Generalized Bézier volumes over simple convex polyhedra

IF 1.3 4区计算机科学 Q3 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Computer Aided Geometric Design Pub Date : 2024-05-03 DOI:10.1016/j.cagd.2024.102338

Kaikai Qin, Yajuan Li, Chongyang Deng

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引用次数: 0

Abstract

In recent years, there has been growing interest in the representation of volumes within the field of geometric modeling (GM). While polygonal patches for surface modeling have been extensively studied, there has been little focus on the representation of polyhedral volumes. Inspired by the polygonal representation of the Generalized Bézier (GB) patch proposed by Várady et al. (2016), this paper introduces a novel method for polyhedral volumetric modeling called the Generalized Bézier (GB) volume.

GB volumes are defined over simple convex polyhedra using generalized barycentric coordinates (GBCs), with the control nets which are a direct generalization of those of tensor-product Bézier volumes. GB volumes can be smoothly connected to adjacent tensor-product Bézier or GB volumes with $G^{1}$ or $G^{2}$ continuity. Besides, when the parametric polyhedron becomes a prism, the GB volume also degenerates into a tensor-product form. We provide some practical examples to demonstrate the advantages of GB volumes. Suggestions for future work are also discussed.

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简单凸多面体上的广义贝塞尔卷

近年来，人们对几何建模（GM）领域中体积的表示越来越感兴趣。虽然用于曲面建模的多边形补丁已被广泛研究，但对多面体体的表示却鲜有关注。受 Várady 等人（2016 年）提出的广义贝塞尔（GB）补丁的多边形表示法的启发，本文介绍了一种用于多面体体积建模的新方法，称为广义贝塞尔（GB）体积。GB 体积是使用广义巴里中心坐标（GBC）在简单凸多面体上定义的，其控制网是张量乘积贝塞尔体积控制网的直接广义化。GB 体积可以与相邻的张量积贝齐尔体积或 GB 体积平滑连接，并具有 G1 或 G2 连续性。此外，当参数多面体变成棱柱时，国标体积也会退化为张量积形式。我们提供了一些实际例子来证明 GB 体积的优势。我们还讨论了对未来工作的建议。

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来源期刊

Computer Aided Geometric Design 工程技术-计算机：软件工程

CiteScore

3.50

自引率

13.30%

发文量

审稿时长

60 days

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.