Fast Mesh Simplification Algorithm Based on Edge Collapse

  • Shixiang Jia
  • Xinting Tang
  • Hui Pan
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 344)


Firstly, we present a new mesh simplification algorithm. The algorithm is based on iterative half-edge contracting, and exploits a new method to measure the cost of collapse which takes the length of contracting edge and the dihedral angles between related triangles into account. The simplification does not introduce new vertex in original mesh, and enables the construction of nested hierarchies on unstructured mesh. In addition, the proposed algorithm adopts the Multiple-Choice approach to find the simplification sequence, which leads to a significant speedup with reduced memory overhead. Then we implement a mesh simplification system based on this algorithm, and demonstrate the effectiveness of our algorithm on various models.


Dihedral Angle Priority Queue Contracting Edge Edge Collapse Internal Data Structure 
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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  1. 1.
    Campbell, F. W., Robson, J. G.: Application of Fourier Analysis to the Visibility of Gratings. Journal of Physiology 197 (1968) 551–566Google Scholar
  2. 2.
    Blakemore, C., Campbell, F. W.: On the Existence of Neurons in the Human Visual System Selectively Sensitive to the Orientation and Size of Retinal Images. Journal of Physiology, 203 (1969) 237–260Google Scholar
  3. 3.
    Wu, J., Kobbelt, L.: Fast Mesh Decimation by Multiple-choice Techniques. In Vision, Modeling and Visualization. IOS Press (2002) 241–248Google Scholar
  4. 4.
    Turk, G.: Re-tilling Polygonal Surfaces. In Proceeding of ACM SIGGRAPH (1992) 55–64Google Scholar
  5. 5.
    Schoroeder, W.J., Zarge, J.A., Lorensen, W. E.: Decimation of Triangle Meshes. In Proc. Of ACM SIGGRAPH (1992) 65–70Google Scholar
  6. 6.
    Rossignac, J., Borrel, P.: Multi-resolution 3D Approximation for Rendering Complex Scenes. In Geometric Modeling in Computer Graphics Springer Verlag (1993) 455–465Google Scholar
  7. 7.
    Hoppe, H., DeRose, T., Duchamp, T., McDonald, J. A., Stuetzle, W.: Mesh optimization. Computer Graphics (SIG-GRAPH’ 93 Proceedings) (1993) 19–26Google Scholar
  8. 8.
    Hoppe, H.: Progressive Meshes. In SIG-GRAPH 96 Conference Proceeding. ACM SIGGRAPH Addison Wesley August (1996) 99–108Google Scholar
  9. 9.
    Cohen, J., Varshney, A., Manocha, D., Turk, G.: Simplification Envelopes. In Proc. Of ACM SIGGRAPH’ 96 (1996) 119–128Google Scholar
  10. 10.
    Derose, T., Lounsbery, M., Warren, J.: Multiresolution Analysis for Surfaces of Arbitrary Topology Type. Technical Report TR 93-10-05 Department of Computer Science University of Washington (1993)Google Scholar
  11. 11.
    Eck, M., Derose, T., Duchamp, T., Hoppe, H., Lousbery, M., Stuetzle, W.: Multiresolution Analysis of Arbitrary Meshes. In Proceeding of ACM SIGGRAPH (1995) 173–182Google Scholar
  12. 12.
    Garland, M., Heckbert, P. S.: Surface Simplification Using Quadric Error Metric. In Proc. SIGGRAPH’97 (1997) 209–216Google Scholar
  13. 13.
    Agarwal, P., Suri, S.: Surface Approximation and Geometric Partitions. In Proceedings of 5th ACM-SIAM Symposium on Discrete Algorithms (1994) 24–33Google Scholar
  14. 14.
    Azar, Y., Broder, A., Karlin, A., Upfal, E.: Balanced Allocations. SIAM Journal on Computing, 29(1) (1999) 180–200zbMATHMathSciNetCrossRefGoogle Scholar
  15. 15.
    Kolchin, V., Sevastyanov, B., Chist-yakov, V.: Random Allocations. John Willey & Sons (1978)Google Scholar
  16. 16.
    Melax, S.: A Simple, Fast, and Effective Polygon Reduction Algorithm. Game Developer November (1998) 44–49Google Scholar
  17. 17.
    Southern, R., Blake, E., Marais, P.: Evaluation of Memoryless Simplification. Technical Report CS01-18-00, University of Cape Town (2001)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Shixiang Jia
    • 1
  • Xinting Tang
    • 1
  • Hui Pan
    • 1
  1. 1.Department of Computer Science and TechnologyLudong UniversityYantaiP.R. China

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