Pseudo-Triangle Visibility Graph: Characterization and Reconstruction
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The visibility graph of a simple polygon represents visibility relations between its vertices. Knowing the correct order of the vertices around the boundary of a polygon and its visibility graph, it is an open problem to locate the vertices in a plane in such a way that it will be consistent with this visibility graph. This problem has been solved for special cases when we know that the target polygon is a tower or a spiral. Knowing that a given visibility graph belongs to a simple polygon with at most three concave chains on its boundary, a pseuodo-triangle, we propose a linear time algorithm for reconstructing one of its corresponding polygons. Moreover, we introduce a set of necessary and sufficient properties for characterizing visibility graphs of pseudo-triangles and propose polynomial algorithms for checking these properties.
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