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 S-2 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 S-2 manifold. In this paper, a skeleton-based representation method of regions on S-2, disk B-spline(DBSC) on S-2 is proposed. Firstly, we give the definition and basic algorithms of DBSC on S-2. Then we provide the calculation method of DBSC on S-2, which includes calculating the boundary points, internal points and their corresponding derivatives. Based on that, we give some modeling methods of DBSC on S-2, including approximation, deformation. In the end, some stunning application examples of DBSC on S-2 are shown. This work lays a theoretical foundation for further applications of DBSC on S-2.