An interior surface generation method for all-hexahedral meshing
- 135 Downloads
This paper describes an all-hexahedral generation method focusing on how to create interior surfaces. It is well known that a solid homeomorphic to a ball with even number of bounding quadrilaterals can be partitioned into a compatible hexahedral mesh where each associated hexahedron corresponds to the intersection of three interior surfaces that are dual to the original hexahedral mesh. However, no such method for creating dual interior surfaces has been developed for generating all-hexahedral meshes of volumes covered with simply connected quadrilaterals. We generate an interior surface as an orientable regular homotopy (or more definitively a sweep) by splitting a dual cycle into several pieces at self-intersecting points and joining the three connected pieces, if the self-intersecting point-types are identical, while we generate a non-orientable surface (containing Möbius bands) if the self-intersecting point-types are distinct. Stitching these simple interior surfaces together allows us to compose more complex interior surfaces. Thus, we propose a generalized method of generating a hexahedral mesh topology by directly creating the interior surface arrangement. We apply the present framework to Schneiders’ open pyramid problem and show an arrangement of interior surfaces that decompose Schneiders’ pyramid into 146 hexahedra.
KeywordsAll-hexahedral mesh generation Interior surface arrangement Dual cycle Schneiders’ pyramid
The authors would like to thank Scott Mitchell (Sandia National Laboratories), Soji Yamakawa (Carnegie Mellon University), and Hiroshi Sakurai (Colorado State University) for their advice and insights into hexahedral meshing.
- 1.Bern M, Eppstein D (2002) Flipping cubical meshes. Proceedings of 10th international meshing roundtable, pp 19–29Google Scholar
- 3.Eppstein D (1996) Linear complexity hexahedral mesh generation. In: Proceedings of 12th annual symposium on computational geometry, pp 58–67Google Scholar
- 4.Folwell NT, Mitchell SA (1998) Reliable whisker weaving via curve contraction. In: Proceedings of 7th international meshing roundtable, pp 365–378Google Scholar
- 6.Müller-Hannemann M (1998) Hexahedral mesh generation with successive dual cycle elimination. In: Proceedongs of 7th international meshing roundtable, pp 379–393Google Scholar
- 7.Mitchell SA (1996) A characterization of the quadrilateral meshes of a surface which admits a compatible hexahedral mesh of enclosed volume. In: Proceedings of 13th annual symposium on theoretical aspect of computer science (STACS ‘96). Lecture Notes in Computer Science 1046, pp 465–476 The brief paper is available online from ftp://ams.sunysb.edu/pub/geometry/msi-workshop/95/samitch.ps.gz
- 8.Owen SJ (1999) Constrained triangulation: application to hex-dominant mesh generation. In: Proceedings, 8th international meshing roundtable, pp 31–41Google Scholar
- 10.Schneiders R (www) http://www-users.informatik.rwth-aachen.de/~roberts/open.html
- 14.Tautges TJ, Mitchell SA (1995) Whisker Weaving: Invalid Connectivity Resolution and Primal Construction Algorithm, Proceedings, 4th International Meshing Roundtable, pp 115–127Google Scholar
- 15.Thurston W (1993) Hexahedral decomposition of polyhedra, posting to Sci. Math, 25 Oct 1993. Available online from http://www.ics.uci.edu/~eppstein/gina/Thurston-hexahedra
- 16.Yamakawa S, Shimada K (2001) Hexhoop: modular templates for converting a hex-dominant mesh to an all-hex mesh. In: 10th International meshing round table, pp 235–246Google Scholar