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Quadrilateral Meshes for PSLGs

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Abstract

We prove that every planar straight line graph with n vertices has a conforming quadrilateral mesh with \(O(n^2)\) elements, all angles \(\le \) 120\(^\circ \) and all new angles \(\ge \) 60\(^\circ \). Both the complexity and the angle bounds are sharp.

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Acknowledgments

The author is partially supported by NSF Grant DMS 13-05233. I thank Joe Mitchell and Estie Arkin for numerous helpful conversations about computational geometry in general, and about the results of this paper in particular. Also thanks to two anonymous referees whose thoughtful remarks and suggestions on two versions of the paper greatly improved the precision and clarity of the exposition. A proof suggested by one of the referees is included in Sect. 8.

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  1. Mathematics Department, Stony Brook University, Stony Brook, NY, 11794-3651, USA

    Christopher J. Bishop

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  1. Christopher J. Bishop
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Correspondence to Christopher J. Bishop.

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Bishop, C.J. Quadrilateral Meshes for PSLGs. Discrete Comput Geom 56, 1–42 (2016). https://doi.org/10.1007/s00454-016-9771-9

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  • DOI: https://doi.org/10.1007/s00454-016-9771-9

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