Pii: S0167-8396(02)00091-2

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 boundarydata 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.  2002 Elsevier Science B.V. All rights reserved.