To modify the shape of a surface, one can change the position of control
points, and remove a row or a column of control points. If the surface
is a rational Bézier or a NURBS surface, one can change the weight
of a control point. If the surface is a B-spline or a NURBS, one can also
change the positions of knots. Note that one cannot add control points;
but, one can add knots by knot insertion ** without** changing
the shape of the surface.

Note that only the control points of a rational Bézier and a NURBS
surface can have weight. The weights of control points of a Bézier
and a B-spline surface are all 1s and are fixed (*i.e.*, cannot be
changed). Let us load the default scene one, which is a NURBS surface, and
select the control point marked with the white rectangle using the right
mouse button. The ** Control Point Update Window** appears. The
bottom part of this window shows the coordinates of this control point. The
little slider, marked with a blue rectangle below, gives the current weight
associated with the selected control point. Sliding the little triangle
will change the value of weight.

The general rule of changing weight is

- Increasing the weight of a control point pulls the surface
toward that control point. If the weight value of the selected
control point is increased to 2, the surface is slightly pulled
toward that control point (the left figure below). If the weight
value is further increased to 5, it is clear that the surface
is pulled further and closer to the control point. In fact,
if the weight is increased to infinity, the surface will pulled
to pass through the control point!
If you compare all three figures, increasing the weight of a control point only affects the area it has influence, while keeps the other parts of the surface unchanged. This is a direct consequence of the

, which means that the impact of a modification on a control point, its weight, or a knot, is local.*local modification property* - Decreasing the weight of a control point pushes the surface away
from that control point. The left figure below shows the result
decreasing the weight of the selected control point from 1 to
0.5. Comparing with the corresponding figure above, one can see
that the surface is flatter near that control point. If the weight
is decreased to 0.1 (the right figure below), the surface becomes
even flatter.
In practice, the weight of a control point should be non-negative. If the weight of a control point is decreased to zero, this means that control point has no influence to the surface and as a result the region near that control point should be flat (the left figure below). If the weight is changed to a negative value, the surface will be pushed further and unpleasant effect may occur. In the right figure below, the weight is changed to -0.6, the surface looks bent and part of it lies outside of the convex hull of the control points. This violates the

. Thus, in general,*convex hull property*.*do not use negative weights*