As an informal motivation the problem, imagine a tower with polygonal footprint, that is located in a beautiful landscape, the "Belvedere Hull" is then related to the directions, in which one would have a view unobstructed by the tower (it is assumed that the tower has roof, so it is not possible to stand on top of it).

Problem:

given a simple, planar polygon, calculate the boundary of the union of all half-lines that do not contain inner points of the polygon, i.e. the "Belvedere Hull".

This problem seems to be related to the visibility from a point inside the polygon, or to the art gallery problem, so I would like to know if this problem has already been considered or, how to tackle it.

Generalizations can easily be envisaged, by either going to higher-dimensional spaces and/or, by replacing the polygon by other, not necessarily connected point-sets.