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

Abstract 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 .