Consider mapping a regular i x j quadrilateral mesh of a rectangle onto a surface. The quality of the mapped mesh of the surface depends heavily on which vertices of the sulface correspond to comers of the rectangle. Our problem is, given an n-sided surface, chose as comers four vertices such that the surface resembles a rectangle are notprespecwed. In general, there is either a goal number or a prescribed number of mesh edges for each bounding curve of the surface. The goals affect the quality

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... of the mesh, and the prescribed edges may makefinding a feasible set of comers difficult. with comers at those vertices. Note that n could be quite large, and the length and width of the rectangle, i and RECEIVED JAN 0 6 1997 The algorithm need only work for surfaces that are roughly rectangular, particularly those without large rejlex angles, as otherwise an unstructured meshing algorithm is used instead. We report on the theory and implementation of algorithm for this problem. S*T I We also give an overview of a solution to a relatedproblem called interval assignment: Given a complex of surfaces sharing curves, globally assign the number of mesh edges or intervak 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 comers. We also note a practical, constructive technique that relies on interval assignment that can generate a quadrilateral mesh of a complex of su~aces such that a compatible hexahedral mesh of the enclosed volume exists.