ᵔ2上的圆盘B样条曲线：基于骨架的2球面区域表示法

IF 2.7 4区计算机科学 Q2 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Computer Graphics Forum Pub Date : 2024-10-24 DOI:10.1111/cgf.15239

Chunhao Zheng, Yuming Zhao, Zhongke Wu, Xingce Wang

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引用次数: 0

摘要

由于二维球面设计的广泛应用，近年来对ᵔ2 流形建模的要求越来越高。由于球体的非欧几里得性质，要找到一种在ᵔ2 流形上表示二维区域的方法有一定的难度。本文提出了一种基于骨架的ᵔ2 上区域表示方法--ᵔ2 上的圆盘 B 样条（DBSC）。首先，我们给出了ᵔ2 上 DBSC 的定义和基本算法。然后，我们给出了ᵔ2 上 DBSC 的计算方法，包括边界点、内部点及其相应导数的计算。在此基础上，我们给出了ᵔ2 上 DBSC 的一些建模方法，包括近似、变形等。最后，展示了一些令人惊叹的ᵔ2 上 DBSC 的应用实例。这项工作为 DBSC 在ᵔ2 上的进一步应用奠定了理论基础。

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Disk B-spline on 𝕊2: A Skeleton-based Region Representation on 2-Sphere

Due to the widespread applications of 2-dimensional spherical designs, there has been an increasing requirement of modeling on the 𝕊² manifold in recent years. Due to the non-Euclidean nature of the sphere, it has some challenges to find a method to represent 2D regions on 𝕊² manifold. In this paper, a skeleton-based representation method of regions on 𝕊², disk B-spline(DBSC) on 𝕊² is proposed. Firstly, we give the definition and basic algorithms of DBSC on 𝕊². Then we provide the calculation method of DBSC on 𝕊², which includes calculating the boundary points, internal points and their corresponding derivatives. Based on that, we give some modeling methods of DBSC on 𝕊², including approximation, deformation. In the end, some stunning application examples of DBSC on 𝕊² are shown. This work lays a theoretical foundation for further applications of DBSC on 𝕊².

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来源期刊

Computer Graphics Forum 工程技术-计算机：软件工程

CiteScore

5.80

自引率

12.00%

发文量

175

审稿时长

3-6 weeks

期刊介绍： Computer Graphics Forum is the official journal of Eurographics, published in cooperation with Wiley-Blackwell, and is a unique, international source of information for computer graphics professionals interested in graphics developments worldwide. It is now one of the leading journals for researchers, developers and users of computer graphics in both commercial and academic environments. The journal reports on the latest developments in the field throughout the world and covers all aspects of the theory, practice and application of computer graphics.