Title :
Point location in Voronoi diagrams of polygons
Author :
Wang, Weizhen ; Yang, Chenglei ; Wang, Xiaoting ; Meng, Xiangxu ; Wei, Min ; Sun, Zheng
Author_Institution :
Sch. of Comput. Sci., Shandong Yingcai Univ., Jinan, China
Abstract :
Given a query point and the Voronoi diagram of a polygon (VD(P)), how to efficiently find the Voronoi region (VR) containing the query point, i.e., the point location in VD(P), is a fundamental operation for many other algorithms based on VD(P), such as path planning, visibility, and so on. A triangulation refinement method for VD(P) is presented in this paper, and then a point-location data structure is provided so that the VR containing the query point can be reported in O(logn) time. The algorithm takes O(n) space and O(nlogn) preprocessing time.
Keywords :
computational geometry; mesh generation; VD-P; VR; Voronoi diagrams; Voronoi region; path planning; point-location data structure; polygons; query point; triangulation refinement method; Voronoi diagram of a polygon; point location; triangulation refinement;
Conference_Titel :
Information Technology in Medicine and Education (ITME), 2012 International Symposium on
Conference_Location :
Hokodate, Hokkaido
Print_ISBN :
978-1-4673-2109-9
DOI :
10.1109/ITiME.2012.6291344