Solvability of G1 Hermite interpolation by spatial Pythagorean-hodograph cubics and its selection scheme

We provide necessary and sufficient conditions for the existence of solutions of G(1) Hermite interpolation problem by spatial PH cubics. To deal with the cases where multiple solutions exist, we also provide a selection scheme to choose one good interpolant curve based on the concept of analytic continuation. (C) 2009 Elsevier B.V. All rights reserved.