Encoding Level-of-Detail Tetrahedral Meshes

  • Neta Sokolovsky
  • Emanuele Danovaro
  • Leila De Floriani
  • Paola Magillo
Conference paper
Part of the Mathematics and Visualization book series (MATHVISUAL)


Level-Of-Detail (LOD) techniques can be a valid support to the analysis and visualisation of volume data sets of large size. In our previous work, we have defined a general LOD model for d-dimensional simplicial meshes, called a Multi-Tessellation (MT), which consists of a partially ordered set of mesh updates. Here, we consider an instance of the MT for tetrahedral meshes, called a Half-Edge MT, which is built through a common simplification operation, half-edge collapse. We discuss two compact encodings for a Half-Edge MT, based on alternative ways to represent the partial order.


Directed Acyclic Graph Tetrahedral Mesh Left Child Base Mesh Volume Visualization 
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  1. 1.
    P. Cignoni, D. Costanza, C. Montani, C. Rocchini, and R. Scopigno. Simplification of tetrahedral volume with accurate error evaluation. In Proceedings IEEE Visualization 2000, pages 85–92. IEEE Computer Society, 2000.Google Scholar
  2. 2.
    P. Cignoni, L. De Floriani, P. Magillo, E. Puppo, and R. Scopigno. Selective refinement queries for volume visualization of unstructured tetrahedral meshes. IEEE Transactions on Visualization and Computer Graphics, 2003.Google Scholar
  3. 3.
    P. Cignoni, L. De Floriani, C. Montani, E. Puppo, and R. Scopigno. Multiresolution modeling and visualization of volume data based on simplicial complexes. In Proceedings 1994 Symposium on Volume Visualization, pages 19–26, Washington, DC, October 1994.Google Scholar
  4. 4.
    E. Danovaro and L. De Floriani. Half-edge Multi-Tessellation: a compact representations for multiresolution tetrahedral meshes. In Proceedings 1st International Symposium on 3D Data Processing Visualization Transmission, pages 494–499, 2002.Google Scholar
  5. 5.
    L. De Floriani and P. Magillo. Multiresolution mesh representation: Models and data structures. In M. Floater, A. Iske, and E. Quak, editors, Tutorials on Multiresolution in Geometric Modelling, pages 363–418. Springer-Verlag, 2002.Google Scholar
  6. 6.
    L. De Floriani, E. Puppo, and P. Magillo. A formal approach to multiresolution modeling. In R. Klein, W. Straßer, and R. Rau, editors, Geometric Modeling: Theory and Practice, pages 302–323. Springer-Verlag, 1997.Google Scholar
  7. 7.
    J. El-Sana and A. Varshney. Generalized view-dependent simplification. Computer Graphics Forum, 18(3):C83–C94, 1999.CrossRefGoogle Scholar
  8. 8.
    B. Gregorski, M. Duchaineau, P. Lindstrom, V. Pascucci, and K. Joy. Interactive view-dependent rendering of large isosurfaces. In Proceedings IEEE Visualization 2002, 2002.Google Scholar
  9. 9.
    G. Greiner and R. Grosso. Hierarchical tetrahedral-octahedral subdivision for volume visualization. The Visual Computer, 16:357–365, 2000.CrossRefGoogle Scholar
  10. 10.
    M. H. Gross and O. G. Staadt. Progressive tetrahedralizations. In Proceedings IEEE Visualization'98, pages 397–402, Research Triangle Park, NC, 1998. IEEE Comp. Soc. Press.Google Scholar
  11. 11.
    B. Hamann and J. L. Chen. Data point selection for piecewise trilinear approximation. Computer Aided Geometric Design, 11:477–489, 1994.MathSciNetCrossRefGoogle Scholar
  12. 12.
    R. Klein and S. Gumhold. Data compression of multiresolution surfaces. In Visualization in Scientific Computing '98, pages 13–24. Springer-Verlag, 1998.Google Scholar
  13. 13.
    M. Lee, L. De Floriani, M., and H. Samet. Constant-time neighbor finding in hierarchical meshes. In Proceedings International Conference on Shape Modeling, pages 286–295, Genova (Italy), May 7–11 2001.Google Scholar
  14. 14.
    M. Ohlberger and M. Rumpf. Adaptive projection operators in multiresolution scientific visualization. IEEE Transactions on Visualization and Computer Graphics, 5(1):74–93, 1999.CrossRefGoogle Scholar
  15. 15.
    V. Pascucci and C. L. Bajaj. Time-critical isosurface refinement and smoothing. In Proceedings 2000 Symposium on Volume Visualization, pages 33–42, October 2000.Google Scholar
  16. 16.
    J. Popovic and H. Hoppe. Progressive simplicial complexes. In Proc. ACM SIGGRAPH '97, pages 217–224, 1997.Google Scholar
  17. 17.
    K. J. Renze and J. H. Oliver. Generalized unstructured decimation. IEEE Computational Geometry & Applications, 16(6):24–32, 1996.CrossRefGoogle Scholar
  18. 18.
    I. J. Trotts, B. Hamann, and K. I. Joy. Simplification of tetrahedral meshes with error bounds. IEEE Transactions on Visualization and Computer Graphics, 5(3):224–237, 1999.CrossRefGoogle Scholar
  19. 19.
    Y. Zhou, B. Chen, and A. Kaufman. Multiresolution tetrahedral framework for visualizing regular volume data. In Proceedings IEEE Visualization'97, pages 135–142. IEEE Computer Society, 1997.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Neta Sokolovsky
    • 1
  • Emanuele Danovaro
    • 2
  • Leila De Floriani
    • 2
  • Paola Magillo
    • 2
  1. 1.Department of Computer ScienceBen Gurion University of the NegevBeer ShevaIsrael
  2. 2.Department of Computer and Information Science (DISI)University of GenovaItaly

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