chew, L. PaulKedem, Klara2007-04-232007-04-231989-01http://techreports.library.cornell.edu:8081/Dienst/UI/1.0/Display/cul.cs/TR89-964https://hdl.handle.net/1813/6880Given 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 $n$).1509077 bytes464857 bytesapplication/pdfapplication/postscripten-UScomputer sciencetechnical reporttechnical report