Parametric curves with Pythagorean binormalsKozak, Jernej (Avtor) Knez, Marjetka (Avtor) Vitrih, Vito (Avtor) pitagorejski hodografpitagorejska binormalaracionalna krivuljadualne koordinaterotacijsko minimizirajoče ogrodjepitagorejska binormalaracionalna krivuljadualne koordinaterotacijsko minimizirajoče ogrodjePythagorean-hodographPythagorean-binormalrational curvedual coordinatesrotation-minimizing frameosculating frameIn this paper, a class of rational spatial curves that have a rational binormal is introduced . Such curves (called PB curves) play an important role in the derivation of rational rotation-minimizing osculating frames. The PB curve construction proposed is based upon the dual curve representation and the Euler-Rodrigues frame obtained from quaternion polynomials. The construction significantly simplifies if the curve is a polynomial one. Further, polynomial PB curves of the degree % 7 and rational PB curves of the degree % 6 that possess rational rotation-minimizing osculating frames are derived, and it is shown that no lower degree curves, constructed from quadratic quaternion polynomials, with such a property exist.20152015-10-15 05:57:55Delo ni kategorizirano7158ISSN: 1019-7168UDK: 519.65OceCobissID: 512095001DOI: 10.1007/s10444-014-9387-7COBISS.SI-ID: 1537835204sl