{"title":"Construction of quasi-Bézier surfaces from boundary conditions","authors":"Yong-Xia Hao, Ting Li","doi":"10.1016/j.gmod.2022.101159","DOIUrl":null,"url":null,"abstract":"<div><p>The quasi-Bézier surface is a kind of commonly used surfaces in CAGD/CAD systems. In this paper, we present a novel approach to construct quasi-Bézier surfaces from the boundary information based on a general second order functional. This functional includes many common functionals as special cases, such as the Dirichlet functional, the biharmonic functional and the quasi-harmonic functional etc. The problem turns into solving simple linear equations<span> about inner control points, and finally the internal control points of the resulting quasi-Bézier surface can be obtained as linear combinations of the given boundary control points. Some representative examples show the effectiveness of the presented method.</span></p></div>","PeriodicalId":55083,"journal":{"name":"Graphical Models","volume":"123 ","pages":"Article 101159"},"PeriodicalIF":2.5000,"publicationDate":"2022-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Graphical Models","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1524070322000352","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: 0
Abstract
The quasi-Bézier surface is a kind of commonly used surfaces in CAGD/CAD systems. In this paper, we present a novel approach to construct quasi-Bézier surfaces from the boundary information based on a general second order functional. This functional includes many common functionals as special cases, such as the Dirichlet functional, the biharmonic functional and the quasi-harmonic functional etc. The problem turns into solving simple linear equations about inner control points, and finally the internal control points of the resulting quasi-Bézier surface can be obtained as linear combinations of the given boundary control points. Some representative examples show the effectiveness of the presented 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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