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COMPUTING CONVEX QUADRANGULATIONS F. AURENHAMMER, M. DEMUTH, AND T. SCHIFFER
 

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

  

Source: Aurenhammer, Franz - Institute for Theoretical Computer Science, Technische Universität Graz

 

Collections: Computer Technologies and Information Sciences