M-band subdivision of multivariate B-spline

摘要

For any integer M ≥ 2 and integer k ≥ 0, the present paper gives the M-band refinement equations of bivariate B-splines in the space S_(3k + 1)~(2k)(△_(mn)~(1)), S_(3k)~(2k - 1)(△_(mn)~(1)), S_(4k + 2)~(3k + 1)(△_(mn)~(2)), S_(4k + 1)~(3k)(△_(mn)~(2)) and S_(4k + 4)~(3k + 2)(△_(mn)~(2)) (where △_(mn)~(1)) and △_(mn)~(2) represent uniform type-1 and type-2 triangulation, respectively) by using Fourier transform and bivariate convolution. Thus, we obtain the subdivision generation of the spline functions defined on type-1 triangulation and type-2 triangulation.