M-Band Subdivision Abstract Of Bivariate B-Splines Of Uniform Partition In Three Directions

In this paper, we mainly discuss the refinability of the bivariate B-splines of uniform partition in three directions. We construct the M- band refinement equations of bivariate B-splines of uniform partition in three directions in four spaces (S-0(-1)(Delta), S-1(0)(Delta), S-3(1)(Delta) and S-4(2) (Delta), respectively) by modifying the definition of initial functions and taking Fourier transform on B-splines defined by convolution.