  Given a set of $n$ points $P$ in the plane, the first layer $L_1$ of $P$ is
formed by the points that appear on $P$'s convex hull. In general, a point
belongs to layer $L_i$, if it lies on the convex hull of the set $P \setminus
\bigcup_{j<i}\{L_j\}$. The \emph{convex layers problem} is to compute the
convex layers $L_i$. Existing algorithms for this problem either do not achieve
the optimal $\mathcal{O}\left(n\log n\right)$ runtime and linear space, or are
overly complex and difficult to apply in practice. We propose a new algorithm
that is both optimal and simple. The simplicity is achieved by independently
computing four sets of monotone convex chains in $\mathcal{O}\left(n\log
n\right)$ time and linear space. These are then merged in
$\mathcal{O}\left(n\log n\right)$ time.
