[{"type":"journal_article","month":"01","day":"01","publist_id":"1997","_id":"4125","issue":"2","date_updated":"2019-04-26T07:22:41Z","date_created":"2018-12-11T12:07:05Z","author":[{"last_name":"Aurenhammer","first_name":"Franz","full_name":"Aurenhammer,Franz"},{"orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","full_name":"Herbert Edelsbrunner","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"}],"title":"An optimal algorithm for constructing the weighted Voronoi diagram in the plane","abstract":[{"text":"Let S denote a set of n points in the plane such that each point p has assigned a positive weight w(p) which expresses its capability to influence its neighbourhood. In this sense, the weighted distance of an arbitrary point x from p is given by de(x,p)/w(p) where de denotes the Euclidean distance function. The weighted Voronoi diagram for S is a subdivision of the plane such that each point p in S is associated with a region consisting of all points x in the plane for which p is a weighted nearest point of S.\n\nAn algorithm which constructs the weighted Voronoi diagram for S in O(n2) time is outlined in this paper. The method is optimal as the diagram can consist of Θ(n2) faces, edges and vertices.","lang":"eng"}],"quality_controlled":0,"volume":17,"date_published":"1984-01-01T00:00:00Z","publisher":"Springer","doi":"10.1016/0031-3203(84)90064-5","intvolume":" 17","publication":"Pattern Recognition","status":"public","extern":1,"page":"251 - 257","citation":{"ama":"Aurenhammer F, Edelsbrunner H. An optimal algorithm for constructing the weighted Voronoi diagram in the plane. *Pattern Recognition*. 1984;17(2):251-257. doi:10.1016/0031-3203(84)90064-5","apa":"Aurenhammer, F., & Edelsbrunner, H. (1984). An optimal algorithm for constructing the weighted Voronoi diagram in the plane. *Pattern Recognition*, *17*(2), 251–257. https://doi.org/10.1016/0031-3203(84)90064-5","ista":"Aurenhammer F, Edelsbrunner H. 1984. An optimal algorithm for constructing the weighted Voronoi diagram in the plane. Pattern Recognition. 17(2), 251–257.","ieee":"F. Aurenhammer and H. Edelsbrunner, “An optimal algorithm for constructing the weighted Voronoi diagram in the plane,” *Pattern Recognition*, vol. 17, no. 2, pp. 251–257, 1984.","short":"F. Aurenhammer, H. Edelsbrunner, Pattern Recognition 17 (1984) 251–257.","mla":"Aurenhammer, Franz, and Herbert Edelsbrunner. “An Optimal Algorithm for Constructing the Weighted Voronoi Diagram in the Plane.” *Pattern Recognition*, vol. 17, no. 2, Springer, 1984, pp. 251–57, doi:10.1016/0031-3203(84)90064-5.","chicago":"Aurenhammer, Franz, and Herbert Edelsbrunner. “An Optimal Algorithm for Constructing the Weighted Voronoi Diagram in the Plane.” *Pattern Recognition* 17, no. 2 (1984): 251–57. https://doi.org/10.1016/0031-3203(84)90064-5."},"publication_status":"published","year":"1984"}]