A Note on Planar Hexagonal Meshes

  • Wenping Wang
  • Yang Liu
Conference paper
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 151)

Abstract

We study the geometry and computation of free-form hexagonal meshes with planar faces (to be called P-Hex meshes). Several existing methods are reviewed and a new method is proposed for computing P-Hex meshes to approximate a given surface. The outstanding issues with these methods and further research directions are discussed.

Keywords

Planar hexagonal meshes Dupin indicatrix polyhedral approximation 

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References

  1. [1]
    H. Almegaard, A. Bagger, J. Gravesen, B. Jüttler, and Z. Sir, Surfaces with piecewise linear support functions over spherical triangulations, in Proceedings of Mathematics of Surfaces XII, LNCS 4647, Springer, 2007.Google Scholar
  2. [2]
    A. Bobenko, T. Hoffmann, and B. Springborn, Minimal surfaces from circle patterns: Geometry from combinatorics, Ann. of Math., 164: 231–264, 2006.MATHCrossRefMathSciNetGoogle Scholar
  3. [3]
    J. Díaz, C. Otero, R. Togores, and C. Manchado, Power diagrams in the design of chordal space structures, in The 2nd International Symposium on Voronoi Diagrams in Science and Engineering, pp. 93–104, 2005.Google Scholar
  4. [4]
    H. Kawaharada and K. Sugihara, Dual subdivision – a new class of subdivision schemes using projective duality, in The 14th International Conference in Central Europe on Computer Graphics, Visualization and Computer Vision, pp. 9–17, 2006.Google Scholar
  5. [5]
    Y. Liu, H. Pottmann, J. Wallner, Y. Yang, and W. Wang, Geometric modeling with conical meshes and developable surfaces, ACM Transactions on Graphics (SIGGRAPH 2006), 25(3): 681–689, 2006.CrossRefGoogle Scholar
  6. [6]
    H. Pottmann, Y. Liu, J. Wallner, A. Bobenko, and W. Wang, Geometry of multi-layer freeform structures for architecture, ACM Transactions on Graphics (SIGGRAPH 2007), 26(3), Article No. 65, 2007.Google Scholar
  7. [7]
    D. Struik, Lectures on classical differential geometry, Cambridge, Addison-Wesley, 1950.MATHGoogle Scholar
  8. [8]
    W. Wang, Y. Liu, D. Yan, B. Chan, R. Ling, and F. Sun, Hexagonal meshes with planar faces, Technical Report, TR-2008-13, Department of Computer Science, The University of Hong Kong, 2008.Google Scholar

Copyright information

© Springer-Verlag New York 2009

Authors and Affiliations

  • Wenping Wang
    • 1
  • Yang Liu
    • 1
  1. 1.Department of Computer ScienceUniversity of Hong KongHong Kong SARP.R. China

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