Computing Simple Paths on Points in Simple Polygons

Authors:
Ovidiu Daescu;Jun Luo
Affiliations:
Department of Computer Science, University of Texas at Dallas, Richardson, USA TX 75080;Department of Information and Computing Sciences, Utrecht University, Utrecht, The Netherlands 3584CH
Venue:
Computational Geometry and Graph Theory
Year:
2008

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Abstract

Given a simple polygon P with m vertices, a set X = {x 1 ,x 2 , ...,x n } of n points within P , a start point s *** X , and an end point t *** X , we give an O (n 3logm + mn ) time, O (n 3 + m ) space algorithm to find O (n 2) simple polygonal paths from s to t that have their vertices among the points in X and stay inside P , or report that no such path exists.