Accession Number:

ADA210104

Title:

Placing the Largest Similar Copy of a Convex Polygon Among Polygonal Obstacles

Descriptive Note:

Technical rept.

Corporate Author:

CORNELL UNIV ITHACA NY DEPT OF COMPUTER SCIENCE

Personal Author(s):

• Chew, L. P.
• Kedem, Klara

Report Date:

1989-01-01

Pagination or Media Count:

21.0

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 to the 4th power n lambda sub 4 kn log n, where lambda sub 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-sqn lambda sub 3 kn log n.

Descriptors:

• *GRAPHS
• *SEQUENCES(MATHEMATICS)
• CONVEX BODIES
• QUADRATIC EQUATIONS
• POLYGONS
• FUNCTIONS
• ALGORITHMS
• BARRIERS

Subject Categories:

• Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE