{"title":"利用误差函数交替进行四次g 2样条圆逼近","authors":"Soo Won Kim, Y. Ahn","doi":"10.12941/JKSIAM.2013.17.171","DOIUrl":null,"url":null,"abstract":"In this paper we present a method of circular arc approximation by quartic Bezier curve. Our quartic approximation method has a smaller error than previous quartic approximation methods due to the alternation of the error function of our quartic approximation. Our method yields a closed form of error so that subdivision algorithm is available, and curvaturecontinuous quartic spline under the subdivision of circular arc with equal-length until error is less than tolerance. We illustrate our method by some numerical examples.","PeriodicalId":41717,"journal":{"name":"Journal of the Korean Society for Industrial and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2013-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"13","resultStr":"{\"title\":\"CIRCLE APPROXIMATION BY QUARTIC G 2 SPLINE USING ALTERNATION OF ERROR FUNCTION\",\"authors\":\"Soo Won Kim, Y. Ahn\",\"doi\":\"10.12941/JKSIAM.2013.17.171\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper we present a method of circular arc approximation by quartic Bezier curve. Our quartic approximation method has a smaller error than previous quartic approximation methods due to the alternation of the error function of our quartic approximation. Our method yields a closed form of error so that subdivision algorithm is available, and curvaturecontinuous quartic spline under the subdivision of circular arc with equal-length until error is less than tolerance. We illustrate our method by some numerical examples.\",\"PeriodicalId\":41717,\"journal\":{\"name\":\"Journal of the Korean Society for Industrial and Applied Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2013-09-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"13\",\"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.2013.17.171\",\"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.2013.17.171","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
CIRCLE APPROXIMATION BY QUARTIC G 2 SPLINE USING ALTERNATION OF ERROR FUNCTION
In this paper we present a method of circular arc approximation by quartic Bezier curve. Our quartic approximation method has a smaller error than previous quartic approximation methods due to the alternation of the error function of our quartic approximation. Our method yields a closed form of error so that subdivision algorithm is available, and curvaturecontinuous quartic spline under the subdivision of circular arc with equal-length until error is less than tolerance. We illustrate our method by some numerical examples.
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