This research is devoted to a systematic discretization of some classical notions of Diierential Geometry and to the study of their deep connections with the theory of integrable diierence equations in multidimensions. The basic example we consider here is the conjugate net 1], whose proper discretization is the quadrilateral lattice 2], 3]. are planar, where T i is the translation operator in ...

In this paper, we build on the mesh improvement methods intended for parallel execution with the paving method [1] and introduce topological changes in an existing quadrilateral-only mesh to improve element shape and nodal valence. This discussion is intended to demonstrate the effectiveness of utilizing mesh cleanup operations as a post-processing step to other mesh generation algorithms. The ...

Boundary-constrained triangulation has long been the domain of Delaunay mesh generation. Another application for constrained triangulation is introduced in this work. A new technique for hexahedral-dominant mesh generation is developed. With this method, known as Hex-Morphing (H-Morph), an initial tetrahedral mesh is provided. The quadrilateral faces of the hexahedra are treated as internal sur...

This paper focuses on the low-order nonconforming rectangular and quadrilateral finite elements approximation of incompressible flow. Beyond the previous research works [9, 8, 4], we propose a general strategy to construct the basis functions. Under several specific constraints, the optimal error estimates are obtained, i.e. the first order accuracy of the velocities in H-norm and the pressure ...

We propose an algorithm to produce automatically a 3-D CAD model from a set of range data, based on non-uniform rational B-splines (NURBS) surface fitting technique. Our goal is to construct automatically continuous geometric models, assuming that the topology of the surface is unknown. In the propose algorithm, the triangulated surface is partitioned in quadrilateral patches, using Morse theor...

It is shown that for any connected graph G and all sufficiently large s, the cartesian product G×Qs has a quadrilateral embedding in some surface, where Qs is the hypercube graph. This answers a question of Pisanski.

In this report, we show that an arbitrarily given quadrilateral can always be interpreted as an image of a parallelogram and that the interpretation is unique aside from a multiplicative constant. Several applications of this theorem are discussed. It could be used to prove an old, geometrical theorem; it could facilitate the matching process when a sequence of images are available; it could be...

In this paper we introduce a coarsening algorithm for quadrilateral meshes that generates quality, quad-only connectivity during level-of-coarsening creation. A novel aspect of this work is development and implementation of a localized adaptation of the polychord collapse operator to better control and preserve important surface components. We describe a novel weighting scheme for automatic del...