Point and line segment reconstruction from visibility information

In general, visibility reconstruction problems involve determining a set of objects in the plane that exhibit a specified set of visibility constraint s. In this paper, an algorithm is presented for reconstructing a set of par allel line segments from specified visibility information contained in an e xtended endpoint visibility graph. The algorithm runs in polynomial time an d relies on simple vector arithmetic to generate a system of linear inequal ities. A related problem, solvable with the same technique, is the point re construction problem, in which the cyclic ordering and the x-coordinates of a set of points is specified. A second contribution is the definition of a n extension of the visibility graph called the Stab Graph, which contains e xtra visibility information.