  Associated with the $r$-Shi arrangement and $r$-Catalan arrangement in
$\Bbb{R}^n$, we introduce a cubic matrix for each region to establish two
bijections in a uniform way. Firstly, the positions of minimal positive entries
in column slices of the cubic matrix will give a bijection from regions of the
$r$-Shi arrangement to $O$-rooted labeled $r$-trees. Secondly, the numbers of
positive entries in column slices of the cubic matrix will give a bijection
from regions of the $r$-Catalan arrangement to pairings of permutation and
$r$-Dyck path. Moreover, the numbers of positive entries in row slices of the
cubic matrix will recover the Pak-Stanley labeling, a celebrated bijection from
regions of the $r$-Shi arrangement to $r$-parking functions.
