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Quadrilateral meshes with provable angle bounds

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Abstract

In this paper, we present an algorithm that utilizes a quadtree data structure to construct a quadrilateral mesh for a simple polygonal region in which no newly created angle is smaller than \({{18.43}}^{\circ} ({=}\hbox{arctan}(\frac{1}{3}))\) or greater than \({{171.86}}^{\circ} ({=}{{135}}^{\circ} + 2\hbox{arctan}(\frac{1}{3}))\). This is the first known result, to the best of our knowledge, on a direct quadrilateral mesh generation algorithm with a provable guarantee on the angles.

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Acknowledgments

The authors would like to thank anonymous reviewers for helpful comments that served to significantly improve the presentation in the paper.

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Authors and Affiliations

  1. Department of Computer Science, St. Joseph’s University, Philadelphia, PA, USA

    F. Betul Atalay

  2. Department of Computer Science, Rutgers University, Camden, NJ, USA

    Suneeta Ramaswami

  3. Department of Computer Science, Bryn Mawr College, Bryn Mawr, PA, USA

    Dianna Xu

Authors
  1. F. Betul Atalay
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  2. Suneeta Ramaswami
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  3. Dianna Xu
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Corresponding author

Correspondence to Suneeta Ramaswami.

Additional information

An extended abstract was presented at the 17th IMR [2]. A video and short paper based on this paper was presented at the 25th SoCG [13].

Suneeta Ramaswami’s research was partially supported by NSF CCF 0830589.

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Atalay, F.B., Ramaswami, S. & Xu, D. Quadrilateral meshes with provable angle bounds. Engineering with Computers 28, 31–56 (2012). https://doi.org/10.1007/s00366-011-0215-0

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