{"title":"Open Problem: A Formula for Calculation of the Voronoi S-region Volume","authors":"N. N. Medvedev, V. Voloshin","doi":"10.1109/ISVD.2013.14","DOIUrl":null,"url":null,"abstract":"Fast and accurate calculation of the volume of additively weighted Voronoi region (Johnson-Mehl nucleus, or Voronoi S-region) is needed in various physical applications. The problem will be solved if an analytical expression could be derived for volume calculation of the pyramid which base is a piece of the hyperboloid surface.","PeriodicalId":344701,"journal":{"name":"2013 10th International Symposium on Voronoi Diagrams in Science and Engineering","volume":"12 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2013-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2013 10th International Symposium on Voronoi Diagrams in Science and Engineering","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ISVD.2013.14","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
Abstract
Fast and accurate calculation of the volume of additively weighted Voronoi region (Johnson-Mehl nucleus, or Voronoi S-region) is needed in various physical applications. The problem will be solved if an analytical expression could be derived for volume calculation of the pyramid which base is a piece of the hyperboloid surface.
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