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Sphere Packing

 Spheres/Circles (bubbles) are used as a means of providing nodal spacing/distribution in the mesh. Size and orientation of "bubbles" may be determined by simulated inter-particle forces.

MESHING
RESEARCH
CORNER

Bern, Marshall and David Eppstein

    "Quadrilateral Meshing by Circle Packing", Proceedings, 6th International meshing Roundtable, Sandia National Laboratories, pp.7-20, October 1997
    keywords:
    • bubble packing
      		•
    • quadrilateral
    • sphere packing
      		•
    • Voronoi diagram
    Abstract
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Bossen, Frank
    "Anisotropic Mesh Generation with Particles", Dissertation, School of Computer Science, Carnegie Mellon University, May 1996
    keywords:
    • bubble
      		•
    • particles
    • physically-based
      		•
    • adaptivity
    • anisotropy
      		•
    • Riemannian metric
    • smoothing
      		•
    Abstract

Bossen, Frank, J. and Paul S. Heckbert
    "A Pliant Method for Anisotropic Mesh Generation", 5th International Meshing Roundtable, Sandia National Laboratories, pp.63-76, October 1996
    keywords:
    • anisotropy
      		•
    • bubble
    • sphere packing
      		•
    • triangle
    Abstract
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Cingoski, V., T. Yokoyama, and H. Yamashita
    "Dynamic Bubble System: An Automatic Mesh Generation System for 2D and 3D Finite Element Mesh Generation in Electromagnetic Field Computations", 2nd Symposium on Trends in Unstructured Mesh Generation, University of Colorado, Boulder, August 1999
    keywords:
    • bubble
      		•
    • EMAG
    • tetrahedra
      		•
    • triangle
    Abstract

Dheeravongkit, Arbtip and Kenji Shimada
    "Inverse Pre-Deformation of Finite Element Mesh for Large Deformation Analysis", Proceedings, 13th International Meshing Roundtable, Williamsburg, VA, Sandia National Laboratories, SAND #2004-3765C, pp.81-94, September 19-22 2004
    keywords:
    • large deformation analysis
      		•
    • inverse pre-deformation
    • bubble mesh
      		•
    • evolving meshes
    Abstract
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George, Paul-Louis
    "Tet Meshing", 8th International Meshing Roundtable, unpublished, October 1999
    keywords:
    • tetrahedra
      		•
    • Delaunay kernel
    • in-sphere predicate
      		•
    • round-off errors
    • adaptivity
      		•
    Abstract

Itoh, Takayuki, Kenji Shimada, Keisuke Inoue, Atsushi Yamada, Tomotake Furuhata
    "Automated Conversion of 2D Triangular Mesh into Quadrilateral Mesh with Directionality Control", Proceedings, 7th International Meshing Roundtable, Sandia National Lab, pp.77-86, October 1998
    keywords:
    • quadrilateral
      		•
    • directionality
    • bubble
      		•
    • physically-based
    • square packing
      		•
    Abstract
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Kennon, Stephen R. and Dale A. Anderson
    "Unstructured Grid Adaption for Non-Convex Domains", Numerical Grid Generation in Computational Fluid Mechanics `88, Pineridge Press, pp.599-609, 1988
    keywords:
    • adaptivity
      		•
    • triangle
    • smoothing
      		•
    • spring analogy
    • physically based
      		•
    • bubble
    Abstract

Laug, Patrick and Houman Borouchaki
    "Surface Grid Generation on Intersecting Spheres", Numerical Grid Generation in Computational Field Simulations, Ed. M. Cross., B. K. Soni, J. F. Thompson, J. Hauser, P. R. Eiseman, Proceedings of the 6th International Conference, held at the University of Greenwich, pp.717-726, July 1998
    keywords:
    • sphere
      		•
    • molecular modeling
    • surface meshing
      		•
    • triangle
    • paramaterization
      		•
    • chemistry
    Abstract

