{"title":"一种改进的Durrmeyer-Bernstein算子及其应用","authors":"Germain E. Randriambelosoa","doi":"10.1155/AMRX.2005.169","DOIUrl":null,"url":null,"abstract":"We present two applications of a modified Durrmeyer-Bernsteinoperator introduced by Goodman and Sharma. A new method isproposed achieving a “good” degree reduction of a Beziercurve with endpoint interpolation. A convenient algorithm will begiven providing an easy and practical method for computing thedegree reduced curve. Then, given a set of (r+1) points, weconstruct a degree n Bezier curve approximation within adistance O(n −1/2 ) from the given points, where n does notdepend on r.","PeriodicalId":89656,"journal":{"name":"Applied mathematics research express : AMRX","volume":"27 1","pages":"169-182"},"PeriodicalIF":0.0000,"publicationDate":"2005-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"On a Modified Durrmeyer-Bernstein Operator and Applications\",\"authors\":\"Germain E. Randriambelosoa\",\"doi\":\"10.1155/AMRX.2005.169\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We present two applications of a modified Durrmeyer-Bernsteinoperator introduced by Goodman and Sharma. A new method isproposed achieving a “good” degree reduction of a Beziercurve with endpoint interpolation. A convenient algorithm will begiven providing an easy and practical method for computing thedegree reduced curve. Then, given a set of (r+1) points, weconstruct a degree n Bezier curve approximation within adistance O(n −1/2 ) from the given points, where n does notdepend on r.\",\"PeriodicalId\":89656,\"journal\":{\"name\":\"Applied mathematics research express : AMRX\",\"volume\":\"27 1\",\"pages\":\"169-182\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2005-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applied mathematics research express : AMRX\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1155/AMRX.2005.169\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied mathematics research express : AMRX","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1155/AMRX.2005.169","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On a Modified Durrmeyer-Bernstein Operator and Applications
We present two applications of a modified Durrmeyer-Bernsteinoperator introduced by Goodman and Sharma. A new method isproposed achieving a “good” degree reduction of a Beziercurve with endpoint interpolation. A convenient algorithm will begiven providing an easy and practical method for computing thedegree reduced curve. Then, given a set of (r+1) points, weconstruct a degree n Bezier curve approximation within adistance O(n −1/2 ) from the given points, where n does notdepend on r.
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