Rational framing motions and spatial rational Pythagorean hodograph curves

Kalkan B., Scharler D. F., Schröcker H., Šír Z.

Computer Aided Geometric Design, vol.99, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 99
  • Publication Date: 2022
  • Doi Number: 10.1016/j.cagd.2022.102160
  • Journal Name: Computer Aided Geometric Design
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Computer & Applied Sciences, INSPEC, MathSciNet, Metadex, zbMATH, DIALNET, Civil Engineering Abstracts
  • Keywords: Rational curve, Tangent indicatrix, Euler-Rodrigues frame, Rational motion, Motion polynomial, Spherical motion
  • Van Yüzüncü Yıl University Affiliated: Yes

Abstract

© 2022 The Author(s)We propose a new method for constructing rational spatial Pythagorean Hodograph (PH) curves based on determining a suitable rational framing motion. While the spherical component of the framing motion is arbitrary, the translation part is determined be a modestly sized and nicely structured system of linear equations. Rather surprisingly, generic input data will only result in polynomial PH curves. We provide a complete characterization of all cases that admit truly rational (non-polynomial) solutions. Examples illustrate our ideas and relate them to existing literature.