{"title":"计算有理参数曲线与有理参数曲面的交点","authors":"Bingwei Zhang , Xi Wu , Jin-San Cheng , Kexin Ding","doi":"10.1016/j.cagd.2024.102275","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we present an algorithm to compute the intersection between a rational curve and a rational surface. Evaluating the parametric curve into the matrix representation of the parametric surface for implicitization, we get a matrix with one variable. We find the intersection from the matrix with the theory of real root isolation of univariate functions without computing its determinant as we have done in <span>Jia et al. (2022)</span>.</p><p>We compare our method with the state-of-the-art methods in <span>Gershon (2022)</span>; <span>Luu Ba (2014)</span>. The given examples show that our algorithms are efficient.</p></div>","PeriodicalId":55226,"journal":{"name":"Computer Aided Geometric Design","volume":"109 ","pages":"Article 102275"},"PeriodicalIF":1.3000,"publicationDate":"2024-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Computing the intersection between a rational parametric curve and a rational parametric surface\",\"authors\":\"Bingwei Zhang , Xi Wu , Jin-San Cheng , Kexin Ding\",\"doi\":\"10.1016/j.cagd.2024.102275\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper, we present an algorithm to compute the intersection between a rational curve and a rational surface. Evaluating the parametric curve into the matrix representation of the parametric surface for implicitization, we get a matrix with one variable. We find the intersection from the matrix with the theory of real root isolation of univariate functions without computing its determinant as we have done in <span>Jia et al. (2022)</span>.</p><p>We compare our method with the state-of-the-art methods in <span>Gershon (2022)</span>; <span>Luu Ba (2014)</span>. The given examples show that our algorithms are efficient.</p></div>\",\"PeriodicalId\":55226,\"journal\":{\"name\":\"Computer Aided Geometric Design\",\"volume\":\"109 \",\"pages\":\"Article 102275\"},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2024-02-08\",\"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/S0167839624000098\",\"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}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computer Aided Geometric Design","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167839624000098","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}
Computing the intersection between a rational parametric curve and a rational parametric surface
In this paper, we present an algorithm to compute the intersection between a rational curve and a rational surface. Evaluating the parametric curve into the matrix representation of the parametric surface for implicitization, we get a matrix with one variable. We find the intersection from the matrix with the theory of real root isolation of univariate functions without computing its determinant as we have done in Jia et al. (2022).
We compare our method with the state-of-the-art methods in Gershon (2022); Luu Ba (2014). The given examples show that our algorithms are efficient.
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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