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arXiv · 2111.04600

Rational Framing Motions and Spatial Rational Pythagorean Hodograph Curves

Bahar Kalkan·Daniel F. Scharler·Hans-Peter Schröcker·Zbyněk Šír
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Abstract

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.

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Bahar Kalkan, Daniel F. Scharler, Hans-Peter Schröcker, Zbyněk Šír. 2021-11-08. Rational Framing Motions and Spatial Rational Pythagorean Hodograph Curves. https://arxiv.org/abs/2111.04600

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