Summary
This paper presents an algorithm that utilizes a quadtree to construct a strictly convex quadrilateral mesh for a simple polygonal region in which no newly created angle is smaller than 
. This is the first known result, to the best of our knowledge, on quadrilateral mesh generation with a provable guarantee on the minimum angle.
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References
Allman, D.J.: A quadrilateral finite element including vertex rotations for plane elasticity analysis. Int. J. Numer. Meth. in Engineering 26, 717–730 (1988)
Benzley, S., Perry, E., Merkley, K., Clark, B., Sjaardema, G.: A Comparison of All Hexahedral and All Tetrahedral Finite Element Meshes for Elastic and Elastic-Plastic Analysis. In: Proc. of the 4th International Meshing Roundtable, pp. 179–192 (1995)
Bern, M., Eppstein, D.: Quadrilateral meshing by circle packing. In: 6th IMR, pp. 7–19 (1997)
Bern, M., Eppstein, D., Gilbert, J.: Provably good mesh generation. J. Comp. Sys. Sci. 48, 384–409 (1994)
Blacker, T., Stephenson, M.: Paving: A new approach to automated quadrilateral mesh generation. Int. J. Numer. Meth. in Engineering 32(4), 811–847 (1991)
Brauer, J.R. (ed.): What every engineer should know about finite element analysis, 2nd edn. Marcel-Dekker, New York (1993)
Cheng, S.-W., Dey, T., Ramos, E., Ray, T.: Quality meshing for polyhedra with small angles. In: Proc. 20th Annual Symposium on Computational Geometry (2004)
Chew, L.P.: Guaranteed-quality mesh generation for curved surfaces. In: Proc. of the 9th ACM Symposium on Computational Geometry, pp. 274–280 (1993)
Chew, L.P.: Guaranteed-quality delaunay meshing in 3d. In: Proc. of the 13th ACM Symposium on Computational Geometry, pp. 391–393 (1997)
Johnston, B.P., Sullivan, J.M., Kwasnik, A.: Automatic conversion of triangular finite meshes to quadrilateral elements. Int. J. Numer. Meth. in Engineering 31(1), 67–84 (1991)
Miller, G.L., Talmor, D., Teng, S.-H., Walkington, N.: A delaunay based numerical method for three dimensions: Generation, formulation, and partition. In: Proc. of the 27th ACM Symposium on the Theory of Computing, pp. 683–692 (1995)
Mitchell, S., Vavasis, S.: Quality Mesh generation in Three Dimensions. In: Proceedings of the 8th Annual Symposium on Computational Geometry, pp. 212–221 (1992)
Ramaswami, S., Siqueira, M., Sundaram, T., Gallier, J., Gee, J.: Constrained quadrilateral meshes of bounded size. Int. J. Comp. Geom. and Appl. 15(1), 55–98 (2005)
Shewchuk, J.: Constrained Delaunay Tetrahedralizations and Provably Good Boundary Recovery. In: Proc. of the 11th International Meshing Roundtable, pp. 193–204 (2002)
Shewchuk, J.R.: Triangle: Engineering a 2D quality mesh generator and Delaunay triangulator. In: Lin, M.C., Manocha, D. (eds.) FCRC-WS 1996 and WACG 1996. LNCS, vol. 1148. Springer, Heidelberg (1996)
Zienkiewicz, O.C., Taylor, R.L.: The finite element method. McGraw-Hill, New York (1989)
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Atalay, F.B., Ramaswami, S., Xu, D. (2008). Quadrilateral Meshes with Bounded Minimum Angle. In: Garimella, R.V. (eds) Proceedings of the 17th International Meshing Roundtable. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87921-3_5
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DOI: https://doi.org/10.1007/978-3-540-87921-3_5
Publisher Name: Springer, Berlin, Heidelberg
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