{"title":"Orthogonality of isometries in the conformal model of the 3D space","authors":"Carlile Lavor , Michael Souza , José Luis Aragón","doi":"10.1016/j.gmod.2021.101100","DOIUrl":null,"url":null,"abstract":"<div><p>Motivated by questions on orthogonality<span> of isometries, we present a new construction of the conformal model of the 3D space using just elementary linear algebra. In addition to pictures that can help the readers to understand the conformal model, our approach allows to obtain matrix representation<span> of isometries that can be useful, for example, in applications of computational geometry<span>, including computer graphics, robotics, and molecular geometry.</span></span></span></p></div>","PeriodicalId":55083,"journal":{"name":"Graphical Models","volume":"114 ","pages":"Article 101100"},"PeriodicalIF":2.5000,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.gmod.2021.101100","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Graphical Models","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1524070321000059","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: 2
Abstract
Motivated by questions on orthogonality of isometries, we present a new construction of the conformal model of the 3D space using just elementary linear algebra. In addition to pictures that can help the readers to understand the conformal model, our approach allows to obtain matrix representation of isometries that can be useful, for example, in applications of computational geometry, including computer graphics, robotics, and molecular geometry.
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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