Flipping cubical meshes

Engineering with Computers

Volumn 18, Issue 3, 2002, Pages 173-187

  Bern, M ^a   Eppstein, D ^b   Erickson, J ^c  

^a PALO ALTO RESEARCH CENTER   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c University of Illinois at Urbana Champaign   (United States)

Author keywords

Flip graph connectivity; Hexahedral meshing; Mesh improvement; Quadrilateral meshing

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; COMPUTER SIMULATION; GRAPH THEORY; MATHEMATICAL TRANSFORMATIONS; THEOREM PROVING;

FLIP GRAPH CONNECTIVITY; HEXAHEDRAL MESHING; MESH IMPROVEMENT; QUADRILATERAL MESHING;

COMPUTATIONAL GEOMETRY;

EID: 0036432840     PISSN: 01770667     EISSN: None     Source Type: Journal    
DOI: 10.1007/s003660200016     Document Type: Article

References (25)

1. Billera, L. J., Sturmfels, B. (1992) Fiber polytopes. Annals of Math. 135(3), 527-549
2. Ziegler, G. M. (1995) Lectures on Polytopes. Graduate Texts in Mathematics 152. Springer-Verlag, New York
3. Canann, S. A., Muthukrishnan, N., Phillips, R. K. (1998) Topological refinement procedures for quadrilateral finite element meshes. Engineering with Computers, 12, 168-177
4. Knupp P., Mitchell, S. A. (1999) Integration of mesh optimization with 3D all-hex mesh generation. Technical Report SAND99-2852, Sandia National Laboratory
5. Mitchell, S. A. (1996) A characterization of the quadrilateral meshes of a surface which admit a compatible hexahedral mesh of the enclosed volume. Proceedings 13th Symposium Theoretical Aspects of Computer Science, 465-476. Springer-Verlag
6. Thurston, W. P. (1993) Hexahedral decomposition of polyhedra. Posting to sci.math, 25 October 1993, http://www.ics.uci.edu/~eppstein/gina/Thurston-hexahedra.html
7. Eppstein, D. (1999) Linear complexity hexahedral mesh generation. Computational Geometry Theory & Applications, 12, 3-16
8. Blind, G., Blind, R. (1998) The almost simple cubical polytopes. Discrete Math. 184, 25-48
9. Joswig, M., Ziegler, G. M. (2000) Neighborly cubical polytopes. Discrete & Computational Geometry, 24(2-3), 325-344
10. Matveev, S., Polyak, M. (2002) Cubic complexes and finite type invariants
11. Maréchal, L. (2001) A new approach to octree-based hexahedral meshing. Proceedings 10th International Meshing Roundtable, 209-221
12. Whiteley, W. (1989) A matroid on hypergraphs, with applications in scene analysis and geometry. Discrete & Computational Geometry, 4, 75-95
13. Boy W. (1903) Über die Curvatura integra und die Topologie geschlossener Flächen. Math. Ann. 57, 151-184.
14. Francis, G. K. (1987) A Topological Picturebook. Springer-Verlag, New York
15. Müller-Hannemann, M. (1999) Hexahedral mesh generation by successive dual cycle elimination. Engineering with Computers, 15, 269-279
16. Mehlhorn, K., Yap, C.-K. (1991) Constructive Whitney-Graustein theorem: Or how to untangle closed planar curves. SIAM J. Computing, 20(4), 603-621
17. Whitney, H. (1937) On regular closed curves in the plane. Composition Math. 4, 276-284
18. Schneiders, R. (n.d.) Open problem. Unpublished web page, http://www-users.informatik.rwth-aachen.de/~roberts/open.html
19. Santos, F. (2000) A point set whose space of triangulations is disconnected. J. American Mathematical Society, 13, 611-637
20. Hanke, S., Ottmann, T., Schuierer, S. (1996) The edge-flipping distance of triangulations. J. Universal Computer Science, 2(8), 570-579
21. Hurtado, F., Noy, M., Urrutia, J. (1999) Flipping edges in triangulations. Discrete & Computational Geometry, 22(3), 333-346
22. Sleator, D. D., Tarjan, R. E., Thurston, W. P. (1988) Rotation distance, triangulations, and hyperbolic geometry. J. American Mathematical Society, 1(3), 647-681
23. Lickorish, W. B. R. (1999) Simplicial moves on complexes and manifolds. Proceedings Kirbyfest, 299-320
24. Edelsbrunner, H., Shah, N. R. (1996) Incremental topological flipping works for regular triangulations. Algorithmica, 15(3), 223-241
25. Joe, B. (1991) Construction of three-dimensional Delaunay triangulations using local transformations. Computer Aided Geometric Design, 8, 123-142