Arc lengths of rational Pythagorean–hodograph curves

In a recent paper (Lee et al., 2014) a family of rational Pythagorean–hodograph (PH) curves is introduced, characterized by constraints on the coefficients of a truncated Laurent series, and used to solve the first-order Hermite interpolation problem. Contrary to a claim made in this paper, it is shown that these rational PH curves have rational arc length functions only in degenerate cases, where the center of the Laurent series is a real value.