Planar C2 cubic spline interpolation under geometric boundary conditions Original Research Article

This paper deals with the problem of C2 cubic spline interpolation under geometric boundary conditions, that is, fixing the unit-tangent vector and the curvature at the end points of a planar point-set. The solvability of the resulting non-linear problem, which is equivalent to a quadratic system with respect to the lengths of the boundary tangent vectors, is exhaustively studied, leading to necessary and sufficient conditions for all possible boundary-data configurations. A robust scheme for the numerical solution of the quadratic system is presented, and the use of the new boundary conditions is illustrated in the context of three examples.