The boundary recovery and sliver elimination algorithms of three-dimensional constrained Delaunay triangulation

A boundary recovery and sliver elimination algorithm of the three‐dimensional 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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Published in:International journal for numerical methods in engineering Vol. 68; no. 2; pp. 192 - 209
Main Authors: Guan, Zhenqun, Song, Chao, Gu, Yuanxian
Format: Journal Article
Language:English
Published: Chichester, UK John Wiley & Sons, Ltd 08.10.2006
Wiley
Subjects:
Algorithms
Boundaries
boundary recovery
Computational techniques
constrained Delaunay triangulation
Constraints
Delaunay triangulation
Exact sciences and technology
Fundamental areas of phenomenology (including applications)
Mathematical methods in physics
Physics
Recovery
sliver element
Slivers
Three dimensional
Topology
Finite element method
constrained Delaunay triangulation
sliver element
Smoothing
boundary recovery
Delaunay triangulation
Modelling
Two phase medium
Topology
Automatic mesh generation
Mesh generation
ISSN:0029-5981, 1097-0207
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Abstract A boundary recovery and sliver elimination algorithm of the three‐dimensional 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 the advantages of the edges/faces swappings algorithm and edges/faces splittings algorithm presented respectively by George and Weatherill, the geometrical recovery procedure can recover the missing boundaries and guarantee the geometry conformity by introducing fewer Steiner points. The topological recovery procedure includes two phases: ‘dressing wound’ and smoothing, which will overcome topology inconsistency between 3D domain boundary triangles and the volume mesh. In order to solve the problem of sliver elements in the three‐dimensional Delaunay triangulation, a method named sliver decomposition is proposed. By extending the algorithm proposed by Canvendish, the presented method deals with sliver elements by using local decomposition or mergence operation. In this way, sliver elements could be eliminated thoroughly and the mesh quality could be improved in great deal. Copyright © 2006 John Wiley & Sons, Ltd.
AbstractList A boundary recovery and sliver elimination algorithm of the three-dimensional 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 the advantages of the edges/faces swappings algorithm and edges/faces splittings algorithm presented respectively by George and Weatherill, the geometrical recovery procedure can recover the missing boundaries and guarantee the geometry conformity by introducing fewer Steiner points. The topological recovery procedure includes two phases: dressing wound and smoothing, which will overcome topology inconsistency between 3D domain boundary triangles and the volume mesh. In order to solve the problem of sliver elements in the three-dimensional Delaunay triangulation, a method named sliver decomposition is proposed. By extending the algorithm proposed by Canvendish, the presented method deals with sliver elements by using local decomposition or mergence operation. In this way, sliver elements could be eliminated thoroughly and the mesh quality could be improved in great deal.
A boundary recovery and sliver elimination algorithm of the three‐dimensional 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 the advantages of the edges/faces swappings algorithm and edges/faces splittings algorithm presented respectively by George and Weatherill, the geometrical recovery procedure can recover the missing boundaries and guarantee the geometry conformity by introducing fewer Steiner points. The topological recovery procedure includes two phases: ‘dressing wound’ and smoothing, which will overcome topology inconsistency between 3D domain boundary triangles and the volume mesh. In order to solve the problem of sliver elements in the three‐dimensional Delaunay triangulation, a method named sliver decomposition is proposed. By extending the algorithm proposed by Canvendish, the presented method deals with sliver elements by using local decomposition or mergence operation. In this way, sliver elements could be eliminated thoroughly and the mesh quality could be improved in great deal. Copyright © 2006 John Wiley & Sons, Ltd.
Author Gu, Yuanxian
Guan, Zhenqun
Song, Chao
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  givenname: Yuanxian
  surname: Gu
  fullname: Gu, Yuanxian
  organization: State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology, Dalian 116024, People's Republic of China
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Cites_doi 10.1016/S0168-874X(96)00063-7
10.1093/comjnl/24.2.162
10.1002/nme.1620371203
10.1016/0045-7825(91)90017-Z
10.1093/comjnl/24.2.167
10.1016/0167-8396(91)90038-D
10.1007/BF02274210
10.1002/nme.1620210210
10.1002/1097-0207(20000910/20)49:1/2<167::AID-NME928>3.0.CO;2-L
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Issue 2
Keywords Finite element method
constrained Delaunay triangulation
sliver element
Smoothing
boundary recovery
Delaunay triangulation
Modelling
Two phase medium
Topology
Automatic mesh generation
Mesh generation
Language English
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References Xu YG, Yang Q, Wu ZZ et al. The algorithm of 3D constrained Delaunay triangulation. The Chinese Journal of Software 2001; 12(1):103-110.
George PL. Improvements on Delaunay-based three-dimensional automatic mesh generator. Finite Element in Analysis and Design 1997; 25:297-317.
Bowyer A. Computing Dirichlet tessellations. The Computer Journal 1981; 24:162-166.
