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.