{"title":"圆弧的c3四次b样条近似的近似阶","authors":"Sungchul Bae, Y. Ahn","doi":"10.12941/JKSIAM.2016.20.151","DOIUrl":null,"url":null,"abstract":"In this paper, we present a C 3 quartic B-spline approximation of circular arcs. The Hausdorff distance between the C 3 quartic B-spline curve and the circular arc is obtained in closed form. Using this error analysis, we show that the approximation order of our approximation method is six. For a given circular arc and error tolerance we find the C 3 quartic B-spline curve having the minimum number of control points within the tolerance. The algorithm yielding the C 3 quartic B-spline approximation of a circular arc is also presented.","PeriodicalId":41717,"journal":{"name":"Journal of the Korean Society for Industrial and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2016-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"APPROXIMATION ORDER OF C 3 QUARTIC B-SPLINE APPROXIMATION OF CIRCULAR ARC\",\"authors\":\"Sungchul Bae, Y. Ahn\",\"doi\":\"10.12941/JKSIAM.2016.20.151\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we present a C 3 quartic B-spline approximation of circular arcs. The Hausdorff distance between the C 3 quartic B-spline curve and the circular arc is obtained in closed form. Using this error analysis, we show that the approximation order of our approximation method is six. For a given circular arc and error tolerance we find the C 3 quartic B-spline curve having the minimum number of control points within the tolerance. The algorithm yielding the C 3 quartic B-spline approximation of a circular arc is also presented.\",\"PeriodicalId\":41717,\"journal\":{\"name\":\"Journal of the Korean Society for Industrial and Applied Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2016-06-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of the Korean Society for Industrial and Applied Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.12941/JKSIAM.2016.20.151\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the Korean Society for Industrial and Applied Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.12941/JKSIAM.2016.20.151","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
APPROXIMATION ORDER OF C 3 QUARTIC B-SPLINE APPROXIMATION OF CIRCULAR ARC
In this paper, we present a C 3 quartic B-spline approximation of circular arcs. The Hausdorff distance between the C 3 quartic B-spline curve and the circular arc is obtained in closed form. Using this error analysis, we show that the approximation order of our approximation method is six. For a given circular arc and error tolerance we find the C 3 quartic B-spline curve having the minimum number of control points within the tolerance. The algorithm yielding the C 3 quartic B-spline approximation of a circular arc is also presented.
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