  Let $P$ be a crossing-free polygon and $\mathcal C$ a set of shortcuts, where
each shortcut is a directed straight-line segment connecting two vertices of
$P$. A shortcut hull of $P$ is another crossing-free polygon that encloses $P$
and whose oriented boundary is composed of elements from $\mathcal C$. Shortcut
hulls find their application in geo-related problems such as the simplification
of contour lines. We aim at a shortcut hull that linearly balances the enclosed
area and perimeter. If no holes in the shortcut hull are allowed, the problem
admits a straight-forward solution via shortest paths. For the more challenging
case that the shortcut hull may contain holes, we present a polynomial-time
algorithm that is based on computing a constrained, weighted triangulation of
the input polygon's exterior. We use this problem as a starting point for
investigating further variants, e.g., restricting the number of edges or bends.
We demonstrate that shortcut hulls can be used for drawing the rough extent of
point sets as well as for the schematization of polygons.
