{"title":"An optimal algorithm for constructing the weighted Voronoi diagram in the plane","date_created":"2018-12-11T12:07:05Z","citation":{"apa":"Aurenhammer, F., & Edelsbrunner, H. (1984). An optimal algorithm for constructing the weighted Voronoi diagram in the plane. *Pattern Recognition*. Springer. https://doi.org/10.1016/0031-3203(84)90064-5","ieee":"F. Aurenhammer and H. Edelsbrunner, “An optimal algorithm for constructing the weighted Voronoi diagram in the plane,” *Pattern Recognition*, vol. 17, no. 2. Springer, pp. 251–257, 1984.","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","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*. Springer, 1984. 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.","short":"F. Aurenhammer, H. Edelsbrunner, Pattern Recognition 17 (1984) 251–257."},"extern":1,"publication":"Pattern Recognition","publist_id":"1997","volume":17,"_id":"4125","month":"01","day":"01","type":"journal_article","page":"251 - 257","date_updated":"2021-01-12T07:54:41Z","abstract":[{"lang":"eng","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."}],"quality_controlled":0,"publication_status":"published","year":"1984","author":[{"full_name":"Aurenhammer,Franz","first_name":"Franz","last_name":"Aurenhammer"},{"first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","full_name":"Herbert Edelsbrunner","orcid":"0000-0002-9823-6833"}],"doi":"10.1016/0031-3203(84)90064-5","status":"public","publisher":"Springer","issue":"2","intvolume":" 17","date_published":"1984-01-01T00:00:00Z"}