{"title":"Rational C1 cubic Powell–Sabin B-splines with application to representation of ruled surfaces","authors":"Jan Grošelj, Ada Šadl Praprotnik","doi":"10.1016/j.cam.2024.116292","DOIUrl":null,"url":null,"abstract":"<div><div>This paper defines rational <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> cubic Powell–Sabin splines and analyses their basic properties. A rational B-spline basis is established and an algorithm for determining the corresponding control points and weights by using the blossoming operator is presented. The capability of the introduced splines to represent rational cubic triangular Bézier patches and quadratic NURPS is discussed and explicit conversion formulas are provided. Moreover, the application of the rational <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> cubic Powell–Sabin splines to representation of ruled surfaces is studied, showing that the cubic splines can give smoother parametrizations than the NURPS.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"457 ","pages":"Article 116292"},"PeriodicalIF":2.6000,"publicationDate":"2024-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computational and Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0377042724005405","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
This paper defines rational cubic Powell–Sabin splines and analyses their basic properties. A rational B-spline basis is established and an algorithm for determining the corresponding control points and weights by using the blossoming operator is presented. The capability of the introduced splines to represent rational cubic triangular Bézier patches and quadratic NURPS is discussed and explicit conversion formulas are provided. Moreover, the application of the rational cubic Powell–Sabin splines to representation of ruled surfaces is studied, showing that the cubic splines can give smoother parametrizations than the NURPS.
期刊介绍：
The Journal of Computational and Applied Mathematics publishes original papers of high scientific value in all areas of computational and applied mathematics. The main interest of the Journal is in papers that describe and analyze new computational techniques for solving scientific or engineering problems. Also the improved analysis, including the effectiveness and applicability, of existing methods and algorithms is of importance. The computational efficiency (e.g. the convergence, stability, accuracy, ...) should be proved and illustrated by nontrivial numerical examples. Papers describing only variants of existing methods, without adding significant new computational properties are not of interest.
The audience consists of: applied mathematicians, numerical analysts, computational scientists and engineers.
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