We present Laguerre Voronoi based subdivision algorithms for the quadrilateral and hexahedral meshing of particle systems within a bounded region in two and three dimensions, respectively. Particles are smooth functions over circular or spherical domains. The algorithm first breaks the bounded region containing the particles into Voronoi cells that are then subsequently decomposed into an initi...

The accuracy and eeciency of the solution to numerical systems depends on the quality of the mesh used. Automatic mesh generation and adaptive reenement methods can, however, produce poor quality elements, even invalid elements, for quadrilateral or hexahedral mesh. We present an optimization-based approach for quadrilateral or hexahedral mesh untangling that maximizes the minimum area or volum...

A uniform finite element mesh rarely provides the best discretization of a domain to accommodate a solution with both optimal efficiency and minimal error. Mesh adaptation can approach a more optimal solution by accommodating regions of the mesh with higher or lower element density. Extensive attention has been given to mesh adaptation in both computational mechanics and computer graphics to pr...

In this paper, double integrals over an arbitrary quadrilateral are evaluated exploiting finite element method. The physical region is transformed into a standard quadrilateral finite element using the basis functions in local space. Then the standard quadrilateral is subdivided into two triangles, and each triangle is further discretized into 4 n right isosceles triangles, with area 1 2n2, and...

Normal and almost normal surfaces are essential tools for algorithmic 3-manifold topology, but to use them requires exponentially slow enumeration algorithms in a high-dimensional vector space. The quadrilateral coordinates of Tollefson alleviate this problem considerably for normal surfaces, by reducing the dimension of this vector space from 7n to 3n (where n is the complexity of the underlyi...

A new technique for automatically generating anisotropic quadrilateral meshes is presented in this paper. The inputs are (1) a 2D geometric domain and (2) a desired anisotropy – defined as a metric tensor over the domain – specifying mesh sizing in two independent directions. Node locations are obtained by closely packing rectangles in accordance with the inputs. The centers of the rectangles, ...

We present a novel approach named T-Base for smoothing planar and surface quadrilateral meshes. Our motivation is that the best shape of quadrilateral element – square – can be virtually divided into a pair of equilateral right triangles by any of its diagonals. When move a node to smooth a quadrilateral, it is optimal to make a pair of triangles divided by a diagonal be equilateral right trian...