Yeah, interesting stuff. So, the whole debate between closed forms and numerical methods is kind of overplayed. Even if you had a closed form for arc length, yo

Yeah, interesting stuff. So, the whole debate between closed forms and numerical methods is kind of overplayed. Even if you had a closed form for arc length, you’d still need numerical methods to compute exp and log. What functions actually work best for arc length? That’s the real question. Also, while some folks are hyped about Pythagorean-Hodograph curves, I think they’re kinda niche. Euler spirals seem more practical, even if you have to compute a special function for them. Numerical solutions tend to be more stable anyway, especially in cases where a closed form might break down, like near straight lines.