New optimized spline functions for interpolation on the hexagonal lattice

We propose new discrete-to-continuous interpolation models for hexagonally sampled data, that generalize two families of splines developed in the literature for the hexagonal lattice, to say the hex- splines and three directional box-splines. This extension is inspired by the construction of MOMS functions in 1-D, that generalize and outperform classical 1-D B-splines [1]. Our new generators have optimal approximation theoretic performances, for exactly the same computation cost as their spline counterparts.