{"title":"基于 A 类矩阵的具有单调曲率的二维贝塞尔曲线","authors":"Aizeng Wang , Chuan He , Yang Song , Gang Zhao","doi":"10.1016/j.cagd.2024.102279","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we construct 2D Bézier curves with monotone curvature using Class A matrices. A new sufficient condition for Class A matrices based on its singular values, is provided and proved, generalizing the 2D typical curves proposed by Mineur et al. (1998). An algorithm is provided utilizing the condition for easier Class A curve creation. Several 2D aesthetic curve examples are constructed to demonstrate the effectiveness of our approach.</p></div>","PeriodicalId":55226,"journal":{"name":"Computer Aided Geometric Design","volume":"110 ","pages":"Article 102279"},"PeriodicalIF":1.3000,"publicationDate":"2024-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"2D Bézier curves with monotone curvature based on Class A matrices\",\"authors\":\"Aizeng Wang , Chuan He , Yang Song , Gang Zhao\",\"doi\":\"10.1016/j.cagd.2024.102279\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper, we construct 2D Bézier curves with monotone curvature using Class A matrices. A new sufficient condition for Class A matrices based on its singular values, is provided and proved, generalizing the 2D typical curves proposed by Mineur et al. (1998). An algorithm is provided utilizing the condition for easier Class A curve creation. Several 2D aesthetic curve examples are constructed to demonstrate the effectiveness of our approach.</p></div>\",\"PeriodicalId\":55226,\"journal\":{\"name\":\"Computer Aided Geometric Design\",\"volume\":\"110 \",\"pages\":\"Article 102279\"},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2024-03-11\",\"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/S016783962400013X\",\"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/S016783962400013X","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
摘要
本文利用 A 类矩阵构建了具有单调曲率的二维贝塞尔曲线。本文提供并证明了基于奇异值的 A 类矩阵的新充分条件，对 Mineur 等人（1998 年）提出的二维典型曲线进行了概括。利用该条件还提供了一种算法，以简化 A 类曲线的创建。我们构建了几个二维美学曲线实例，以证明我们方法的有效性。
2D Bézier curves with monotone curvature based on Class A matrices
In this paper, we construct 2D Bézier curves with monotone curvature using Class A matrices. A new sufficient condition for Class A matrices based on its singular values, is provided and proved, generalizing the 2D typical curves proposed by Mineur et al. (1998). An algorithm is provided utilizing the condition for easier Class A curve creation. Several 2D aesthetic curve examples are constructed to demonstrate the effectiveness of our approach.
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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