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Browsing by Author "Sir, Zbynek"

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    Rational Framing Motions and Spatial Rational Pythagorean Hodograph Curves
    (Elsevier, 2022) Kalkan, Bahar; Scharler, Daniel F.; Schroecker, Hans-Peter; Sir, Zbynek
    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.