{"title":"拟圆样条:一种保形逼近","authors":"Howell G.W., Fausett D.W., Fausett L.V.","doi":"10.1006/cgip.1993.1007","DOIUrl":null,"url":null,"abstract":"<div><p>The \"quasi-circular spline\" is introduced as a new method for approximating closed, smooth planar shapes from curvature information. A current application is the measurement of shapes of solid rocket booster cross-sections. Because of the efficiency of the algorithm and its desirable geometric properties, it is also particularly appropriate for computer graphics. The simplicity and efficiency of the quasi-circular spline compare well with previously proposed schemes which are important in graphical applications. It is invariant under the transformations of the Euclidean group. Furthermore, it is shape-preserving in that the quasi-circular spline approximation to a convex planar curve is also convex. Sufficient conditions for convergence are described, and <em>O</em>(<em>h</em><sup>2</sup>) approximation to sufficiently smooth curves is demonstrated.</p></div>","PeriodicalId":100349,"journal":{"name":"CVGIP: Graphical Models and Image Processing","volume":"55 2","pages":"Pages 89-97"},"PeriodicalIF":0.0000,"publicationDate":"1993-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1006/cgip.1993.1007","citationCount":"2","resultStr":"{\"title\":\"Quasi-circular Splines: A Shape-Preserving Approximation\",\"authors\":\"Howell G.W., Fausett D.W., Fausett L.V.\",\"doi\":\"10.1006/cgip.1993.1007\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The \\\"quasi-circular spline\\\" is introduced as a new method for approximating closed, smooth planar shapes from curvature information. A current application is the measurement of shapes of solid rocket booster cross-sections. Because of the efficiency of the algorithm and its desirable geometric properties, it is also particularly appropriate for computer graphics. The simplicity and efficiency of the quasi-circular spline compare well with previously proposed schemes which are important in graphical applications. It is invariant under the transformations of the Euclidean group. Furthermore, it is shape-preserving in that the quasi-circular spline approximation to a convex planar curve is also convex. Sufficient conditions for convergence are described, and <em>O</em>(<em>h</em><sup>2</sup>) approximation to sufficiently smooth curves is demonstrated.</p></div>\",\"PeriodicalId\":100349,\"journal\":{\"name\":\"CVGIP: Graphical Models and Image Processing\",\"volume\":\"55 2\",\"pages\":\"Pages 89-97\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1993-03-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1006/cgip.1993.1007\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"CVGIP: Graphical Models and Image Processing\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S1049965283710072\",\"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/S1049965283710072","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Quasi-circular Splines: A Shape-Preserving Approximation
The "quasi-circular spline" is introduced as a new method for approximating closed, smooth planar shapes from curvature information. A current application is the measurement of shapes of solid rocket booster cross-sections. Because of the efficiency of the algorithm and its desirable geometric properties, it is also particularly appropriate for computer graphics. The simplicity and efficiency of the quasi-circular spline compare well with previously proposed schemes which are important in graphical applications. It is invariant under the transformations of the Euclidean group. Furthermore, it is shape-preserving in that the quasi-circular spline approximation to a convex planar curve is also convex. Sufficient conditions for convergence are described, and O(h2) approximation to sufficiently smooth curves is demonstrated.