Planar quintic G2 Hermite interpolation with minimum strain energy

In this paper, we study planar quintic G2 Hermite interpolation with minimum strain energy. To match arbitrary G2 Hermite data, a quintic curve is expressed in terms of four free parameters that encode the local reparameterization at the endpoints and are available for further optimization. We express the approximate strain energy as a quartic function in four parameters, whose minimum can be found by solving an optimization problem of two parameters relating to the magnitudes of endpoint tangent vectors. A feasible region is used while searching the optimal values of these two parameters such that the interpolating curve can preserve tangent directions and avoid singularities at the endpoints. We then solve this constrained minimization problem via the proximal gradient method. Several comparative examples are provided to demonstrate the effectiveness of the proposed method and applications to shape design are also shown.