Optimal parameterization of rational quadratic curves

This short note presents a simple analytical solution to the problem of determining the optimal parameterization of rational quadratic curves. Optimality is measured with respect to arc length by means of the L2-norm. The presented result is based on a method of Farouki [Farouki, R.T., 1997. Optimal parameterizations. Computer Aided Geometric Design 14, 153–168] and Jüttler [Jüttler, B., 1997. A vegetarian approach to optimal parameterizations. Computer Aided Geometric Design 14, 887–890], who solve the optimal parameterization problem analytically in the case of polynomial curves, but suggest a numerical procedure for rational curves.