B-spline Surfaces: Important Properties

Several important properties of B-spline surfaces are listed here. These properties can be proved easily by applying the same techniques used for Bézier curves. Please compare these important properties with those of B-spline curves'. Please recall that the equation of a B-spline surface is the following

where the degrees in the u- and v-directions are p and q, respectively, and there are m+1 rows and n+1 columns of control points.