Optimal [formula omitted] 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 G2 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.