  The computation of the fundamental group of the complement of an algebraic
plane curve has been theoretically solved since Zariski-van Kampen, but actual
computations are usually cumbersome. In this work, we describe the notion of
Wirtinger presentation of such a group relying on the real picture of the curve
and with the same combinatorial flavor as the classical Wirtinger presentation;
we determine a significant family of curves for which Wirtinger presentation
provides the required fundamental group. The above methods allow us to compute
that fundamental group for an infinite subfamily of hypocycloids, relating them
with Artin groups.
