Kalkan, BaharScharler, Daniel F.Schroecker, Hans-PeterSir, Zbynek2025-05-102025-05-1020220167-83961879-233210.1016/j.cagd.2022.1021602-s2.0-85141505932https://doi.org/10.1016/j.cagd.2022.102160https://hdl.handle.net/20.500.14720/10237Sir, Zbynek/0000-0003-1701-5973; Schrocker, Hans-Peter/0000-0003-2601-6695; Kalkan Tasdemir, Bahar/0000-0001-5740-2180We 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.eninfo:eu-repo/semantics/openAccessRational CurveTangent IndicatrixEuler-Rodrigues FrameRational MotionMotion PolynomialSpherical MotionArticle99Q2Q2WOS:000892772100001