A NURBS curve generalizes the B-spline. It is the combination of a set
of piecewise rational functions with n+1 control points 
and associated weights 
:
where u is the parametric variable and 
are B-spline
basis functions. Assuming basis functions of degree k-1, a NURBS
curve has n+k+1 knots 
in nondecreasing sequence: 
. The basis functions are defined
recursively as
with
The parametric domain is 
. In many
applications, the end knots are repeated with multiplicity k in
order to interpolate the initial and final control points 
and 
.
