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Optimal G^2 Hermite Interpolation for 3D Curves

The following code solves an optimal curve completion problem, where the Frenet frames and the curvatures at the end points are given.

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

Cite As

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.

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MATLAB Release Compatibility
Created with R2019b
Compatible with any release
Platform Compatibility
Windows macOS Linux