Rational B-splines:

In this case

hence

An extension of this definition is to change the uniform knots u_k = k/N into a non-uniform set {u₀, u₁, u₂, . . . , u_{N  + J + 1}}.

Now ,the non-uniform B-splines B_{i, j} (u) is described by

B _i,j(u) = (u- u_i / u_i-j - u_i )  B_{i, j -1} (u) +( u _i-j-1 - u_i/u_i-j-1 -u_{i-j )}           B_{i -1, j -1} (u),           j = 0, 1, . . . , N +

 The only limitation on the knots is that it is non-decreasing.  The non- uniform rational B-spline of order J is then given by

In modern CAD, NURBS is one of the most popular design curves. But as an example, we shall consider the Rational quadratic curves-conic sections.