Li, Xiang-Yang, Shang-Hua Teng and Alper Ungor
    "Biting: Advancing Front Meets Sphere Packing", 2nd Symposium on Trends in Unstructured Mesh Generation, University of Colorado, Boulder, August 1999
    keywords:
    • bubble
      		•
    • sphere packing
    • tetrahedra
      		•
    • advancing front
    • biting
      		•
    Abstract

Li, Xiang-Yang, Shang-Hua Teng and Alper Ungor
    "Biting: advancing front meets sphere packing", International Journal for Numerical Methods in Engineering, John Wiley, Vol 49, Num 1, pp.61-81, September 10-20 2000
    keywords:
    • advancing front
      		•
    • paving
    • circle packing
      		•
    • biting
    • bubble meshing
      		•
    • sphere packing
    • triangle
      		•
    • tetrahedra
    Abstract

Li, Xiang-Yang, Shang-Hua Teng and Alper Ungor
    "Biting Ellipses to Generate Anisotropic Mesh", Proceedings, 8th International Meshing Roundtable, South Lake Tahoe, CA, U.S.A., pp.97-108, October 1999
    keywords:
    • anisotropy
      		•
    • metrics
    • biting
      		•
    • advancing front
    • sphere packing
      		•
    • tetrahedra
    Abstract
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Li, Xiang-Yang, Shang-Hua Teng and Alper Ungor
    "Biting Spheres in 3D", Proceedings, 8th International Meshing Roundtable, South Lake Tahoe, CA, U.S.A., pp.85-95, October 1999
    keywords:
    • quality
      		•
    • advancing front
    • plastering
      		•
    • sphere packing
    • biting
      		•
    • tetrahedra
    Abstract
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Li, Xiang-Yang, Shang-Hua Teng, Alper Ungor
    "Simultaneous Refinement and Coarsening Adaptive Meshing with Moving Boundaries", Proceedings, 7th International Meshing Roundtable, Sandia National Lab, pp.201-210, October 1998
    keywords:
    • combustion
      		•
    • adaptivity
    • coarsening
      		•
    • refinement
    • moving boundary
      		•
    • sphere-packing
    • Delaunay
      		•
    Abstract
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Liu, Jianfei and Rongxi Tang
    "Ball-Packing Method: A New Approach for Quality Automatic Triangulation of Arbitrary Domains", Proceedings, 6th International Meshing Roundtable, Sandia National Laboratories, pp.85-96, October 1997
    keywords:
    • ball packing
      		•
    • density
    • line meshing
      		•
    • sphere packing
    • surface meshing
      		•
    • triangles
    Abstract

Miller, Gary L., Dafna Talmor, Shang-Hua Teng, Noel Walkington and Han Wang
    "Control Volume Meshes using Sphere Packing: Generation, Refinement and Coarsening", 5th International Meshing Roundtable, Sandia National Laboratories, pp.47-62, October 1996
    keywords:
    • coarsening
      		•
    • control volume
    • Delaunay
      		•
    • refinement
    • sliver
      		•
    • sphere packing
    • tetrahedron
      		•
    Abstract
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Palmerio, B. and A. Dervieux
    "2-D and 3-D Unstructured Mesh Adaption Relying on Physical Analogy", Numerical Grid Generation in Computational Fluid Mechanics `88, Pineridge Press, pp.653-662, 1988
    keywords:
    • adaptivity
      		•
    • physically based
    • bubble
      		•
    • triangle
    • tetrahedra
      		•
    Abstract

Shimada, Kenji and David C. Gossard
    "Automatic triangular mesh generation of trimmed parametric surfaces for finite element analysis", Computer Aided Geometric Design, Elsevier, Vol 15, pp.199-222, 1998
    keywords:
    • bubble meshing
      		•
    • Delaunay triangulation
    • dynamic simulation
      		•
    • physically based model
    • sphere packing
      		•
    • triangulation
    • Voronoi polygons
      		•
    Abstract

