Updated 02 Oct 2019
This Matlab software solves a 2-point 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.
The example file is executed in Matlab using example_G2_Hermite_Interpolation
Herzog, Raoul, and Philippe Blanc. “Optimal G2 Hermite Interpolation for 3D Curves.” Computer-Aided Design, vol. 117, Elsevier BV, Dec. 2019, p. 102752, doi:10.1016/j.cad.2019.102752.