{"title":"星座中具有给定同伦的最短电路","authors":"D. Michelucci, M. Neveu","doi":"10.2312/SM.20041405","DOIUrl":null,"url":null,"abstract":"A polynomial method is described for computing the shortest circuit with a prescribed homotopy on a surface. The surface is not described by a mesh but by a constellation: a set of sampling points. Points close enough (their distance is less than a prescribed threshold) are linked with an edge: the induced graph is not a triangulation but still permits to compute homologic and homotopic properties. Advantages of constellations over meshes are their simplicity and robustness.","PeriodicalId":405863,"journal":{"name":"ACM Symposium on Solid Modeling and Applications","volume":"31 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2004-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Shortest circuits with given homotopy in a constellation\",\"authors\":\"D. Michelucci, M. Neveu\",\"doi\":\"10.2312/SM.20041405\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A polynomial method is described for computing the shortest circuit with a prescribed homotopy on a surface. The surface is not described by a mesh but by a constellation: a set of sampling points. Points close enough (their distance is less than a prescribed threshold) are linked with an edge: the induced graph is not a triangulation but still permits to compute homologic and homotopic properties. Advantages of constellations over meshes are their simplicity and robustness.\",\"PeriodicalId\":405863,\"journal\":{\"name\":\"ACM Symposium on Solid Modeling and Applications\",\"volume\":\"31 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2004-06-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACM Symposium on Solid Modeling and Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2312/SM.20041405\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACM Symposium on Solid Modeling and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2312/SM.20041405","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Shortest circuits with given homotopy in a constellation
A polynomial method is described for computing the shortest circuit with a prescribed homotopy on a surface. The surface is not described by a mesh but by a constellation: a set of sampling points. Points close enough (their distance is less than a prescribed threshold) are linked with an edge: the induced graph is not a triangulation but still permits to compute homologic and homotopic properties. Advantages of constellations over meshes are their simplicity and robustness.
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