{"title":"On Sweep-plane Analysis of Laguerre Voronoi Diagram","authors":"M. Gavrilova, J. Rokne","doi":"10.1109/ISVD.2007.32","DOIUrl":null,"url":null,"abstract":"We discuss application of the sweep-plane technique for the construction of weighted Voronoi diagram in Laguerre geometry (or Laguerre Voronoi diagram). It is shown that the attempt to construct Laguerre Voronoi diagram utilizing the sweep-plane approach transforms the original problem for a given set of weighted sites to the problem of constructing Laguerre diagram for a different set of sites. It follows that the weighted Voronoi diagram in Laguerre geometry is an invariant of a family of all input sets of sites.","PeriodicalId":148710,"journal":{"name":"4th International Symposium on Voronoi Diagrams in Science and Engineering (ISVD 2007)","volume":"63 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2007-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"4th International Symposium on Voronoi Diagrams in Science and Engineering (ISVD 2007)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ISVD.2007.32","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 2
Abstract
We discuss application of the sweep-plane technique for the construction of weighted Voronoi diagram in Laguerre geometry (or Laguerre Voronoi diagram). It is shown that the attempt to construct Laguerre Voronoi diagram utilizing the sweep-plane approach transforms the original problem for a given set of weighted sites to the problem of constructing Laguerre diagram for a different set of sites. It follows that the weighted Voronoi diagram in Laguerre geometry is an invariant of a family of all input sets of sites.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