Sapidis N, Perucchio R. Delaunay triangulation of arbitrarily shaped planar domains. CAGD 1991; 8:421-437.
Joe B. Construction of three-dimensional Delaunay triangulations using local transformations. Computer Aided Geometric Design 1991; 8:123-142.
Karamete BK, Beall MW, Shephard MS. Triangulation of arbitrary polyhedra to support automatic mesh generators. International Journal for Numerical Methods in Engineering 2000; 49:167-191.
Freitag L. On combining Laplacian and optimization-based mesh smoothing techniques. Trends in unstructured mesh generation. ASME 1997; AMD-220:37-43.
Canvendish JC, Field DA, Frey WH. An approach to automatic three-dimensional finite element meshes generation. International Journal for Numerical Methods in Engineering 1985; 21:329-347.
Watson DF. Computing the n-dimensional Delaunay tessellations with application to Voronoi polytopes. The Computer Journal 1981; 24:167-172.
Baker TJ. Automatic mesh generation for complex three-dimensional regions using a constrained Delaunay triangulation. Engineering with Computers 1989; 5:161-175.
Min WD, Tang ZS. The Delaunay triangulation of a point set within an arbitrary 2D domain. The Chinese Journal of Computer 1995; 18(5):357-364.
Weatherill NP, Hassan O. Efficient three-dimensional Delaunay triangulation with automatic point creation and imposed boundary constraints. International Journal for Numerical Methods in Engineering 1994; 37:2005-2039.
George PL, Hecht F, Saltel E. Automatic mesh generator with specified boundary. Computer Methods in Applied Mechanics and Engineering 1991; 92:269-288.
Joe B. GEOMPACK-A software package for the generation of meshes using geometric algorithms. Advances in Engineering Software 1991; 56(13):325-331.
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References_xml – reference: Bowyer A. Computing Dirichlet tessellations. The Computer Journal 1981; 24:162-166.
– reference: Sapidis N, Perucchio R. Delaunay triangulation of arbitrarily shaped planar domains. CAGD 1991; 8:421-437.
– reference: Karamete BK, Beall MW, Shephard MS. Triangulation of arbitrary polyhedra to support automatic mesh generators. International Journal for Numerical Methods in Engineering 2000; 49:167-191.
– reference: Baker TJ. Automatic mesh generation for complex three-dimensional regions using a constrained Delaunay triangulation. Engineering with Computers 1989; 5:161-175.
– reference: Joe B. GEOMPACK-A software package for the generation of meshes using geometric algorithms. Advances in Engineering Software 1991; 56(13):325-331.
– reference: Weatherill NP, Hassan O. Efficient three-dimensional Delaunay triangulation with automatic point creation and imposed boundary constraints. International Journal for Numerical Methods in Engineering 1994; 37:2005-2039.
– reference: George PL, Hecht F, Saltel E. Automatic mesh generator with specified boundary. Computer Methods in Applied Mechanics and Engineering 1991; 92:269-288.
– reference: Freitag L. On combining Laplacian and optimization-based mesh smoothing techniques. Trends in unstructured mesh generation. ASME 1997; AMD-220:37-43.
– reference: Xu YG, Yang Q, Wu ZZ et al. The algorithm of 3D constrained Delaunay triangulation. The Chinese Journal of Software 2001; 12(1):103-110.
– reference: Min WD, Tang ZS. The Delaunay triangulation of a point set within an arbitrary 2D domain. The Chinese Journal of Computer 1995; 18(5):357-364.
– reference: Canvendish JC, Field DA, Frey WH. An approach to automatic three-dimensional finite element meshes generation. International Journal for Numerical Methods in Engineering 1985; 21:329-347.
– reference: Joe B. Construction of three-dimensional Delaunay triangulations using local transformations. Computer Aided Geometric Design 1991; 8:123-142.
– reference: George PL. Improvements on Delaunay-based three-dimensional automatic mesh generator. Finite Element in Analysis and Design 1997; 25:297-317.
– reference: Watson DF. Computing the n-dimensional Delaunay tessellations with application to Voronoi polytopes. The Computer Journal 1981; 24:167-172.
