Editing Non-uniform rational B-spline (section)

=== General form of a NURBS curve ===

Using the definitions of the basis functions <math>N_{i,n}</math> from the previous paragraph, a NURBS curve takes the following form:<ref name="nurbs-book" />
<math display="block">C(u) = \sum_{i=1}^{k} {\frac
	{N_{i,n}(u)w_i}
	{\sum_{j=1}^k N_{j,n}(u)w_j}}
	\mathbf{P}_i = \frac
	{\sum_{i=1}^k {N_{i,n}(u)w_i \mathbf{P}_i}}
	{\sum_{i=1}^k {N_{i,n}(u)w_i}}
	</math>

In this, <math>k</math> is the number of control points <math>\mathbf{P}_i</math> and <math>w_i</math> are the corresponding weights. The denominator is a normalizing factor that evaluates to one if all weights are one. This can be seen from the partition of unity property of the basis functions. It is customary to write this as
<math display="block">C(u) = \sum_{i=1}^k R_{i,n}(u)\mathbf{P}_i</math>
in which the functions
<math display="block">R_{i,n}(u) = {N_{i,n}(u)w_i \over \sum_{j=1}^k N_{j,n}(u)w_j}</math>
are known as the ''rational basis functions''.