Planar cubic G 1 interpolatory splines with small strain energy

Abstract In this paper, a classical problem of the construction of a cubic G 1 continuous interpolatory spline curve is considered. The only data prescribed are interpolation points, while tangent directions are unknown. They are constructed automatically in such a way that a particular minimization of the strain energy of the spline curve is applied. The resulting spline curve is constructed locally and is regular, cusp-, loop-and fold-free. Numerical examples demonstrate that it is satisfactory as far as the shape of the curve is concerned