{"title":"Quaternionic Bézier parameterizations of bidegree (2,1)","authors":"R. Krasauskas, S. Zube","doi":"10.1016/j.cagd.2024.102375","DOIUrl":null,"url":null,"abstract":"<div><p>Earlier results on various quaternionic Bézier parametrizations of Darboux cyclides are extended to bidegree <span><math><mo>(</mo><mn>2</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span> parameterizations of a wider class of surfaces containing at least two families of circles. The focus is on one special family of such parametrizations, which depends on 4 control points and defines a pencil of surfaces tangent along the common circle. This construction is used for parametrizing two-oval Darboux cyclides and generating the Gaussian map for rational offsets of ellipsoids and two-sheet hyperboloids.</p></div>","PeriodicalId":55226,"journal":{"name":"Computer Aided Geometric Design","volume":"113 ","pages":"Article 102375"},"PeriodicalIF":1.3000,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computer Aided Geometric Design","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167839624001092","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, SOFTWARE ENGINEERING","Score":null,"Total":0}
引用次数: 0
Abstract
Earlier results on various quaternionic Bézier parametrizations of Darboux cyclides are extended to bidegree parameterizations of a wider class of surfaces containing at least two families of circles. The focus is on one special family of such parametrizations, which depends on 4 control points and defines a pencil of surfaces tangent along the common circle. This construction is used for parametrizing two-oval Darboux cyclides and generating the Gaussian map for rational offsets of ellipsoids and two-sheet hyperboloids.
期刊介绍：
The journal Computer Aided Geometric Design is for researchers, scholars, and software developers dealing with mathematical and computational methods for the description of geometric objects as they arise in areas ranging from CAD/CAM to robotics and scientific visualization. The journal publishes original research papers, survey papers and with quick editorial decisions short communications of at most 3 pages. The primary objects of interest are curves, surfaces, and volumes such as splines (NURBS), meshes, subdivision surfaces as well as algorithms to generate, analyze, and manipulate them. This journal will report on new developments in CAGD and its applications, including but not restricted to the following:
-Mathematical and Geometric Foundations-
Curve, Surface, and Volume generation-
CAGD applications in Numerical Analysis, Computational Geometry, Computer Graphics, or Computer Vision-
Industrial, medical, and scientific applications.
The aim is to collect and disseminate information on computer aided design in one journal. To provide the user community with methods and algorithms for representing curves and surfaces. To illustrate computer aided geometric design by means of interesting applications. To combine curve and surface methods with computer graphics. To explain scientific phenomena by means of computer graphics. To concentrate on the interaction between theory and application. To expose unsolved problems of the practice. To develop new methods in computer aided geometry.
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