An optimal visibility graph algorithm for triangulated simple polygons
- 319 Downloads
LetP be a triangulated simple polygon withn sides. The visibility graph ofP has an edge between every pair of polygon vertices that can be connected by an open segment in the interior ofP. We describe an algorithm that finds the visibility graph ofP inO(m) time, wherem is the number of edges in the visibility graph. Becausem can be as small asO(n), the algorithm improves on the more general visibility algorithms of Asanoet al. [AAGHI] and Welzl [W], which take Θ(n 2) time, and on Suri'sO(m logn) visibility graph algorithm for simple polygons [S].
Key wordsSimple polygon Visibility graph Triangulation Shortest path Shortest-path map
Unable to display preview. Download preview PDF.
- [B]B. Baumgart: A polyhedral representation for computer vision.Proceedings of the AFIPS National Computer Conference, Anaheim, California, 1975, pp. 589–596.Google Scholar
- [CG]B. Chazelle and L. Guibas: Visibility and intersection problems in plane geometry.Proceedings of the ACM Symposium on Computational Geometry, Baltimore, 1985, pp. 135–146.Google Scholar
- [GM]S. K. Ghosh and D. M. Mount: An output sensitive algorithm for computing visibility graphs.Proceedings of the 28th IEEE Symposium on Foundations of Computer Science, Los Angeles, 1987, pp. 11–19.Google Scholar
- [GMPR]L. Guibas, E. McCreight, M. Plass, and J. Roberts: A new representation for linear lists.Proceedings of the Ninth ACM Symposium on Theory of Computing, Boulder, Colorado, 1977, pp. 49–60.Google Scholar
- [HeM]S. Hertel and K. Mehlhorn: Fast triangulation of a simple polygon.Proceedings of the Conference on Foundations of Computing Theory, New York, 1983, pp. 207–218.Google Scholar
- [S]S. Suri: Private communication, 1986.Google Scholar