Geometric Hermite interpolation by cubic G1G1 splines

In this paper, geometric Hermite interpolation by planar cubic G1G1 splines is studied. Three data points and three tangent directions are interpolated per polynomial segment. Sufficient conditions for the existence of such a G1G1 spline are determined that cover most of the cases encountered in practical applications. The existence requirements are based only upon geometric properties of data and can easily be verified in advance. The optimal approximation order 6 is confirmed, too.