Quadrilateral Meshing by Circle Packing

Proceedings, 6th International meshing Roundtable, Sandia National Laboratories, pp.7-20, October 1997

MESHING
RESEARCH
CORNER

Marshall Bern: Xerox Palo Alto Research Center, 3333 Coyote Hill Road, Palo Alto, CA, 94304; http://www.parc.xerox.com/csl/members/bern/; bern@parc.xerox.com.

David Eppstein: Department of Information and Computer Science, University of California, Irvine, CA 92697-3425; http://www.ics.uci.edu/~eppstein; eppstein@ics.uci.edu

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 Voronoi diagram, (2) all elements have two opposite 90 degree angles, (3) all elements are kites, or (4) all angles are at most 120 degrees. In each case the total number of elements is 0(n), where n is the number of input vertices.

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