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192
Wellcentered triangulation
, 2010
"... Meshes composed of wellcentered simplices have nice orthogonal dual meshes (the dual Voronoi diagram). This is useful for certain numerical algorithms that prefer such primaldual mesh pairs. We prove that wellcentered meshes also have optimality properties and relationships to Delaunay and minm ..."
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Cited by 26 (7 self)
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Meshes composed of wellcentered simplices have nice orthogonal dual meshes (the dual Voronoi diagram). This is useful for certain numerical algorithms that prefer such primaldual mesh pairs. We prove that wellcentered meshes also have optimality properties and relationships to Delaunay
Wellcentered Planar Triangulation  An Iterative Approach
, 2007
"... We present an iterative algorithm to transform a given planar triangle mesh into a wellcentered one by moving the interior vertices while keeping the connectivity fixed. A wellcentered planar triangulation is one in which all angles are acute. Our approach is based on minimizing a certain energy ..."
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Cited by 9 (5 self)
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We present an iterative algorithm to transform a given planar triangle mesh into a wellcentered one by moving the interior vertices while keeping the connectivity fixed. A wellcentered planar triangulation is one in which all angles are acute. Our approach is based on minimizing a certain energy
Reconstruction and Representation of 3D Objects with Radial Basis Functions
 Computer Graphics (SIGGRAPH ’01 Conf. Proc.), pages 67–76. ACM SIGGRAPH
, 2001
"... We use polyharmonic Radial Basis Functions (RBFs) to reconstruct smooth, manifold surfaces from pointcloud data and to repair incomplete meshes. An object's surface is defined implicitly as the zero set of an RBF fitted to the given surface data. Fast methods for fitting and evaluating RBFs al ..."
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Cited by 505 (1 self)
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We use polyharmonic Radial Basis Functions (RBFs) to reconstruct smooth, manifold surfaces from pointcloud data and to repair incomplete meshes. An object's surface is defined implicitly as the zero set of an RBF fitted to the given surface data. Fast methods for fitting and evaluating RBFs
Geometric and Combinatorial Properties of WellCentered Triangulations in Three and Higher Dimensions
, 912
"... An nsimplex is said to be nwellcentered if its circumcenter lies in its interior. We introduce several other geometric conditions and an algebraic condition that can be used to determine whether a simplex is nwellcentered. These conditions, together with some other observations, are used to des ..."
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Cited by 1 (0 self)
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to describe restrictions on the local combinatorial structure of simplicial meshes in which every simplex is wellcentered. In particular, it is shown that in a 3wellcentered (2wellcentered) tetrahedral mesh there are at least 7 (9) edges incident to each interior vertex, and these bounds are sharp
Triangulation of Simple 3D Shapes with WellCentered Tetrahedra
"... Summary. A completely wellcentered tetrahedral mesh is a triangulation of a three dimensional domain in which every tetrahedron and every triangle contains its circumcenter in its interior. Such meshes have applications in scientific computing and other fields. We show how to triangulate simple do ..."
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Summary. A completely wellcentered tetrahedral mesh is a triangulation of a three dimensional domain in which every tetrahedron and every triangle contains its circumcenter in its interior. Such meshes have applications in scientific computing and other fields. We show how to triangulate simple
DiamondKite Adaptive Quadrilateral Meshing∗
"... We describe a family of quadrilateral meshes based on diamonds, rhombi with 60 ◦ and 120 ◦ angles, and kites with 60◦, 90◦, and 120 ◦ angles, that can be adapted to a local size function by local subdivision operations. Our meshes use a number of elements that is within a constant factor of the mini ..."
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topology gives a pair of dual wellcentered meshes adapted to the given size function. 1
Triangulation of simple 3D shapes with wellcentered tetrahedra, in: R.V. Garimella (Ed
 Proceedings of the 17th International Meshing Roundtable
, 2008
"... Abstract. A completely wellcentered tetrahedral mesh is a triangulation of a three dimensional domain in which every tetrahedron and every triangle contains its circumcenter in its interior. Such meshes have applications in scientific computing and other fields. We show how to triangulate simple do ..."
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Cited by 9 (3 self)
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Abstract. A completely wellcentered tetrahedral mesh is a triangulation of a three dimensional domain in which every tetrahedron and every triangle contains its circumcenter in its interior. Such meshes have applications in scientific computing and other fields. We show how to triangulate simple
Weighted triangulations for geometry processing
"... In this paper, we investigate the use of weighted triangulations as discrete, augmented approximations of surfaces for digital geometry processing. By incorporating a scalar weight per mesh vertex, we introduce a new notion of discrete metric that defines an orthogonal dual structure for arbitrary t ..."
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Cited by 3 (0 self)
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known in implicit form only. Finally, we demonstrate how weighted triangulations provide a faster and more robust approach to a series of geometry processing applications, including the generation of wellcentered meshes, selfsupporting surfaces, and sphere packing.
A new meshless local PetrovGalerkin (MLPG) approach in computational mechanics
 Comput. Mech
, 1998
"... Abstract: A comparison study of the efficiency and accuracy of a variety of meshless trial and test functions is presented in this paper, based on the general concept of the meshless local PetrovGalerkin (MLPG) method. 5 types of trial functions, and 6 types of test functions are explored. Differe ..."
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Cited by 312 (54 self)
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. The MLPG5 method (wherein the local, nodalbased test function, over a local subdomainΩs (or Ωte) centered at a node, is the Heaviside step function) avoids the need for both a domain integral in the attendant symmetric weakform as well as a singular integral. Convergence studies in the numerical
Bubble Mesh: Automated Triangular Meshing of NonManifold Geometry by Sphere Packing
 ACM SYMPOSIUM ON SOLID MODELING AND APPLICATIONS
, 1995
"... This paper presents a new computational method for fully automated triangular mesh generation, consistently applicable to wireframe, surface, solid, and nonmanifold geometries. The method, called bubble meshing, is based on the observation that a pattern of tightly packed spheres mimics a Voronoi d ..."
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Cited by 61 (11 self)
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diagram, from which a set of wellshaped Delaunay triangles and tetrahedra can be created by connecting the centers of the spheres. Given a domain geometry and a nodespacing function, spheres are packed on geometric entities, namely, vertices, edges, faces, and volumes, in ascending order of dimension
Results 1  10
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192