Normal art galleries: Wall in - all in (Q714897)

An art gallery is a simple polygon, and the subject of visual coverage of art galleries has developed quite substantially. This paper focuses on the relation between the visual coverage of the walls and the rest of the gallery. The notion of a normal gallery, a gallery in which any configuration of guards that visually covers the walls necessarily covers the entire gallery, is introduced in this work, and several sufficient conditions for a gallery to be normal are established. For example, any star gallery is normal and any gallery with at most two reflex corners is normal. Besides, a polynomial time algorithm is provided to check if a given gallery is normal with respect to a given finite set of positions within the gallery. From a practical point view, checking if a configuration of guards covers the walls of a gallery may be an easier task than checking if it covers the entire gallery, therefore, the study of the property ``wall in - all in'' of the normal galleries is meaningful and a full characterization of normal galleries is a future work to do.