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Validity-Preserving Simplification of Very Complex Polyhedral Solids

  • Carlos Andújar
  • Dolors Ayala
  • Pere Brunet
Part of the Eurographics book series (EUROGRAPH)

Abstract

In this paper we introduce the Discretized Polyhedra Simplification (DPS), a framework for polyhedra simplification using space decomposition models. The DPS is based on a new error measurement and provides a sound scheme for error-bounded, geometry and topology simplification while preserving the validity of the model. A method following this framework, Direct DPS, is presented and discussed. Direct DPS uses an octree for topology simplification and error control, and generates valid solid representations. Our method is also able to generate approximations which do not interpenetrate the original model, either being completely contained in the input solid or bounding it. Unlike most of the current methods, restricted to triangle meshes, our algorithm can deal and also produces faces with arbitrary complexity.

Keywords

Computer Graphic Decomposition Scheme Triangle Mesh Direct Solid Vertex Color 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    C. Andnjar, D. Ayala, P. Brunet, R. Joan, and J. Solé. Automatic generation of multiresolution boundary representations. Computer Graphics Forum, 1996.Google Scholar
  2. 2.
    Carlos Andnjar. The discretized polyhedra simplification: A framework for polyhedra simplification based on decomposition schemes. Technical report, Universitat Politecnica de Catalunya, LSI-98-XR, 1998.Google Scholar
  3. 3.
    Taosong He at al. Controlled topology simplification. IEEE Transactions on Visualization and Computer Graphics, 2 (2): 171–184, 1996.CrossRefGoogle Scholar
  4. 4.
    D. Ayala, C. Andtúar, and P. Brunet. Automatic simplification of orthogonal polyhedra. In D.W. Fellner, editor, Modelling Virtual Worlds Distribuited Graphics, pages 137–147. Internationallen Workshop MVD’95, Infix, 1995.Google Scholar
  5. 5.
    P. Brunet, R. Juan, Isabel Navazo, J. Sole, and D. Tost. Scientific Visualization. Advances and challenges. Academic Press, 1988.Google Scholar
  6. 6.
    T.A. Funkhouserand C.H. Sequin. Adaptive display algorithm for interactive frame rates during visualization of complex virtual environments. In Proc. SIGGRAPH,pages 247–254, 1993. Computer Graphics Proceedings, Annual Conference Series.Google Scholar
  7. 7.
    H. Hoppe. Progressive meshes. Computer Graphics, 30 (Annual Conference Series): 99–108, 1996.MathSciNetGoogle Scholar
  8. 8.
    William Lorensen and Harvey Cline. Marching cubes: A high resolution 3d surface construction algorithm. In Proc. SIGGRAPH,pages 44–50, 1987. Computer Graphics vol. 21 no. 4.Google Scholar
  9. 9.
    N. Megiddo. Linear-time algorithms for linear programming in 3d and related problems. Siam J. Computer, 12 (4): 759–776, 1983.MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    C. Montani, R. Scateni, and R. Scopigno. Discretized marching cubes. In Visualization’94, pages 281–287. IEEE Computer Society Press, 1994.Google Scholar
  11. 11.
    Isabel Navazo. Contribucio a les tecniques de modelat geometric d’objectes polimerics usant la codificacio amb arbres octals (written in Catalan). PhD thesis, Universitat Politecnica de Catalunya, 1986.Google Scholar
  12. 12.
    J. Rossignac and P. Borrel. Multiresolution 3D aproximations for rendering complex scenes. In Modeling in Computer Graphics. Springer-Verlag, 1993.Google Scholar
  13. 13.
    W. J. Schroeder, J. A. Zarge, and W. E. Lorensen. Decimation of triangle meshes. In Proc. SIGGRAPH,pages 65–70, 1992. Computer Graphics vol. 26 no. 2.Google Scholar

Copyright information

© Springer-Verlag/Wien 1999

Authors and Affiliations

  • Carlos Andújar
    • 1
  • Dolors Ayala
    • 1
  • Pere Brunet
    • 1
  1. 1.Dept. LSIUniversitat Politècnica de CatalunyaBarcelonaSpain

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