B-splines on 3-D tetrahedron partition in four-directional mesh

It is more difficult to construct 3-D splines than in 2-D case. Some result s in the three directional meshes of bivariate case have been extended to 3 -D case and corresponding tetrahedron partition has been constructed. The s upport of related B-splines and their recurrent formulas on integration and differentiation-difference are obtained. The results of this paper can be extended into higher dimension spaces, and can be also used in wavelet anal ysis, because of the relationship between spline and wavelets