
Journal for Geometry and Graphics 22 (2018), No. 2, 163181 Copyright Heldermann Verlag 2018 PH Curves with NonPrimitive Hodographs Petroula Dospra Dept. of Mathematics, Aristotle University, 54124 Thessaloniki, Greece petroula.dospra@gmail.com We present a necessary and sufficient condition under which a PH curve generated by a primitive quaternion polynomial has a nonprimitive hodograph. Such curves are regular PH curves, and we give a characterization of these curves in terms of their associated quaternion polynomial. This work leads to the problem of the production of RRMF curves by others of lower degree. Furthermore, we present some geometrical properties of RRMF curves with nonprimitive hodographs of degrees 5 and 7. Keywords: Pythagoreanhodograph curves, rotationminimizing frame, curves with rational rotation minimizing frame, nonprimitive hodograph. MSC: 65D17; 68U07, 53A04 [ Fulltextpdf (358 KB)] 