  In the usual aim of discrete tomography, the reconstruction of an unknown
discrete set is considered, by means of projection data collected along a set
$U$ of discrete directions. Possible ambiguous reconstructions can arise if and
only if switching components occur, namely, if and only if non-empty images
exist having null projections along all the directions in $U$. In order to
lower the number of allowed reconstructions, one tries to incorporate possible
extra geometric constraints in the tomographic problem. In particular, the
class $\mathbb{P}$ of horizontally and vertically convex connected sets
(briefly, $hv$-convex polyominoes) has been largely considered. In this paper
we introduce the class of $hv$-convex switching components, and prove some
preliminary results on their geometric structure. The class includes all
switching components arising when the tomographic problem is considered in
$\mathbb{P}$, which highly motivates the investigation of such configurations.
It turns out that the considered class can be partitioned in two disjointed
subclasses of closed patterns, called windows and curls, respectively. It
follows that all windows have a unique representation, while curls consist of
interlaced sequences of sub-patterns, called $Z$-paths, which leads to the
problem of understanding the combinatorial structure of such sequences. We
provide explicit constructions of families of curls associated to some special
sequences, and also give additional details on further allowed or forbidden
configurations by means of a number of illustrative examples.
