Applying inversion to construct planar, rational spirals that satisfy two-point G2 Hermite data

A method of two-point G2 Hermite interpolation with spirals is proposed. To construct a sought for curve, the inversion is applied to an arc of some other spiral. To illustrate the method, inversions of parabola are considered in detail. The resulting curve is 4th degree rational. The method allows the matching of a wide range of boundary conditions, including those which require an inflection. Although not all G2 Hermite data can be matched with a spiral generated from a parabolic arc, introducing one intermediate G2 data solves the problem. Expanding the method by involving other spirals arcs is also discussed.