  We give a short proof that a uniform noncrossing partition of the regular
$n$-gon weakly converges toward Aldous's Brownian triangulation of the disk, in
the sense of the Hausdorff topology. This result was first obtained by Curien &
Kortchemski, using a more complicated encoding. Thanks to a result of Marchal
on strong convergence of Dyck paths toward the Brownian excursion, we
furthermore give an algorithm that allows to recursively construct a sequence
of uniform noncrossing partitions for which the previous convergence holds
almost surely.
  In addition, we also treat the case of uniform noncrossing pair partitions of
even-sided polygons.
