Abstract
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.
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Disser, Y., Mihalák, M., Widmayer, P. (2010). Reconstructing a Simple Polygon from Its Angles. In: Kaplan, H. (eds) Algorithm Theory - SWAT 2010. SWAT 2010. Lecture Notes in Computer Science, vol 6139. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13731-0_2
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DOI: https://doi.org/10.1007/978-3-642-13731-0_2
Publisher Name: Springer, Berlin, Heidelberg
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