Basis Functions:

The coefficient of control point p_i,j is the product of two one-dimensional B-spline basis functions, one in the u-direction, N_i,p (u), and the other in the v-direction, N_j,q (v). All of the products are two-dimensional B-spline functions.

The two-dimensional basis functions are illustrated as wire-frame surfaces. As the control points are on the similar row, the basis function in the u-direction is fixed whereas the basic functions in the v-direction change. In general, As B-spline basis functions are non-zero only on a few consecutive knot spans (that means the local modification scheme), the two-dimensional B-spline basis functions are non-zero lying on the product of two, knot spans upon which at least one one-dimensional basis function is non-zero.