Shimada, Kenji, Atsushi Yamada and Takayuki Itoh
    "Anisotropic Triangular Meshing of Parametric Surfaces via Close Packing of Ellipsoidal Bubbles", Proceedings, 6th International Meshing Roundtable, Sandia National Laboratories, pp.375-390, October 1997
    keywords:
    • anisotropy
      		•
    • bubble
    • Delaunay
      		•
    • surface
    • triangle
      		•
    Abstract
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Shimada, Kenji, Jia-Huei Liao and Takayuki Itoh
    "Quadrilateral Meshing with Directionality Control through the Packing of Square Cells", Proceedings, 7th International Meshing Roundtable, Sandia National Lab, pp.61-76, October 1998
    keywords:
    • quadrilateral
      		•
    • directionality
    • Voronoi
      		•
    • Delaunay
    • bubble
      		•
    • physically-based
    Abstract
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van der Burg, J.W.
    "An accurate and robust algorithm for the in-sphere criterion for automated Delaunay-based tetrahe-dral grid generation", Numerical Grid Generation in Computational Field Simulations, Ed. M. Cross., B. K. Soni, J. F. Thompson, J. Hauser, P. R. Eiseman, Proceedings of the 6th International Conference, held at the University of Greenwich, pp.497-506, July 1998
    keywords:
    • Delaunay
      		•
    • tetrahedra
    • circumsphere
      		•
    • in-sphere criterion
    • round-off error
      		•
    Abstract

Viswanath, Naveen, Kenji Shimada, Takayuki Itoh
    "Quadrilateral Meshing with Anisotropy and Directionality Control via Close Packing of Rectangular Cells", Proceedings, 9th International Meshing Roundtable, Sandia National Laboratories, pp.217-225, October 2000
    keywords:
    • anisotropy
      		•
    • computational geometry
    • quadrilateral
      		•
    • circumcircle test
    • bubble packing
      		•
    • Delaunay
    • quadrilateral packing
      		•
    Abstract
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Yamada, Atsushi, Kenji Shimada and Takayuki Itoh
    "Energy-Minimizing Approach to Meshing Curved Wire-Frame Models", 5th International Meshing Roundtable, Sandia National Laboratories, pp.179-194, October 1996
    keywords:
    • bubble
      		•
    • energy-minimization
    • sphere packing
      		•
    • triangle
    Abstract
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Yamada, Atsushi, Kenji Shimada and Takayuki Itoh
    "Meshing Curved Wire-Frame Models Through Energy Minimization and Packing of Ellipses", International Journal for Numerical Methods in Engineering, John Wiley & Sons, Num 46, pp.1221-1236, 1999
    keywords:
    • bubble
      		•
    • anisotropy
    • surface modeling
      		•
    • wire-frame models
    • quadrilateral
      		•
    • triangle
    • surface meshing
      		•
    Abstract

Yamakawa, Soji and Kenji Shimada
    "High Quality Anisotropic Tetrahedral Mesh Generation Via Ellipsoidal Bubble Packing", Proceedings, 9th International Meshing Roundtable, Sandia National Laboratories, pp.263-273, October 2000
    keywords:
    • tetrahedra
      		•
    • bubble packing
    • anisotropy
      		•
    • graded mesh
    • ellipsoid
      		•
    • advancing front
    • physically-based
      		•
    Abstract
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Yamakawa, Soji; Shimada, Kenji
    "Anisotropic tetrahedral meshing via bubble packing and advancing front", International Journal for Numerical Methods in Engineering, John Wiley & Sons, Ltd., Vol 57, Num 13, pp.1923 - 1942, August 2003
    keywords:
    • advancing front
      		•
    • anisotropy
    • bubble packing
      		•
    • Delaunay
    • local transformation
      		•
    • tetrahedral mesh
    Abstract

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