  Given a parametric polynomial curve $\gamma:[a,b]\rightarrow \mathbb{R}^n$,
how can we sample a random point $\mathfrak{x}\in \mathrm{im}(\gamma)$ in such
a way that it is distributed uniformly with respect to the arc-length?
Unfortunately, we cannot sample exactly such a point-even assuming we can
perform exact arithmetic operations. So we end up with the following question:
how does the method we choose affect the quality of the approximate sample we
obtain? In practice, there are many answers. However, in theory, there are
still gaps in our understanding. In this paper, we address this question from
the point of view of complexity theory, providing bounds in terms of the size
of the desired error.
