{"title":"Jacobi–PIA algorithm for bi-cubic B-spline interpolation surfaces","authors":"Chengzhi Liu, Juncheng Li, Lijuan Hu","doi":"10.1016/j.gmod.2022.101134","DOIUrl":null,"url":null,"abstract":"<div><p><span>Based on the Jacobi splitting of collocation matrices, we in this paper exploited the Jacobi–PIA format for bi-cubic B-spline surfaces. We first present the Jacobi–PIA scheme in term of matrix product<span>, which has higher computational efficiency than that in term of matrix-vector product. To analyze the convergence of Jacobi–PIA, we transform the matrix product iterative scheme into the equivalent matrix-vector product scheme by using the properties of the </span></span>Kronecker product. We showed that with the optimal relaxation factor, the Jacobi–PIA format for bi-cubic B-spline surface converges to the interpolation surface. Numerical results also demonstrated the effectiveness of the proposed method.</p></div>","PeriodicalId":55083,"journal":{"name":"Graphical Models","volume":"120 ","pages":"Article 101134"},"PeriodicalIF":2.5000,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Graphical Models","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S152407032200011X","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"COMPUTER SCIENCE, SOFTWARE ENGINEERING","Score":null,"Total":0}
引用次数: 3
Abstract
Based on the Jacobi splitting of collocation matrices, we in this paper exploited the Jacobi–PIA format for bi-cubic B-spline surfaces. We first present the Jacobi–PIA scheme in term of matrix product, which has higher computational efficiency than that in term of matrix-vector product. To analyze the convergence of Jacobi–PIA, we transform the matrix product iterative scheme into the equivalent matrix-vector product scheme by using the properties of the Kronecker product. We showed that with the optimal relaxation factor, the Jacobi–PIA format for bi-cubic B-spline surface converges to the interpolation surface. Numerical results also demonstrated the effectiveness of the proposed method.
期刊介绍：
Graphical Models is recognized internationally as a highly rated, top tier journal and is focused on the creation, geometric processing, animation, and visualization of graphical models and on their applications in engineering, science, culture, and entertainment. GMOD provides its readers with thoroughly reviewed and carefully selected papers that disseminate exciting innovations, that teach rigorous theoretical foundations, that propose robust and efficient solutions, or that describe ambitious systems or applications in a variety of topics.
We invite papers in five categories: research (contributions of novel theoretical or practical approaches or solutions), survey (opinionated views of the state-of-the-art and challenges in a specific topic), system (the architecture and implementation details of an innovative architecture for a complete system that supports model/animation design, acquisition, analysis, visualization?), application (description of a novel application of know techniques and evaluation of its impact), or lecture (an elegant and inspiring perspective on previously published results that clarifies them and teaches them in a new way).
GMOD offers its authors an accelerated review, feedback from experts in the field, immediate online publication of accepted papers, no restriction on color and length (when justified by the content) in the online version, and a broad promotion of published papers. A prestigious group of editors selected from among the premier international researchers in their fields oversees the review process.
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