2L-convex polyominoes: Geometrical aspects

A polymino $P$ is called $2L$-convex if for every two cells there exists a monotone path included in $P$ with at most $2$ changes of direction. This paper studies the geometrical aspects of a sub-class of $2L$-convex polyominoes called $Im^{0,0}_{2L}$ and states a characterization of it in terms of monotone paths. In a second part, 4 geometries are introduced and the tomographical point of view is investigated using the switching components (that is the elements of this sub-class that have the same projections). Finally, some unicity results are given for the reconstruction of these polyominoes according to their projections.