2021/11/08 by Bahar Kalkan, Daniel F. Scharler, Kalkan, Bahar +5 · 1 citation
Engineering · Mathematics · Computer Science · #Advanced Numerical Analysis Techniques #Mathematics and Applications #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2111.04600
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.