Parametric curves with Pythagorean binormal

Jernej Kozak, Marjeta Krajnc, Vito Vitrih
2014 Advances in Computational Mathematics  
In 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 conformal 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
more » ... PB curves of the degree ≥ 6 that possess rational rotation-minimizing conformal frames are derived, and it is shown that no lower degree curves with such a property exist.
doi:10.1007/s10444-014-9387-7 fatcat:xfoza35surgv3lmcz25rb6ez2i