2024/11/07 by Jan Grošelj, Grošelj, Jan, Hendrik Speleers +1
Engineering · #Advanced Numerical Analysis Techniques
paper · pdf · doi:10.48550/arxiv.2411.05170
In this paper, we investigate C2 super-smoothness of the full C1 cubic spline space on a Powell-Sabin refined triangulation, for which a B-spline basis can be constructed. Blossoming is used to identify the C2 smoothness conditions between the functionals of the dual basis. Some of these conditions can be enforced without difficulty on general triangulations. Others are more involved but greatly simplify if the triangulation and its corresponding Powell-Sabin refinement possess certain symmetries. Furthermore, it is shown how the C2 smoothness constraints can be integrated into the spline representation by reducing the set of basis functions. As an application of the super-smooth basis functions, a reduced spline space is introduced that maintains the cubic precision of the full C1 spline space.