We introduce a simplification algorithm for meshes composed of quadrilateral
elements. Our technique can handle models with sharp features, and can be used
for re-meshing polygonal, i.e. tri- and quad-dominant, meshes into fully quad-meshes.
It is reminiscent of edge-collapse based methods for triangle meshes, but takes a
novel appraoch to the challenging problem of maintaining the quad structure during
level-of-detail creation. The method consists of a set of unit operations applied
to the dual of the mesh, each designed to maintain the quadrilateral structure and
topology of the mesh. Geometric shape is maintained by a simple extension of a quadric
error metric to quad meshes. The technique is straightforward to implement and efficient
enough to be applied to real-world models.