{"title":"Nonlinear Weighted Subdivision Schemes","authors":"Rongin Uwitije, Xuhui Wang, Jiansong Deng","doi":"10.1007/s40304-023-00383-1","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we present new variants of both the de Casteljau subdivision algorithm for curves and Doo–Sabin subdivision algorithm for surfaces. Our subdivision schemes are built on nonlinear weighted averaging rules which are induced by monotonic functions. These averaging rules are used instead of midpoint averaging rule in the mentioned well-known subdivision algorithms. The analysis shows that the smoothness of the subdivision schemes for curves is inherited from the smoothness of the function which induces the averaging rule used in the refinement of the schemes. The results show that with our subdivision schemes, both convex surfaces and concave surfaces can be generated by the same scheme. This happens by only interchanging the weights of two adjacent points when computing the edge points in the subdivision refinement. This is an advantage since a designer can adjust the limit shape according to his interests.</p>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s40304-023-00383-1","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we present new variants of both the de Casteljau subdivision algorithm for curves and Doo–Sabin subdivision algorithm for surfaces. Our subdivision schemes are built on nonlinear weighted averaging rules which are induced by monotonic functions. These averaging rules are used instead of midpoint averaging rule in the mentioned well-known subdivision algorithms. The analysis shows that the smoothness of the subdivision schemes for curves is inherited from the smoothness of the function which induces the averaging rule used in the refinement of the schemes. The results show that with our subdivision schemes, both convex surfaces and concave surfaces can be generated by the same scheme. This happens by only interchanging the weights of two adjacent points when computing the edge points in the subdivision refinement. This is an advantage since a designer can adjust the limit shape according to his interests.
期刊介绍：
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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