Improving Angular Speed Uniformity by Piecewise Radical Reparameterization

For a rational parameterization of a curve, it is desirable that its angular speed is as uniform as possible. Hence, given a rational parameterization, one wants to find re-parameterization with better uniformity. One natural way is to use piecewise rational reparameterization. However, it turns out that the piecewise rational reparameterization does not help when the angular speed of the given rational parameterization is zero at some points on the curve. In this paper, we show how to overcome the challenge by using piecewise radical reparameterization.