Optimal G2 Hermite interpolation for 3D curves

Abstract We consider a Hermite interpolation problem for a 3D curve where the functional to be minimized is defined as the integral of squared norm of the third parametric derivative, subject to G 2 continuity constraints at the end points. The first order necessary optimality condition of the variational problem leads to a parametric transition curve with quintic polynomials. The determination of coefficients is given by a polynomial system with 2 unknowns. Stationary points correspond to positive roots of the resultant which is a degree 9 polynomial. Although the formulated variational problem is non-convex, the proposed approach leads to the global solution, which can be computed in a reliable and fast manner.