For spaces of constant, linear, and quadratic splines of maximal smoothness on the Powell-Sabin 12-split of a triangle, Cohen, Lyche and Riesenfeld recently discovered so-called S-bases. These are simplex spline bases with B-spline-like properties on a single macrotriangle, which are tied together a...

Pseudo-splines form a family of subdivision schemes that provide a natural blend between interpolating schemes and approximating schemes, including the Dubuc–Deslauriers schemes and B-spline schemes. Using a generating function approach, we derive expressions for the symbols of the symmetric m-ary p...

Using a generating function approach, we derive expressions for the symbols of the symmetric m-ary pseudo-spline subdivision schemes. We show that their masks have a positive (discrete-time) Fourier transform, making it possible to compute the exact Hölder regularity algebraically as the spectral ra...