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.
ASJC Scopus subject areas
- Theoretical Computer Science
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics