# David Eppstein - Publications

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**Quadrilateral meshing by circle packing**.

M. Bern
and D. Eppstein.

*2nd CGC
Worksh. Computational Geometry*, Durham, North Carolina, 1997.

*6th Int. Meshing Roundtable,* Park
City, Utah, 1997, pp. 7–19.

arXiv:cs.CG/9908016.

*Int. J. Comp. Geom. & Appl.* 10 (4): 347–360, 2000.
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:

- The elements form the cells of a Voronoi diagram,
- The elements each have two opposite 90 degree angles,
- All elements are kites, or
- All angles are at most 120 degrees.

In each case the total number of elements is O(*n*).
The 120-degree bound is optimal; if a simply-connected region has all
angles at least 120 degrees, any mesh of that region has a 120 degree
angle.
(BibTeX –
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Publications –
David Eppstein –
Theory Group –
Inf. & Comp. Sci. –
UC Irvine

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