**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.

*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.

Publications – David Eppstein – Theory Group – Inf. & Comp. Sci. – UC Irvine

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