{"title":"递归细分与超几何函数","authors":"L. Ivrissimtzis, N. Dodgson, M. Sabin","doi":"10.1109/SMI.2002.1003525","DOIUrl":null,"url":null,"abstract":"We describe a method for efficient calculation of coefficients for subdivision schemes. We work on the unit sphere and we express the z-coordinate of all the existing points as power series in the variable cos /spl theta/. Any linear combination of them is also a power series in cos /spl theta/ and, by solving a linear system, we determine the linear combination that will give the smoothest interpolation of the sphere at a particular point.","PeriodicalId":267347,"journal":{"name":"Proceedings SMI. Shape Modeling International 2002","volume":"29 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2002-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Recursive subdivision and hypergeometric functions\",\"authors\":\"L. Ivrissimtzis, N. Dodgson, M. Sabin\",\"doi\":\"10.1109/SMI.2002.1003525\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We describe a method for efficient calculation of coefficients for subdivision schemes. We work on the unit sphere and we express the z-coordinate of all the existing points as power series in the variable cos /spl theta/. Any linear combination of them is also a power series in cos /spl theta/ and, by solving a linear system, we determine the linear combination that will give the smoothest interpolation of the sphere at a particular point.\",\"PeriodicalId\":267347,\"journal\":{\"name\":\"Proceedings SMI. Shape Modeling International 2002\",\"volume\":\"29 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2002-05-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings SMI. Shape Modeling International 2002\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/SMI.2002.1003525\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings SMI. Shape Modeling International 2002","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SMI.2002.1003525","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Recursive subdivision and hypergeometric functions
We describe a method for efficient calculation of coefficients for subdivision schemes. We work on the unit sphere and we express the z-coordinate of all the existing points as power series in the variable cos /spl theta/. Any linear combination of them is also a power series in cos /spl theta/ and, by solving a linear system, we determine the linear combination that will give the smoothest interpolation of the sphere at a particular point.
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