Hello! In my engine I''d like to implement camera path with parametric curves. Bezier curves work fine, but I can''t use arc length parametrization, so the movement is not continouos (faster, where the curvature is bigger). Can you please tell what kind of curve should I use, or how can I correct my bezier curve?

Why cant you use the arc length formula? is because you dont know how to do it? in that case:

The length of a curve (x = f(t), y = g(t)) from (t = a) to (t = b) can be described like this:

integral((a to b), sqrt((dx/dt)^2 + (dy/dt)^2))dt

(anyone know how to write the integral symbol?)

So, you know the starting a-value, just set the integral equation equal to the desired length and calculate the b-value (but with a high degree bezier curve it will be really difficult to solve, and you''ll probably have to use approximation, which is slow)

Thanks for the reply. A knew the arc length formula, but its too slow to compute...

It might work to set t = weighted bezier curve from 0-1, where you adjust the weights using the distances between the controlpoints in the original curve. Not as acurate but it think it will be alot faster.