An efficient motion-planning algorithm for a convex polygonal object in two-dimensional polygonal space

K. Kedem, M. Sharir

Research output: Contribution to journalArticlepeer-review

Abstract

We present an efficient algorithm for planning the motion of a convex polygonal body B in two-dimensional space bounded by a collection of polygonal obstacles. Our algorithm extends and combines the techniques of Leven and Sharir and of Sifrony and Sharir used for the case in which B is a line segment (a "ladder"). It also makes use of the results of Kedem and Sharir on the planning of translational motion of B amidst polygonal obstacles, and of a recent result of Leven and Sharir on the number of free critical contacts of B with such polygonal obstacles. The algorithm runs in time O(knλ6(kn) log kn), where k is the number of sides of B, n is the number of obstacle edges, and λ,(q) is an almost linear function of q yielding the maximal number of connected portions of q continuous functions which compose the graph of their lower envelope, where it is assumed that each pair of these functions intersect in at most s points.

Original languageEnglish
Pages (from-to)43-75
Number of pages33
JournalDiscrete and Computational Geometry
Volume5
Issue number1
DOIs
StatePublished - Dec 1990

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