Arc-length coordinates:

 
A surface is parameterized in arc length if:

$$\begin{array}{rcl} u &=& \int_{u=u_0}^{u} \vert\vert\frac{\d... ...ert\frac{\delta\xi}{\delta v}(u, v)\vert\vert dv\\ \end{array}$$

This is rarely the case.