We review recent results on Integrable Discrete Geometry. It turns out that most of the known (continuous and/or discrete) integrable systems are particular symmetries of the quadrilateral lattice, a multidimensional lattice characterized by the planarity of its elementary quadrilaterals. Therefore the linear property of planarity seems to be a basic geometric property underlying integrability....

Triangle meshes have been nearly ubiquitous in computer graphics, and a large body of data structures and geometry processing algorithms based on them has been developed in the literature. At the same time, quadrilateral meshes, especially semi-regular ones, have advantages for many applications, and significant progress was made in quadrilateral mesh generation and processing during the last s...

Low-distortion parameterization of 3D meshes is a fundamental problem in computer graphics. Several widely used approaches have been presented for triangular meshes. But no direct parameterization techniques are available for quadrilateral meshes yet. In this paper, we present a parameterization technique for non-closed quadrilateral meshes based on mesh simplification. The parameterization is ...

In this paper we present an efficient face-based connectivity coding technique for the special class of quadrilateral and the hybrid triangular-quadrilateral meshes. This work extends the main ideas of non-split encoding presented by the first contribution of the authors (Khattab, Abd El-Latif, Abdel Wahab and Tolba, 2007) for triangle meshes and improves over the compression results provided s...

The axial stiffness of the connection joints in a transmission tower will affect stability bearing capacity tower. different forms has effects on capacities triangular and quadrilateral lattice towers. This paper takes towers as comparative research objects considers influence single-limb, single-plate joint (SLSPJ) double-limb, double-plate (DLDPJ) Under vertical load, are studied from hte thr...

A non–oscillatory, high resolution reconstruction method on quadrilateral meshes in 2D is presented. It is a two–dimensional extension of Marquina’s hyperbolic method. The generalization to quadrilateral meshes allows the method to simulate realistic flow problems in complex domains. An essential point in the construction of the method is a second order accurate approximation of gradients on an...

Algorithms of quadrilateral mesh partition and optimization based on cloud data are proposed in the paper. Quadrilateral meshes are partite by means of dynamic edge-extending according to the types of the nodes. The mesh optimization algorithms are designed, and topology optimization of degree 2 and 3 node and region mesh optimization processing based on viewpoint are programmed and debugged as...

This paper presents the development of a 2D solver for inviscid and viscous compressible flows using the spectral difference (SD) method for unstructured grids with mixed elements. A mixed quadrilateral and triangular grid is first refined using one-level h-refinement to generate a quadrilateral grid while keeping the curvature of boundary edges. The SD method designed for quadrilateral meshes ...

We consider a quadrilateral ’mini’ finite element for approximating the solution of Stokes equations using a quadrilateral mesh. We use the standard bilinear finite element space enriched with element-wise defined bubble functions for the velocity and the standard bilinear finite element space for the pressure space. With a simple modification of the standard bubble function we show that a sing...