Over Constrained Superspline Spaces

The table below indicates the limitations of reducing the dimension by imposing (symmetric) supersmoothness. Even though the dimension may still be greater than 264 not all 264 conditions can be imposed.

Double Clough-Tocher Super Splines  
n V0 V4 V5 E01 E04 E05 E45 F014 F015 F045 dim count
1 2   7               281 245
2 2 6                 287 260
3 2           6       305 260
4 2             2     341 252
5 2                 2 341 260
6 2         3         389 252
7 2       2           404 260
8 2               1   417 245
9 2     1             475 228

Double Clough-Tocher Super Splines