Copy For Citation
Kalkan B., Scharler D. F., Schröcker H., Šír Z.
Computer Aided Geometric Design, vol.99, 2022 (SCI-Expanded)
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Publication Type:
Article / Article
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Volume:
99
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Publication Date:
2022
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Doi Number:
10.1016/j.cagd.2022.102160
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Journal Name:
Computer Aided Geometric Design
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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
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Keywords:
Rational curve, Tangent indicatrix, Euler-Rodrigues frame, Rational motion, Motion polynomial, Spherical motion
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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.