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On Optimal Bilinear Quadrilateral Meshes
"... . The novelty of this work is in presenting interesting error properties of two types of asymptotically "optimal" quadrilateral meshes for bilinear approximation. The first type of mesh has an error equidistributing property where the maximum interpolation error is asymptotically the same ..."
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. The novelty of this work is in presenting interesting error properties of two types of asymptotically "optimal" quadrilateral meshes for bilinear approximation. The first type of mesh has an error equidistributing property where the maximum interpolation error is asymptotically
Meshing Of Hexagons Into Convex Quadrilaterals
"... E#cient electromagnetic analysis of the composite metallic and dielectric structures in the frequency domain based on the Method of Moments applied to the Surface Integral Equations is provided, if building blocks have the form of bilinear surfaces (in particular, flat quads), and if analysis is sup ..."
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Cited by 1 (0 self)
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. The e#ectiveness of the approach is illustrated on a typical example. This method is implemented in the software tool for antenna design [6]. Keywords: hexagon, quadrilateral, mesh, combinatorial counting 1.
Are Bilinear Quadrilaterals Better Than Linear Triangles?
"... This paper compares the theoretical effectiveness of bilinear approximation over quadrilaterals with linear approximation over triangles. Anisotropic mesh transformation is used to generate asymptotically optimally efficient meshes for piecewise linear interpolation over triangles and bilinear inter ..."
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Cited by 16 (0 self)
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This paper compares the theoretical effectiveness of bilinear approximation over quadrilaterals with linear approximation over triangles. Anisotropic mesh transformation is used to generate asymptotically optimally efficient meshes for piecewise linear interpolation over triangles and bilinear
Global Structure Optimization of Quadrilateral Meshes
"... We introduce a fully automatic algorithm which optimizes the highlevel structure of a given quadrilateral mesh to achieve a coarser quadrangular base complex. Such a topological optimization is highly desirable, since stateoftheart quadrangulation techniques lead to meshes which have an appropria ..."
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Cited by 21 (5 self)
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We introduce a fully automatic algorithm which optimizes the highlevel structure of a given quadrilateral mesh to achieve a coarser quadrangular base complex. Such a topological optimization is highly desirable, since stateoftheart quadrangulation techniques lead to meshes which have
Quadrilateral mesh simplification
 In ACM SIGGRAPH Asia 2008 papers
, 2008
"... Figure 1: Our simplification algorithm can be used to generate a pure quad levelofdetail hierarchy. The algorithm preserves topology during simplification, and attempts to optimize geometric fidelity and quad structure (vertex valences near 4) throughout the process. We introduce a simplification ..."
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Cited by 23 (5 self)
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algorithm for meshes composed of quadrilateral elements. It is reminiscent of edgecollapse based methods for triangle meshes, but takes a novel approach to the challenging problem of maintaining the quadrilateral connectivity during levelofdetail creation. The method consists of a set of unit operations
OPTIMAL ANGLE BOUNDS FOR QUADRILATERAL MESHES
"... Abstract. We show that any simple planar ngon can be meshed in linear time by O(n) quadrilaterals with all new angles bounded between 60 and 120 degrees. 1991 Mathematics Subject Classification. Primary: 30C62 Secondary: Key words and phrases. Quadrilateral meshes, Riemann mapping, thick/thin decom ..."
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Cited by 5 (3 self)
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Abstract. We show that any simple planar ngon can be meshed in linear time by O(n) quadrilaterals with all new angles bounded between 60 and 120 degrees. 1991 Mathematics Subject Classification. Primary: 30C62 Secondary: Key words and phrases. Quadrilateral meshes, Riemann mapping, thick
Adaptive TriangularQuadrilateral Mesh Generation
 Intl. J. Numer. Methods Eng
, 1998
"... In this paper, we begin by recalling an adaptive mesh generation method governed by isotropic and anisotropic discrete metric maps, by means of the generation of a unit mesh with respect to a Riemannian structure. We propose then an automatic triangular to quadrilateral mesh conversion scheme, which ..."
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Cited by 46 (2 self)
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In this paper, we begin by recalling an adaptive mesh generation method governed by isotropic and anisotropic discrete metric maps, by means of the generation of a unit mesh with respect to a Riemannian structure. We propose then an automatic triangular to quadrilateral mesh conversion scheme
Quadrilateral h(div) finite elements
 SIAM J. NUMER. ANAL
"... We consider the approximation properties of quadrilateral finite element spaces of vector fields defined by the Piola transform, extending results previously obtained for scalar approximation. The finite element spaces are constructed starting with a given finite dimensional space of vector fields ..."
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Cited by 46 (5 self)
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on a square reference element, which is then transformed to a space of vector fields on each convex quadrilateral element via the Piola transform associated to a bilinear isomorphism of the square onto the element. For affine isomorphisms, a necessary and sufficient condition for approximation of order
Quadrilateral Mesh Generation via Geometrically Optimized Domain Decomposition
 Proceedings, 6th International Meshing Roundtable, Sandia National Laboratories
, 1997
"... . An algorithm using a geometric optimization technique for generating quadrilateral meshes for twodimensional polygonal regions is presented. In a first stage the possibly multiply connected region is decomposed into simple subregions. This decomposition uses a geometry based optimization for selec ..."
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Cited by 6 (0 self)
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. An algorithm using a geometric optimization technique for generating quadrilateral meshes for twodimensional polygonal regions is presented. In a first stage the possibly multiply connected region is decomposed into simple subregions. This decomposition uses a geometry based optimization
Local Refinement of Quadrilateral Meshes
, 2008
"... Subelement patterns using bisection of edges and schemes for selecting edges to be split are described for the local refinement of elements in allquadrilateral and quadrilateraldominant planar meshes. Subelement patterns using trisection of edges are also described for the local refinement of ele ..."
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Subelement patterns using bisection of edges and schemes for selecting edges to be split are described for the local refinement of elements in allquadrilateral and quadrilateraldominant planar meshes. Subelement patterns using trisection of edges are also described for the local refinement
Results 1  10
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