Geometric interpolation by planar cubic <i>G</i> ¹ splines

In this paper, geometric interpolation by G(1) cubic spline is studied. A wide class of sufficient conditions that admit a G(1) cubic spline interpolant is determined. In particular, convex data as well as data with inflection points are included. The existence requirements are based upon geometric properties of data entirely, and can be easily verified in advance. The algorithm that carries out the verification is added.