Reconstruction of polygons from visibility information is known to be a difficult problem in general. In this paper, we consider a special case: reconstruction of orthogonal polygons from horizontal and vertical visibility information and show that this reconstruction can be performed in O(n log n) time. 
Jackson and Wismath REF studied the reconstruction of orthogonal polygons from horizontal and vertical visibility information and gave an O(n log n) time reconstruction algorithm.
Orthogonal polygon reconstruction from stabbing information
Comput. Geom.
Comput. Geom.
Mathematics Computer Science