– volume: 18
  start-page: 357
  issue: 5
  year: 1995
  end-page: 364
  article-title: The Delaunay triangulation of a point set within an arbitrary 2D domain
  publication-title: The Chinese Journal of Computer
– volume: 8
  start-page: 421
  year: 1991
  end-page: 437
  article-title: Delaunay triangulation of arbitrarily shaped planar domains
  publication-title: CAGD
– volume: 5
  start-page: 161
  year: 1989
  end-page: 175
  article-title: Automatic mesh generation for complex three‐dimensional regions using a constrained Delaunay triangulation
  publication-title: Engineering with Computers
– volume: AMD‐220
  start-page: 37
  year: 1997
  end-page: 43
  article-title: On combining Laplacian and optimization‐based mesh smoothing techniques. Trends in unstructured mesh generation
  publication-title: ASME
– volume: 12
  start-page: 103
  issue: 1
  year: 2001
  end-page: 110
  article-title: The algorithm of 3D constrained Delaunay triangulation
  publication-title: The Chinese Journal of Software
– volume: 21
  start-page: 329
  year: 1985
  end-page: 347
  article-title: An approach to automatic three‐dimensional finite element meshes generation
  publication-title: International Journal for Numerical Methods in Engineering
– volume: 37
  start-page: 2005
  year: 1994
  end-page: 2039
  article-title: Efficient three‐dimensional Delaunay triangulation with automatic point creation and imposed boundary constraints
  publication-title: International Journal for Numerical Methods in Engineering
– volume: 56
  start-page: 325
  issue: 13
  year: 1991
  end-page: 331
  article-title: GEOMPACK—A software package for the generation of meshes using geometric algorithms
  publication-title: Advances in Engineering Software
– volume: 25
  start-page: 297
  year: 1997
  end-page: 317
  article-title: Improvements on Delaunay‐based three‐dimensional automatic mesh generator
  publication-title: Finite Element in Analysis and Design
– year: 1997
– volume: 49
  start-page: 167
  year: 2000
  end-page: 191
  article-title: Triangulation of arbitrary polyhedra to support automatic mesh generators
  publication-title: International Journal for Numerical Methods in Engineering
– volume: 24
  start-page: 162
  year: 1981
  end-page: 166
  article-title: Computing Dirichlet tessellations
  publication-title: The Computer Journal
– volume: 92
  start-page: 269
  year: 1991
  end-page: 288
  article-title: Automatic mesh generator with specified boundary
  publication-title: Computer Methods in Applied Mechanics and Engineering
– volume: 24
  start-page: 167
  year: 1981
  end-page: 172
  article-title: Computing the n‐dimensional Delaunay tessellations with application to Voronoi polytopes
  publication-title: The Computer Journal
– volume: 8
  start-page: 123
  year: 1991
  end-page: 142
  article-title: Construction of three‐dimensional Delaunay triangulations using local transformations
  publication-title: Computer Aided Geometric Design
– ident: e_1_2_1_10_2
  doi: 10.1016/S0168-874X(96)00063-7
– volume: 12
  start-page: 103
  issue: 1
  year: 2001
  ident: e_1_2_1_4_2
  article-title: The algorithm of 3D constrained Delaunay triangulation
  publication-title: The Chinese Journal of Software
– ident: e_1_2_1_5_2
  doi: 10.1093/comjnl/24.2.162
– ident: e_1_2_1_13_2
– ident: e_1_2_1_7_2
  doi: 10.1002/nme.1620371203
– volume: 220
  start-page: 37
  year: 1997
  ident: e_1_2_1_15_2
  article-title: On combining Laplacian and optimization‐based mesh smoothing techniques. Trends in unstructured mesh generation
  publication-title: ASME
– ident: e_1_2_1_11_2
  doi: 10.1016/0045-7825(91)90017-Z
– ident: e_1_2_1_6_2
  doi: 10.1093/comjnl/24.2.167
– ident: e_1_2_1_8_2
  doi: 10.1016/0167-8396(91)90038-D
– ident: e_1_2_1_9_2
  doi: 10.1007/BF02274210
– volume: 56
  start-page: 325
  issue: 13
  year: 1991
  ident: e_1_2_1_12_2
  article-title: GEOMPACK—A software package for the generation of meshes using geometric algorithms
  publication-title: Advances in Engineering Software
– volume: 18
  start-page: 357
  issue: 5
  year: 1995
  ident: e_1_2_1_2_2
  article-title: The Delaunay triangulation of a point set within an arbitrary 2D domain
  publication-title: The Chinese Journal of Computer
– ident: e_1_2_1_16_2
  doi: 10.1002/nme.1620210210
– volume: 8
  start-page: 421
  year: 1991
  ident: e_1_2_1_3_2
  article-title: Delaunay triangulation of arbitrarily shaped planar domains
  publication-title: CAGD
– ident: e_1_2_1_14_2
  doi: 10.1002/1097-0207(20000910/20)49:1/2<167::AID-NME928>3.0.CO;2-L
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Snippet A boundary recovery and sliver elimination algorithm of the three‐dimensional constrained Delaunay triangulation is proposed for finite element mesh...
A boundary recovery and sliver elimination algorithm of the three-dimensional constrained Delaunay triangulation is proposed for finite element mesh...
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StartPage 192
SubjectTerms Algorithms
Boundaries
boundary recovery
Computational techniques
constrained Delaunay triangulation
Constraints
Delaunay triangulation
Exact sciences and technology
Fundamental areas of phenomenology (including applications)
Mathematical methods in physics
Physics
Recovery
sliver element
Slivers
Three dimensional
Topology
Title The boundary recovery and sliver elimination algorithms of three-dimensional constrained Delaunay triangulation
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Volume 68
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