# ICS 269, Spring 1997: Theory Seminar

## 3 October 1997:

Quadrilateral Meshing by Circle Packing

David Eppstein, ICS, UC Irvine

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,
- all elements 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*), where *
n* is the number of input vertices.
(Joint work with Marshall Bern, published at the 6th International
Meshing Roundtable)