An improved algorithm for reconstructing a simple polygon from its visibility angles ?
Given a cyclically ordered vertex sequence of an unknown simple polygon P of n vertices and, for each vertex v of P, the sequence of angles defined by all the visible vertices of v in P, we study the problem of reconstructing the polygon P  (up to similarity). An O ( n 3 log n ) time algorithm has been proposed for this problem (by Disser, Mihalk, and Widmayer in 2011 [5]). We show in this paper that the running time of the algorithm in the previous work can be reduced to O(n2) O ( n 2 ) time by new observations on the geometric structures of the problem.
visibility angles polygon reconstruction visibility graph