Rational Parametric Curves:
We might generalize the polynomial curves above into rational curves by utilizing homogeneous coordinates in 
define and
.
The Nth degree rational curve is specified by
Therefore
Rational B-splines
In this case
hence
An extension of this definition is to modify the uniform knots uk = k/N into a non-uniform set {u0, u1, u2, . . . , uN + J + 1}.
Now the non-uniform B-splines Bi, j (u) is described by
