The surface analogue of the B-spline curve is the B-spline surface
(patch). This is a tensor product surface
defined by a topologically rectangular
set of control points
,
,
and two knot vectors
and
associated with each parameter
,
. The corresponding integral B-spline surface is given by

(1.86)

Parametric lines on a B-spline surface are obtained by letting
, or
. A parametric line with
is a B-spline
curve in
with
as its knot vector and vertices
,
given by
.

Some of the properties of the B-spline curves can be easily extended
to surfaces such as:

Geometry invariance property.

End points geometric property.

Convex hull property.

B-spline to Bézier property.

However, no variation diminishing property is known for B-spline
surface patches.

Next: 1.5 Generalization of B-spline
Up: 1.4 B-spline curves and
Previous: 1.4.3 Algorithms for B-spline
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December 2009