  We explore the separability of point sets in the plane by a
restricted-orientation convex hull, which is an orientation-dependent, possibly
disconnected, and non-convex enclosing shape that generalizes the convex hull.
Let $R$ and $B$ be two disjoint sets of red and blue points in the plane, and
$\mathcal{O}$ be a set of $k \geq 2$ lines passing through the origin. We study
the problem of computing the set of orientations of the lines of $\mathcal{O}$
for which the $\mathcal{O}$-convex hull of $R$ contains no points of $B$.
  For $k=2$ orthogonal lines we have the rectilinear convex hull. In optimal
$O(n \log n)$ time and $O(n)$ space, $n = \vert R \vert + \vert B \vert$, we
compute the set of rotation angles such that, after simultaneously rotating the
lines of $\mathcal{O}$ around the origin in the same direction, the rectilinear
convex hull of $R$ contains no points of $B$. We generalize this result to the
case where $\mathcal{O}$ is formed by $k \geq 2$ lines with arbitrary
orientations. In the counter-clockwise circular order of the lines of
$\mathcal{O}$, let $\alpha_i$ be the angle required to clockwise rotate the
$i$th line so it coincides with its successor. We solve the problem in this
case in $O(1/\Theta \cdot N \log N)$ time and $O(1/\Theta \cdot N)$ space,
where $\Theta = \min \{ \alpha_1,\ldots,\alpha_k \}$ and $N=\max\{k,\vert R
\vert + \vert B \vert \}$. We finally consider the case in which $\mathcal{O}$
is formed by $k=2$ lines, one of the lines is fixed, and the second line
rotates by an angle that goes from $0$ to $\pi$. We show that this last case
can also be solved in optimal $O(n\log n)$ time and $O(n)$ space, where $n =
\vert R \vert + \vert B \vert$.
