An improved algorithm for reconstructing a simple polygon from the visibility angles

Authors:
Danny Z. Chen;Haitao Wang
Affiliations:
Department of Computer Science and Engineering, University of Notre Dame, Notre Dame, IN;Department of Computer Science and Engineering, University of Notre Dame, Notre Dame, IN
Venue:
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Year:
2011

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Abstract

We study the problem of reconstructing a simple polygon: 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, reconstruct the polygon P (up to similarity). An O(n3logn) time algorithm has been proposed for this problem. We present an improved algorithm with running time O(n2), based on new observations on the geometric structures of the problem. Since the input size (i.e., the total number of input visibility angles) is Θ(n2) in the worst case, our algorithm is worst-case optimal.