Reconstructing a Simple Polygon from Its Angles

  • Yann Disser
  • Matúš Mihalák
  • Peter Widmayer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6139)


We study the problem of reconstructing a simple polygon from angles measured at the vertices of the polygon. We assume that at each vertex, a sensing device returns the sequence of angles between each pair of vertices that are visible. We prove that the sequence of angle measurements at all vertices of a simple polygon in cyclic order uniquely determines the polygon up to similarity. Furthermore, we propose an algorithm that reconstructs the polygon from this information in polynomial time.


Short Path Greedy Algorithm Angle Measurement Reconstruction Problem Simple Polygon 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Yann Disser
    • 1
  • Matúš Mihalák
    • 1
  • Peter Widmayer
    • 1
  1. 1.Institute of Theoretical Computer ScienceETH Zürich 

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