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

Zheng, Chunhao; Zhao, Yuming; Wu, Zhongke; Wang, Xingce

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

Files

cgf15239.pdf (9.16 MB)

Date

2024

Authors

Zheng, Chunhao
Zhao, Yuming
Wu, Zhongke
Wang, Xingce

Publisher

The Eurographics Association and John Wiley & Sons Ltd.

Abstract

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.

CCS Concepts: Computing methodologies → Parametric curve and surface models

        @article{10.1111:cgf.15239
,
journal = {Computer Graphics Forum},
title = {{Disk B-spline on S2: A Skeleton-based Region Representation on 2-Sphere
}},
author = {Zheng, Chunhao and 
Zhao, Yuming and 
Wu, Zhongke and 
Wang, Xingce
},
year = {2024
},
publisher = {The Eurographics Association and John Wiley & Sons Ltd.
},
ISSN = {1467-8659
},
DOI = {10.1111/cgf.15239
}
}