A circle-preserving C² Hermite interpolatory subdivision scheme with tension control

We present a tension-controlled 2-point Hermite interpolatory subdivision scheme that is capable of reproducing circles starting from a sequence of sample points with any arbitrary spacing and appropriately chosen first and second derivatives. Whenever the tension parameter is set equal to 1, the limit curve coincides with the rational quintic Hermite interpolant to the given data and has guaranteed C² continuity, while for other positive tension values, continuity of curvature is conjectured and empirically shown by a wide range of experiments.