Fair, G2- and C2-continuous circle splines for the interpolation of sparse data points

This paper presents a carefully chosen curve blending scheme between circles, which is based on angles, rather than point positions. The result is a class of circle splines that robustly produce fair-looking G2-continuous curves without any cusps or kinks, even through rather challenging, sparse sets of interpolation points. With a simple reparameterization the curves can also be made C2-continuous. The same method is usable in the plane, on the sphere, and in 3D space.