Local Modification Scheme :

N_i,p (u) N_j,q (v) is zero if (u, v) is outside of the rectangle [u_i, u_{i + p + 1}) × [v_j, v_{j + q + 1}).

From the local modification method property, we know that in the u-direction N_i,p (u) is non-zero on [u_i, u_{i + p + 1}) and zero elsewhere. The local modification m,etheod property of B-spline surfaces directly follows from the curve case. If control point p_{3, 2} is moved to a new location.

• p (u ,v) is C ^p-s (resp., C ^q-t) continuous in the u (resp., v) direction if u (resp., v) is refer to a knot of multiplicity s (resp., t).
• Affine Invariance: It means that to apply an affine transformation to a B-spline surface one may apply the transformation to all of the control points and the surface indicated through the transformed control points is similar to the one attained by applying the same transformation to the surface's equation.

• Variation Diminishing Property : No such thing presents for surfaces.
• If m = p, n = q, and U = {0, 0, . . . , 0, 1, 1, . . . , 1}, then a B-spline surface becomes a Bézier surface.