Reparametrize of cubic bezier curve in arclength

Question

I am looking for a way to re-parametrize the cubic Bezier curve in t domain to cubic bezier curve in S (arclength) domain. Thanks

Answer 1

This is impossible (using rational functions, anyway). The only Bezier curves that can be parameterized by arclength are linear ones (of degree one). See ...

R.T. Farouki, T. Sakkalis
Real rational curves are not unit speed
Computer Aided Geometric Design, 8 (1991), pp. 151–157

If you explain why you want to do this, perhaps there is some alternative solution to your problem.