P. Bose, L. Guibas, A. Lubiw, M. Overmars, D. Souvaine, J. Urrutia
{"title":"泛光灯问题","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":"{\"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}","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}
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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