Topological criterion for selection of quintic Pythagorean-hodograph Hermite interpolants

A topological approach to identifying the “good” interpolant among the four distinct solutions to the first–order Hermite interpolation problem for planar quintic Pythagorean–hodograph curves is presented. An existence theorem is proved, together with a complete analysis of uniqueness/non– uniqueness properties. A simple formula for finding the “good” solution, without appealing to curve fairness or energy integrals, is also presented.