Converting a quadrilateral input mesh into a C surface with one bi-3 tensorproduct spline patch per facet is a classical challenge. We give explicit local averaging formulas for the spline control points. Where the quadrilateral mesh is not regular, the patches have two internal double knots, the least number and multiplicity to always allow for an unbiased G construction.

In this paper, a three dimensional analysis of arbitrary straight-sided quadrilateral nanocomposite plates are investigated. The governing equations are based on three-dimensional elasticity theory which can be used for both thin and thick nanocomposite plates. Although the equations can support all the arbitrary straight-sided quadrilateral plates but as a special case, the numerical results f...

This paper discusses the modification of Varignon's theorem on quadrilaterals by dividing sides quadrilateral into three, four, five to become parts. The process proving it is done in a very simple way, namely using congruence. result obtained that area ​​the plane formed from has relationship with basic quadrilateral.

The use of polygonal meshes, especially triangle meshes, is manifold but a lot of algorithms require the mesh to be structured in a certain way and cannot be applied to an arbitrarily shaped mesh. The process of replacing an arbitrary mesh by a structured one is called remeshing. Triangle meshes with subdivision connectivity are an important class of structured meshes and have been studied thor...

Laplace–Beltrami operator and its discretization play a central role in the fields of image processing, computer graphics, computer aided geometric design and so on. In this paper, a discrete scheme for Laplace–Beltrami operator over quadrilateral meshes is constructed based on a bilinear interpolation of the quadrilateral. Convergence results for the proposed discrete scheme are established un...

In this paper, we present a new method for quadrilateral mesh generation in complex 2D domains, based on deferred constraint insertion. Our method is especially designed to handle complex geological cross-sections and multi-fractured media. We first introduce a new algorithm for triangular mesh generation: starting with a initial mesh, in general simple and regular, we adaptively modify it in o...

The Modified Direct Method (MDM) is an iterative mesh smoothing method for smoothing planar and surface meshes, which is developed from the non-iterative smoothing method originated by Balendran [1]. When smooth planar meshes, the performance of the MDM is effectively identical to that of Laplacian smoothing, for triangular and quadrilateral meshes; however, the MDM outperforms Laplacian smooth...

This article presents special quadrilateral quadratic refinement elements, which provide geometry and field continuity across Tjunctions where two elements are connected to one side of a larger quadrilateral. The main idea in element refinement is to place one or more nodes outside the element area and to modify element shape functions in order to maintain continuity at refinement edges. Specia...

The 3D meshing process begins with the definition of the outer geometry. With a CAD system and a 2d quadrilateral mesh generator, a closed all-quadrilateral mesh is obtained, which is the start point for the process that this communication describes. Once imposed the outer quadrilateral mesh, the connectivity between the inner elements becomes strongly conditioned. Following the guidelines of t...

Axillary neuropathy due to entrapment of the nerve in the quadrilateral space is seen rarely. Here, we describe a 24-year-old patient diagnosed with isolated axillary neuropathy that mimicked quadrilateral space syndrome. Quadrilateral or quadrangular space syndrome (QSS), first described by Cahill and Palmer in 1983, was defined as the entrapment of the distal branch of the axillary nerve and ...