 
Summary: COMPUTING CONVEX QUADRANGULATIONS
F. AURENHAMMER, M. DEMUTH, AND T. SCHIFFER
ABSTRACT. We use projected Delaunay tetrahedra and a maximum in
dependent set approach to compute large subsets of convex quadrangu
lations on a given set of points in the plane. The new method improves
over the popular pairing method based on triangulating the point set.
INTRODUCTION
Quadrangulations Generating a mesh in a geometric domain is a step
prior to many computational tasks, in finiteelement based applications as
well as in computer graphics, geographic information systems, computa
tional geometry, and other areas. Irregular meshes (i.e., meshes with vary
ing vertex degree) are preferred in many cases, due to their flexibility and
adaptability. Again, meshes that are homogenous (having a fixed number of
vertices per element) are desired. The most popular ones among such ho
mogenous irregular meshed are triangulations and quadrangulations or, by
another name, quadrilateral meshes. The literature on triangulations is vast;
we make no attempt to survey even parts of it here, but rather refer to two
quite complete introductory surveys on quadrangulations [21, 4], which are
the topic of the present paper.
Compared to triangulations, quadrangulations are not very well under
