I've read the chapters on curves from two different books on diff. geometry and both say that if a curve is regular, then there exists a unit-velocity reparametrization. But regularness depends on the choice of parametrization. For instance, both the curves (t,t²) and (t³,t^6) are parametrization of the parabola y=x², but only the first is regular. So I ask, is there a criterion to determine whether or not a parametrized curve admits a regular reparametrization?