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Constrained boundary recovery for three dimensional Delaunay triangulations
 International Journal for Numerical Methods in Engineering 2004
"... A new constrained boundary recovery method for three dimensional Delaunay triangulations is presented. It successfully resolves the difficulties related to the minimal addition of Steiner points and their good placement. Application to full mesh generation are discussed and numerical examples are pr ..."
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Cited by 7 (4 self)
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A new constrained boundary recovery method for three dimensional Delaunay triangulations is presented. It successfully resolves the difficulties related to the minimal addition of Steiner points and their good placement. Application to full mesh generation are discussed and numerical examples
A Robust Implementation For ThreeDimensional Delaunay Triangulations
, 1995
"... This paper presents Detri 2.2, an implementation for Delaunay triangulations of threedimensional point sets. The code uses a variant of the randomized incrementalflip algorithm, and employs a symbolic perturbation scheme to achieve robustness. The algorithm's time complexity is quadratic in n ..."
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Cited by 13 (0 self)
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This paper presents Detri 2.2, an implementation for Delaunay triangulations of threedimensional point sets. The code uses a variant of the randomized incrementalflip algorithm, and employs a symbolic perturbation scheme to achieve robustness. The algorithm's time complexity is quadratic
Fast randomized point location without preprocessing in two and threedimensional Delaunay triangulations
 Computational Geometry—Theory and Applications
, 1999
"... This paper studies the point location problem in Delaunay triangulations without preprocessing and additional storage. The proposed procedure finds the query point by simply “walking through ” the triangulation, after selecting a “good starting point ” by random sampling. The analysis generalizes an ..."
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Cited by 63 (4 self)
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and extends a recent result for d D 2 dimensions by proving this procedure takes expected time close to O.n1=.dC1/ / for point location in Delaunay triangulations of n random points in d D 3 dimensions. Empirical results in both two and three dimensions show
Fast Randomized Point Location without Preprocessing in Two and ThreeDimensional Delaunay Triangulations
, 1996
"... This paper studies the point location problem in Delaunay triangulations without preprocessing and additional storage. The proposed procedure finds the query point simply by "walking through" the triangulation, after selecting a "good starting point" by random sampling. The analy ..."
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. The analysis generalizes and extends a recent result for d = 2 dimensions by proving this procedure to take expected time close to O(n^(1/(d+1))) for point location in Delaunay triangulations of n random points in d = 3 dimensions. Empirical results in both two and three dimensions show that this procedure
Dense Point Sets Have Sparse Delaunay Triangulations
"... Delaunay triangulations and Voronoi diagrams are one of the most thoroughly studies objects in computational geometry, with numerous applications including nearestneighbor searching, clustering, finiteelement mesh generation, deformable surface modeling, and surface reconstruction. Many algorithms ..."
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Cited by 29 (2 self)
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algorithms in these application domains begin by constructing the Delaunay triangulation or Voronoi diagram of a set of points in R³. Since threedimensional Delaunay triangulations can have complexity Ω(n²) in the worst case, these algorithms have worstcase running time \Omega (n2). However, this behavior
THREEDIMENSIONAL TRIANGULATIONS FROM LOCAL TRANSFORMATIONS
, 1989
"... A new algorithm is presented that uses a local transformation procedure to construct a triangulation of a set of n threedimensional points that is pseudolocally optimal with respect to the sphere criterion. It is conjectured that this algorithm always constructs a Delaunay triangulation, and this ..."
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Cited by 79 (5 self)
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A new algorithm is presented that uses a local transformation procedure to construct a triangulation of a set of n threedimensional points that is pseudolocally optimal with respect to the sphere criterion. It is conjectured that this algorithm always constructs a Delaunay triangulation
Perturbations and Vertex Removal in a 3D Delaunay Triangulation
 SODA
, 2003
"... Though Delaunay triangulations are very well known geometric data structures, the problem of the robust removal of a vertex in a threedimensional Delaunay triangulation is still a problem in practice. We propose a simple method that allows to remove any vertex even when the points are in very degen ..."
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Cited by 24 (6 self)
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Though Delaunay triangulations are very well known geometric data structures, the problem of the robust removal of a vertex in a threedimensional Delaunay triangulation is still a problem in practice. We propose a simple method that allows to remove any vertex even when the points are in very
Vertex Deletion for 3D Delaunay Triangulations
"... Abstract. We show how to delete a vertex q from a threedimensional Delaunay triangulation DT(S) in expected O(C ⊗ (P)) time, where P is the set of vertices neighboring q in DT(S) and C ⊗ (P) is an upper bound on the expected number of tetrahedra whose circumspheres enclose q that are created during ..."
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Cited by 1 (0 self)
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Abstract. We show how to delete a vertex q from a threedimensional Delaunay triangulation DT(S) in expected O(C ⊗ (P)) time, where P is the set of vertices neighboring q in DT(S) and C ⊗ (P) is an upper bound on the expected number of tetrahedra whose circumspheres enclose q that are created
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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. 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
The boundary recovery and sliver elimination algorithms of threedimensional constrained Delaunay triangulation
"... A boundary recovery and sliver elimination algorithm of the threedimensional constrained Delaunay triangulation is proposed for finite element mesh generation. The boundary recovery algorithm includes two main procedures: geometrical recovery procedure and topological recovery procedure. Combining ..."
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A boundary recovery and sliver elimination algorithm of the threedimensional constrained Delaunay triangulation is proposed for finite element mesh generation. The boundary recovery algorithm includes two main procedures: geometrical recovery procedure and topological recovery procedure. Combining
Results 1  10
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1,722