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Marching cubes without skinny triangles
 Computing in Science and Engineering
, 2009
"... All intext references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately. ..."
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Cited by 2 (0 self)
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All intext references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately.
A Delaunay Refinement Algorithm for Quality 2Dimensional Mesh Generation
, 1995
"... We present a simple new algorithm for triangulating polygons and planar straightline graphs. It provides "shape" and "size" guarantees: All triangles have a bounded aspect ratio. The number of triangles is within a constant factor of optimal. Such "quality" triangulatio ..."
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Cited by 241 (0 self)
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;quality" triangulations are desirable as meshes for the nite element method, in which the running time generally increases with the number of triangles, and where the convergence and stability may be hurt by very skinny triangles. The technique we use  successive refinement of a Delaunay triangulation  extends a mesh
Anisotropic Voronoi Diagrams and GuaranteedQuality Anisotropic Mesh Generation
 in SCG ’03: Proceedings of the nineteenth annual symposium on Computational geometry
, 2003
"... We introduce anisotropic Voronoi diagrams, a generalization of multiplicatively weighted Voronoi diagrams suitable for generating guaranteedquality meshes of domains in which long, skinny triangles are required, and where the desired anisotropy varies over the domain. We discuss properties of aniso ..."
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Cited by 60 (2 self)
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We introduce anisotropic Voronoi diagrams, a generalization of multiplicatively weighted Voronoi diagrams suitable for generating guaranteedquality meshes of domains in which long, skinny triangles are required, and where the desired anisotropy varies over the domain. We discuss properties
SPACES AND ELLIPTIC EQUATIONS IN 2D
"... Abstract. We study the approximation properties of some general finiteelement spaces constructed using improved graded meshes. In our results, either the approximating function or the function to be approximated (or both) are in a weighted Sobolev space. The finiteelement spaces that we define are ..."
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construction of these spaces that does not lead to long, “skinny ” triangles. Our results are then used to obtain hmquasioptimal rates of convergence for the FEM approximation of solutions of strongly elliptic interface/boundary value problems.
Centroidal Voronoi Tesselation of Line Segments and Graphs
"... Figure 1: Starting from a mesh (A) and a template skeleton (B), our method fits the skeleton to the mesh (C) and outputs a segmentation (D). Our main contribution is an extension of Centroidal Voronoi Tesselation to line segments, using approximated Voronoi Diagrams of segments (E). Segment Voronoi ..."
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Cited by 13 (0 self)
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the computation of CVT for graphs as a continuous variational problem, and present a simple approximated method to solve this problem. Our method is robust in the sense that it is independent of degeneracies in the input mesh, such as skinny triangles, Tjunctions, small gaps or multiple connected components. We
The Delaunay triangulation maximizes the mean inradius
, 1994
"... I prove that amongst all triangulations of a planar point set the Delaunay triangulation maximizes the arithmetic mean of the inradii of the triangles. 1 Introduction A triangulation of a set of points is a partition of the convex hull into triangles. The Delaunay triangulation is a well known tri ..."
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Cited by 10 (0 self)
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triangulation, being the planar dual of the famous Voronoi diagram. Most applications of triangulations require that the triangulation should avoid `skinny' triangles. Many different measures of the skinniness of a triangle have been proposed. One of these is the inradius (radius of the inscribed circle
Survivor: the Trigonometry Challenge
, 2005
"... A mathematical drama involves marooned students, a triangle, and a tense competition between classical and rational trigonometry. 1 Three guys make a triangle We’ve been marooned on a desert island for a month with plenty of food, pens and paper, but little entertainment. As a diversion from lying i ..."
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A mathematical drama involves marooned students, a triangle, and a tense competition between classical and rational trigonometry. 1 Three guys make a triangle We’ve been marooned on a desert island for a month with plenty of food, pens and paper, but little entertainment. As a diversion from lying