Choosing Corners of Rectangles

The algorithm need only work for surfaces that are roughly rectangular, particularly those without large reflex angles, as otherwise an unstructured meshing algorithm is used instead. We report on the theory and implementation of algorithms for this problem.
We also give an overview of a solution to a related problem called interval assignment: Given a complex of surfaces sharing curves, globally assign the number of mesh edges or intervals for each curve such that it is possible to mesh each surface according to its prescribed quadrilateral meshing algorithm, and assigned and user prescribed boundary mesh edges and corners. We also note a practical, constructive technique that relies on interval assignment that can generate a quadrilateral mesh of a complex of surfaces such that a compatible hexahedral mesh of the enclosed volume exists.
Scott A. Mitchell, "Choosing Corners of Rectangles for Mapped Meshing." ACM Press, in proc. 13th Annual Symposium on Computational Geometry, June 46 1997, pp 8793. URL:http:choosingcorners.html