** Degree elevation** is one of the several fundamental geometric
algorithms that permit to modify the defining parameters of a surface

For a surface, one can degree elevate in either the *u*- or the
*v*- direction. In this case, every row or column of control points
will be modified by the curve elevation algorithm for curves.

We shall use a NURBS surface defined by 6 rows and 6 columns of control
points and degrees 4 and 3 in the *u*-direction and the
*v*-direction, respectively. You can
click **here** to download a copy of this
file **deg-elev.dat** for your practice.

To show the impact on the control points, the surfaces will be displayed
using **Display**, followed by
**Rendering Method**, followed by
**Wireframe**, followed by
**Detail Level 1**. The knot curves are
also shown. Note that the knot distribution in the *u*-direction is
0 (multiplicity 5), 0.5 (simple) and 1 (multiplicity 5), and the
knot distribution in the *v*-direction is
0 (multiplicity 4), 1/3 (simple), 2/3 (simple), and 1 (multiplicity 4).
The following is the initial surface, shown in wireframe and rendered patch.

Let us increase the degree by one in the *u*-direction. Select
**Advanced Features**, followed by
**Degree Elevation**, followed by
**on U**. The result is shown below.
As you can see the shape of the surface does not change, and each "row" of
the original control points is replaced by a set of new control point.
Now there still are 6 rows; but, the number of columns (*i.e.*, the
number of control points on each row) increases to 8 from 6.

Let us increase the degree by one in the *v*-direction. Select
**Advanced Features**, followed by
**Degree Elevation**, followed by
**on V**. The following figures show
the result. The number of columns is the same (*i.e.*, 8); but, the
number of rows (*i.e.*, the number of control points on each column)
increases to 9 from 6.

Please check the change of the number of knots in each direction, and
verify the fundamental identity. You can get the number of knot
information from the ** Tracing Window**.