If you want guarantees, use adaptive subdivision: estimate the deviation between the line and the curve, split only where the error exceeds your tolerance, and let the step size grow with curvature. Fixed‑step is simpler to code, but you either waste samples in flat areas or miss tight turns unless you choose an absurdly small step. In practice, a hybrid works best: start with a few fixed steps for a baseline, then refine adaptively only where the curvature spikes. Use a cheap error metric, like the perpendicular distance from the control point to the chord, and stop subdividing once that distance is negligible. That gives you visual fidelity with minimal overhead.

Sounds like a good plan—just keep the bound tight enough that the curve never feels “stiff” between sample points. It’s all about that invisible line of symmetry between speed and smoothness.

Exactly, tweak until the curve feels like a single straight line in the eye, not a jagged stair. If it still feels off, lower the tolerance a fraction, otherwise you’ll be paying the price for “smoothness” later. Keep it tight, keep it clean.