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Creators/Authors contains: "Bishop, ChristopherJ."

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  1. (, Proceedings of the 2022 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA))
    For any simple polygon P we compute the optimal upper and lower angle bounds for triangulating P with Steiner points, and show that these bounds can be attained (except in one special case). The sharp angle bounds for an N -gon are computable in time O(N ), even though the number of triangles needed to attain these bounds has no bound in terms of N alone. In general, the sharp upper and lower bounds cannot both be attained by a single triangulation, although this does happen in some cases. Surprisingly, we prove the optimal angle bounds for polygonal triangulations are the same as for triangular dissections. The proof of this verifies, in a stronger form, a 1984 conjecture of Gerver. 
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