Non-uniform interpolatory subdivision via splines

We present a framework for deriving non-uniform interpolatory subdivision algorithms closely related to non-uniform spline interpolants. Families of symmetric non-uniform interpolatory 2n2n-point schemes of smoothness Cn−1Cn−1 are presented for n=2,3,4n=2,3,4 and even higher order, as well as a variety of non-uniform 6-point schemes with C3C3 continuity.