Abstract.
We prove that a unique simple polygon is determined, up to similarity, by the interior angles at its vertices and the cross-ratios of diagonals of any given triangulation. (The cross-ratio of a diagonal is the product of the ratio of edge lengths for the two adjacent triangles.) This establishes a conjecture of Driscoll and Vavasis, and shows the correctness of a key step of their algorithm for computing Schwarz—Christoffel transformations mapping a disk to a polygon.
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Received April 10, 1998, and in revised form March 24, 1999.
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Snoeyink, J. Cross-Ratios and Angles Determine a Polygon . Discrete Comput Geom 22, 619–631 (1999). https://doi.org/10.1007/PL00009481
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DOI: https://doi.org/10.1007/PL00009481