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696
Parallel Construction of Quadtrees and Quality Triangulations
, 1999
"... We describe e#cient PRAM algorithms for constructing unbalanced quadtrees, balanced quadtrees, and quadtreebased finite element meshes. Our algorithms take time O(log n) for point set input and O(log n log k) time for planar straightline graphs, using O(n + k/ log n) processors, where n measure ..."
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Cited by 72 (8 self)
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polygon), along with some extra vertices, called Steiner points. Not all triangulations, however, serve equally well; numerical and discretization error depend on the quality of the triangulation, meaning the shapes and sizes of triangles. A typical quality guarantee gives a lower bound on the minimum
Construction Of ThreeDimensional ImprovedQuality Triangulations Using Local Transformations
, 1995
"... . Threedimensional Delaunay triangulations are the most common form of threedimensional triangulations known, but they are not very suitable for tetrahedral finite element meshes because they tend to contain poorlyshaped sliver tetrahedra. In this paper, we present an algorithm for constructing im ..."
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Cited by 41 (3 self)
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improvedquality triangulations with respect to a tetrahedron shape measure. This algorithm uses combinations of two or more local transformations to improve a given triangulation towards an optimal triangulation. Experimental results on finite element meshes show that this algorithm is much more effective
Guaranteed quality triangulation of molecular skin surfaces
 In Proc. IEEE Visualization
, 2004
"... Figure 1: Molecular models of an ADNA molecule. The leftmost shows the ball and stick model; the center left and right show the solvent accessible model and molecular skin model respectively; the rightmost shows the zoomed mesh details in the box of the center right figure. We present an efficient ..."
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Cited by 22 (3 self)
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algorithm to mesh the macromolecules surface model represented by the skin surface defined by Edelsbrunner. Our algorithm overcomes several challenges residing in current surface meshing methods. First, we guarantee the mesh quality with a provable lower bound of 21 ◦ on its minimum angle. Second, we ensure
Terminaledges Delaunay (smallangle based) algorithm for the quality triangulation problem
"... The terminaledge Delaunay algorithm, initially called LeppDelaunay algorithm, deals with the construction of sizeoptimal (adapted to the geometry) quality triangulation of complex objects. In two dimensions, the algorithm can be formulated in terms of the Delaunay insertion of both midpoints o ..."
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Cited by 4 (0 self)
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The terminaledge Delaunay algorithm, initially called LeppDelaunay algorithm, deals with the construction of sizeoptimal (adapted to the geometry) quality triangulation of complex objects. In two dimensions, the algorithm can be formulated in terms of the Delaunay insertion of both midpoints
Implicit Fairing of Irregular Meshes using Diffusion and Curvature Flow
, 1999
"... In this paper, we develop methods to rapidly remove rough features from irregularly triangulated data intended to portray a smooth surface. The main task is to remove undesirable noise and uneven edges while retaining desirable geometric features. The problem arises mainly when creating highfidelit ..."
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Cited by 542 (23 self)
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In this paper, we develop methods to rapidly remove rough features from irregularly triangulated data intended to portray a smooth surface. The main task is to remove undesirable noise and uneven edges while retaining desirable geometric features. The problem arises mainly when creating high
LEPPDelaunay algorithm: a robust tool for producing sizeoptimal quality triangulations
 Proc. of the 8th Int. Meshing Roundtable
, 1999
"... . The LEPPDelaunay algorithm for the quality triangulation problem can be formulated in terms of the Delaunay insertion of midpoints of terminal edges (the common longestedge of a pair of Delaunay triangles) and boundary edges in the current mesh. In this paper we discuss theoretical results ..."
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Cited by 5 (2 self)
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. The LEPPDelaunay algorithm for the quality triangulation problem can be formulated in terms of the Delaunay insertion of midpoints of terminal edges (the common longestedge of a pair of Delaunay triangles) and boundary edges in the current mesh. In this paper we discuss theoretical results
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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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
Arc triangulations
 PROC. 26TH EUR. WORKSH. COMP. GEOMETRY (EUROCG’10)
, 2010
"... The quality of a triangulation is, in many practical applications, influenced by the angles of its triangles. In the straight line case, angle optimization is not possible beyond the Delaunay triangulation. We propose and study the concept of circular arc triangulations, a simple and effective alter ..."
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Cited by 26 (3 self)
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The quality of a triangulation is, in many practical applications, influenced by the angles of its triangles. In the straight line case, angle optimization is not possible beyond the Delaunay triangulation. We propose and study the concept of circular arc triangulations, a simple and effective
High Quality Compatible Triangulations
 PROCEEDINGS OF 11TH INTERNATIONAL MESHING ROUNDTABLE
, 2002
"... Compatible meshes are isomorphic meshing of the interiors of two polygons having a correspondence between their vertices. Compatible meshing may be used for constructing sweeps, suitable for finite element analysis, between two base polygons. They may also be used for meshing a given sequence of pol ..."
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Cited by 12 (2 self)
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of polygons forming a sweep. We present a method to compute compatible triangulations of planar polygons with a very small number of Steiner (interior) vertices. Being close to optimal in terms of the number of Steiner vertices, these compatible triangulations are usually not of high quality, i.e., do
Results 1  10
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696