Rational Framing Motions and Spatial Rational Pythagorean Hodograph Curves
Metric Geometry
2022-10-25 v2 Numerical Analysis
Numerical Analysis
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.
Keywords
Cite
@article{arxiv.2111.04600,
title = {Rational Framing Motions and Spatial Rational Pythagorean Hodograph Curves},
author = {Bahar Kalkan and Daniel F. Scharler and Hans-Peter Schröcker and Zbyněk Šír},
journal= {arXiv preprint arXiv:2111.04600},
year = {2022}
}