{"title":"Chaiken算法在几何级数中带结点b样条曲线上的推广","authors":"Goldman R., Warren J.","doi":"10.1006/cgip.1993.1004","DOIUrl":null,"url":null,"abstract":"<div><p>Chaiken′s algorithm is a procedure for inserting new knots into uniform quadratic B-spline curves by doubling the control points and taking two successive averages. Lane and Riesenfeld showed that Chaiken′s algorithm extends to uniform B-spline curves of arbitrary degree. By generalizing the notion of successive averaging, we further extend Chaiken′s algorithm to B-spline curves of arbitrary degree for knot sequences in geometric and affine progression.</p></div>","PeriodicalId":100349,"journal":{"name":"CVGIP: Graphical Models and Image Processing","volume":"55 1","pages":"Pages 58-62"},"PeriodicalIF":0.0000,"publicationDate":"1993-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1006/cgip.1993.1004","citationCount":"10","resultStr":"{\"title\":\"An Extension of Chaiken′s Algorithm to B-Spline Curves with Knots in Geometric Progression\",\"authors\":\"Goldman R., Warren J.\",\"doi\":\"10.1006/cgip.1993.1004\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Chaiken′s algorithm is a procedure for inserting new knots into uniform quadratic B-spline curves by doubling the control points and taking two successive averages. Lane and Riesenfeld showed that Chaiken′s algorithm extends to uniform B-spline curves of arbitrary degree. By generalizing the notion of successive averaging, we further extend Chaiken′s algorithm to B-spline curves of arbitrary degree for knot sequences in geometric and affine progression.</p></div>\",\"PeriodicalId\":100349,\"journal\":{\"name\":\"CVGIP: Graphical Models and Image Processing\",\"volume\":\"55 1\",\"pages\":\"Pages 58-62\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1993-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1006/cgip.1993.1004\",\"citationCount\":\"10\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"CVGIP: Graphical Models and Image Processing\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S1049965283710047\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"CVGIP: Graphical Models and Image Processing","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1049965283710047","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
An Extension of Chaiken′s Algorithm to B-Spline Curves with Knots in Geometric Progression
Chaiken′s algorithm is a procedure for inserting new knots into uniform quadratic B-spline curves by doubling the control points and taking two successive averages. Lane and Riesenfeld showed that Chaiken′s algorithm extends to uniform B-spline curves of arbitrary degree. By generalizing the notion of successive averaging, we further extend Chaiken′s algorithm to B-spline curves of arbitrary degree for knot sequences in geometric and affine progression.
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