A D-NURBS surface has a similar structure to the curve. Proceeding analogously from (2), we define
Again, the control points and weights comprise the generalized
coordinates and are assembled into vectors 
, 
, and
. Two subscripts are now associated with the generalized
coordinates, reflecting the surface parameters u and v. For
concreteness, we order the components in these vectors such that the
second subscript varies faster than the first, although this
convention does not affect the derived results.
As before, we can write 
instead of 
. By analogy to 
in (4) and
(6), we obtain for the D-NURBS surface
However, the contents of the Jacobian 
differ from those in
the curve case. To arrive at an explicit expression for , let
, for 
, and 
, be a
diagonal matrix whose entries are
and let the 3-vector
As before, the 
and 
are
assembled into 
and 
, respectively. Hence,
Note that is now a 
matrix.
