P. Bose, L. Guibas, A. Lubiw, M. Overmars, D. Souvaine, J. Urrutia
{"title":"The Floodlight Problem","authors":"P. Bose, L. Guibas, A. Lubiw, M. Overmars, D. Souvaine, J. Urrutia","doi":"10.1142/S0218195997000090","DOIUrl":null,"url":null,"abstract":"Given three angles summing to 2π, given n points in the plane and a tripartition k1 + k2 + k3 = n, we can tripartition the plane into three wedges of the given angles so that the i-th wedge contains ki of the points. This new result on dissecting point sets is used to prove that lights of specified angles not exceeding π can be placed at n fixed points in the plane to illuminate the entire plane if and only if the angles sum to at least 2π. We give O(nlog n) algorithms for both these problems.","PeriodicalId":285210,"journal":{"name":"International Journal of Computational Geometry and Applications","volume":"119 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1997-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"53","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Computational Geometry and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/S0218195997000090","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 53
Abstract
Given three angles summing to 2π, given n points in the plane and a tripartition k1 + k2 + k3 = n, we can tripartition the plane into three wedges of the given angles so that the i-th wedge contains ki of the points. This new result on dissecting point sets is used to prove that lights of specified angles not exceeding π can be placed at n fixed points in the plane to illuminate the entire plane if and only if the angles sum to at least 2π. We give O(nlog n) algorithms for both these problems.
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