A NURBS surface is the generalization of the tensor-product B-spline surface. It is defined over the parametric variables u and v as
A NURBS surface has (m+1)(n+1) control points and weights . Assuming basis functions along the two parametric axes of degree k-1 and l-1, respectively, the number of knots is (m+k+1)(n+l+1). The nondecreasing knot sequence is along the u-axis and along the v-axis. The parametric domain is and . If the end knots have multiplicity k and l in the u and v axis respectively, the surface patch will interpolate the four corners of the boundary control points.