Voronoi的圆图变得简单了

4th International Symposium on Voronoi Diagrams in Science and Engineering (ISVD 2007) Pub Date : 2007-07-09 DOI:10.1109/ISVD.2007.37

F. Anton, D. Mioc, C. Gold

{"title":"Voronoi的圆图变得简单了","authors":"F. Anton, D. Mioc, C. Gold","doi":"10.1109/ISVD.2007.37","DOIUrl":null,"url":null,"abstract":"Proximity queries among circles could be effectively answered if the Delaunay graph for sets of circles could be computed in an efficient and exact way. In this paper, we first show a necessary and sufficient condition of connectivity of the Voronoi diagram of circles. Then, we show how the Delaunay graph of circles (the dual graph of the Voronoi diagram of circles) can be computed exactly, and in a much simpler way, by computing the eigenvalues of a two by two matrix.","PeriodicalId":148710,"journal":{"name":"4th International Symposium on Voronoi Diagrams in Science and Engineering (ISVD 2007)","volume":"115 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2007-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"The Voronoi diagram of circles made easy\",\"authors\":\"F. Anton, D. Mioc, C. Gold\",\"doi\":\"10.1109/ISVD.2007.37\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Proximity queries among circles could be effectively answered if the Delaunay graph for sets of circles could be computed in an efficient and exact way. In this paper, we first show a necessary and sufficient condition of connectivity of the Voronoi diagram of circles. Then, we show how the Delaunay graph of circles (the dual graph of the Voronoi diagram of circles) can be computed exactly, and in a much simpler way, by computing the eigenvalues of a two by two matrix.\",\"PeriodicalId\":148710,\"journal\":{\"name\":\"4th International Symposium on Voronoi Diagrams in Science and Engineering (ISVD 2007)\",\"volume\":\"115 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2007-07-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"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.2007.37\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","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.2007.37","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 4

摘要

如果能高效准确地计算出圆集的Delaunay图，就能有效地解决圆间的邻近查询问题。本文首先给出了Voronoi圆图连通性的一个充分必要条件。然后，我们展示了如何通过计算2 × 2矩阵的特征值，以一种更简单的方式精确地计算Delaunay圆图(Voronoi圆图的对偶图)。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

The Voronoi diagram of circles made easy

Proximity queries among circles could be effectively answered if the Delaunay graph for sets of circles could be computed in an efficient and exact way. In this paper, we first show a necessary and sufficient condition of connectivity of the Voronoi diagram of circles. Then, we show how the Delaunay graph of circles (the dual graph of the Voronoi diagram of circles) can be computed exactly, and in a much simpler way, by computing the eigenvalues of a two by two matrix.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

4th International Symposium on Voronoi Diagrams in Science and Engineering (ISVD 2007)

自引率

0.00%

发文量