Quadtree, ray shooting and approximate minimum weight Steiner triangulation

We present a quadtree-based decomposition of the interior of a polygon with holes. The complete decomposition yields a constant factor approximation of the minimum weight Steiner triangulation (MWST) of the polygon. We show that this approximate MWST supports ray shooting queries in the query-sensitive sense as de ned by Mitchell, Mount and Suri. A proper truncation of our quadtreebased decomposition yields another constant factor approximation of the MWST. For a polygon with n vertices, the complexity of this approximateMWST is O(nlogn) and it can be constructed in O(nlogn) time. The running time is optimalin the algebraic decision tree model. The work described in this paper has been supported by the Research Grants Council of Hong Kong, China (Project no. HKUST 650/95E). The work was conducted when the second author was studying at the Department of Computer Science, HKUST. A preliminary version appears in Proceedings of International Symposium on Algorithms and Computation, 1998, ...

• Type: Journal
• Year: 2002
• Where: COMGEO
• Authors: Siu-Wing Cheng, Kam-Hing Lee
• Keywords: Applied Computing, COMGEO 2002, Constant Factor Approximation, Decomposition, Hong Kong