Engineering with Computers

, Volume 26, Issue 3, pp 303–316 | Cite as

An interior surface generation method for all-hexahedral meshing

  • Tatsuhiko Suzuki
  • Shigeo Takahashi
  • Jason Shepherd
Original Article


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.


All-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.


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Copyright information

© Springer-Verlag London Limited 2009

Authors and Affiliations

  • Tatsuhiko Suzuki
    • 1
  • Shigeo Takahashi
    • 2
  • Jason Shepherd
    • 3
  1. 1.Digital Process Ltd.Atsugi cityJapan
  2. 2.The University of TokyoKashiwa cityJapan
  3. 3.Sandia National Laboratories, Data Analysis and Visualization DepartmentAlbuquerqueUSA

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