Parametric curves with Pythagorean binormal

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 rational 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. Keywords Pythagorean-hodograph · Pythagorean-binormal · rational curve · dual coordinates · rotation-minimizing frame · conformal frame Mathematics Subject Classification (2000) 65D17 · 53A04

• Type: Journal
• Year: 2015
• Where: ADCM
• Authors: Jernej Kozak, Marjeta Krajnc, Vito Vitrih
• Keywords: ADCM 2015, Database