Geodesic
PH Curves with Non-Primitive Hodographs
Journal for geometry and graphics, Tome 22 (2018) no. 2, pp. 163-181 Cet article a éte moissonné depuis la source Heldermann Verlag

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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.
Classification : 65D17, 68U07, 53A04
Mots-clés : Pythagorean-hodograph curves, rotation-minimizing frame, curves with rational rotation minimizing frame, non-primitive hodograph 
@article{JGG_2018_22_2_JGG_2018_22_2_a1,
     author = {P. Dospra },
     title = {PH {Curves} with {Non-Primitive} {Hodographs}},
     journal = {Journal for geometry and graphics},
     pages = {163--181},
     year = {2018},
     volume = {22},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JGG_2018_22_2_JGG_2018_22_2_a1/}
}
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P. Dospra . PH Curves with Non-Primitive Hodographs. Journal for geometry and graphics, Tome 22 (2018) no. 2, pp. 163-181. http://geodesic.mathdoc.fr/item/JGG_2018_22_2_JGG_2018_22_2_a1/