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Journal for Geometry and Graphics 22 (2018), No. 2, 163--181
Copyright Heldermann Verlag 2018

PH Curves with Non-Primitive Hodographs

Petroula Dospra
Dept. of Mathematics, Aristotle University, 54124 Thessaloniki, Greece

We present a necessary and sufficient condition under which a PH curve generated by a primitive quaternion polynomial has a non-primitive 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 non-primitive hodographs of degrees 5 and 7.

Keywords: Pythagorean-hodograph curves, rotation-minimizing frame, curves with rational rotation minimizing frame, non-primitive hodograph.

MSC: 65D17; 68U07, 53A04

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