{"title":"分段三维欧拉螺旋","authors":"D. Ben-Haim, G. Harary, A. Tal","doi":"10.1145/1839778.1839810","DOIUrl":null,"url":null,"abstract":"3D Euler spirals are visually pleasing, due to their property of having their curvature and their torsion change linearly with arc-length. This paper presents a novel algorithm for fitting piecewise 3D Euler spirals to 3D curves with G2 continuity and torsion continuity. The algorithm can also handle sharp corners. Our piecewise representation is invariant to similarity transformations and it is close to the input curves up to an error tolerance.","PeriodicalId":216067,"journal":{"name":"Symposium on Solid and Physical Modeling","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2010-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"12","resultStr":"{\"title\":\"Piecewise 3D Euler spirals\",\"authors\":\"D. Ben-Haim, G. Harary, A. Tal\",\"doi\":\"10.1145/1839778.1839810\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"3D Euler spirals are visually pleasing, due to their property of having their curvature and their torsion change linearly with arc-length. This paper presents a novel algorithm for fitting piecewise 3D Euler spirals to 3D curves with G2 continuity and torsion continuity. The algorithm can also handle sharp corners. Our piecewise representation is invariant to similarity transformations and it is close to the input curves up to an error tolerance.\",\"PeriodicalId\":216067,\"journal\":{\"name\":\"Symposium on Solid and Physical Modeling\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2010-09-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"12\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Symposium on Solid and Physical Modeling\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/1839778.1839810\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Symposium on Solid and Physical Modeling","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/1839778.1839810","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
3D Euler spirals are visually pleasing, due to their property of having their curvature and their torsion change linearly with arc-length. This paper presents a novel algorithm for fitting piecewise 3D Euler spirals to 3D curves with G2 continuity and torsion continuity. The algorithm can also handle sharp corners. Our piecewise representation is invariant to similarity transformations and it is close to the input curves up to an error tolerance.
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