Quadrilateral Meshing by Circle Packing (1997) [24 citations — 2 self]
http://www.cs.berkeley.edu/~jrs/meshpapers/BernEpp
http://www.ics.uci.edu/~eppstein/pubs/BerEpp-MRT-9
http://www.imr.sandia.gov/papers/imr6/bern97.ps.gz
http://http.cs.berkeley.edu/~jrs/meshpapers/BernEp
http://www.cs.duke.edu/CGC/workshop97/abstracts/ep
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author = {Marshall Bern and David Eppstein},
title = {Quadrilateral Meshing by Circle Packing},
booktitle = {International Journal of Computational Geometry and Applications},
year = {1997},
pages = {7--20}
}
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Abstract:
We use circle-packing methods to generate quadrilateral meshes for polygonal domains, with guaranteed bounds both on the quality and the number of elements. We show that these methods can generate meshes of several types: (1) the elements form the cells of a Vorono diagram, (2) all elements have two opposite 90 # angles, (3) all elements are kites, or (4) all angles are at most 120 # . In each case the total number of elements is O(n), where n is the number of input vertices. 1 Introduction We investigate here problems of unstructured quadrilateral mesh generation for polygonal domains, with two conflicting requirements. First, we require there to be few quadrilaterals, linear in the number of input vertices; this is appropriate for methods in which high order basis functions are used, or in multiblock grid generation in which each quadrilateral is to be further subdivided into a structured mesh. Second, we require some guarantees on the quality of the mesh: either the elements themse...
