Skip to main content

Part of the book series: Mathematics and Visualization ((MATHVISUAL))

Abstract

We survey recent developments in compact representations of 3D mesh data. This includes: methods to reduce the complexity of meshes by simplification, thereby reducing the number of vertices and faces in the mesh; methods to resample the geometry in order to optimize the vertex distribution; methods to compactly represent the connectivity data (the graph structure defined by the edges) of the mesh; methods to compactly represent the geometry data (the vertex coordinates) of a mesh.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. P. Alliez and M. Desbrun. Valence-driven connectivity encoding for 3D meshes. Computer Graphics Forum 20, 2001, 480–489.

    Article  Google Scholar 

  2. P. Alliez and M. Desbrun. Progressive compression for lossless transmission of triangle meshes. SIGGRAPH 2001, 195–202.

    Google Scholar 

  3. B. G. Baumgart. A polyhedron representation for computer vision. Proc. of the Nat. Comp. Conf., 1975, 589–596.

    Google Scholar 

  4. M. Botsch and L. Kobbelt. Resampling feature and blend regions in polygonal meshes for surface anti-aliasing. Computer Graphics Forum, 2001, C402-C410.

    Google Scholar 

  5. M. Chow. Optimized geometry compression for realtime rendering. Proc. IEEE Vis., 1997, 347–354.

    Google Scholar 

  6. P. Cignoni, C. Montani, and R. Scopigno. A comparison of mesh simplification algorithms. Computers & Graphics, 1998, 37–54.

    Google Scholar 

  7. P. Cignoni, C. Montani, and R. Scopigno. Metro: Measuring error on simplified surfaces. Computer Graphics Forum, 1998, 167–174.

    Google Scholar 

  8. P. Cignoni, C. Montani, C. Rocchini, R. Scopigno, and M. Tarini. Preserving attribute values on simplified meshes by re-sampling detail textures. The Visual Computer, 1999, 519–539.

    Google Scholar 

  9. J. Cohen, A. Varshney, D. Manocha, G. Turk, H. Weber, P. Agarwal, F. Brooks, and W. Wright. Simplification envelopes. SIGGRAPH 1996, 119–128.

    Google Scholar 

  10. J. Cohen, M. Olano, and D. Manocha. Appearance preserving simplification. SIGGRAPH 1998, 115–122.

    Google Scholar 

  11. D. Cohen-Or, D. Levin, and O. Remez. Progressive compression of arbitrary triangle meshes. Proc. IEEE Vis., 1999, 67–72.

    Google Scholar 

  12. G. V. Cormack and R. N. Horspool. Algorithms for adaptive Huffman codes. Inform. Proc. Letters 18, 1984, 159–165.

    Article  MathSciNet  Google Scholar 

  13. M. Deering. Geometry compression. Proc. SIGGRAPH 1995, 13–20.

    Google Scholar 

  14. M. Eck, T. DeRose, T. Duchamp, H. Hoppe, M. Lounsbery, W. Stuetzle. Multiresolution analysis of arbitrary meshes. SIGGRAPH 1995, 173–182.

    Google Scholar 

  15. M. Floater. Parameterization and smooth approximation of surface triangulations. Comput. Aided Geom. Design 14, 1997, 231–250.

    Article  MathSciNet  MATH  Google Scholar 

  16. M. S. Floater and K. Hormann. Parameterization of triangulations and unorganized points. This volume.

    Google Scholar 

  17. M. S. Floater, K. Hormann, and M. Reimers. Parameterization of manifold triangulations. Approximation Theory X: Abstract and Classical Analysis, C. K. Chui, L. L. Schumaker, and J. Stöckler (eds.), Vanderbilt University Press, Nashville, 2002, 197–209.

    Google Scholar 

  18. M. Garland and P. Heckbert. Surface simplification using quadric error metrics. SIGGRAPH 1997, 209–216.

    Google Scholar 

  19. M. Garland and P. Heckbert. Simplifying surfaces with color and texture using quadric error metrics. Proc. IEEE Vis., 1998, 264–270.

    Google Scholar 

  20. A. Gersho and R. Grey. Vector quantization and signal compression. Kluwer, Boston, 1992.

    Book  MATH  Google Scholar 

  21. A. Gueziec, G. Taubin, F. Lazarus, and W. Horn. Converting sets of polygons to manifold surfaces by cutting and stitching. IEEE Visualization, 1998, 383–390.

    Google Scholar 

  22. S. Gumhold and W. Straßer. Real time compression of triangle mesh connectivity. SIGGRAPH 1998, 133–140.

    Google Scholar 

  23. S. Gumhold. New bounds on the encoding of planar triangulations. Tech. Rep. WSI-2000–1, Univ. of Tübingen, 2000.

    Google Scholar 

  24. I. Guskov, W. Sweldens, and P. Schröder. Multiresolution signal processing for meshes. SIGGRAPH 1999, 325–334.

    Google Scholar 

  25. I. Guskov, K. Vidimce, W. Sweldens, and P. Schröder. Normal meshes. SIGGRAPH 2000, 95–102.

    Google Scholar 

  26. H. Hoppe, T. DeRose, T. Duchamp, J. McDonald, and W. Stuetzle. Mesh optimization. SIGGRAPH 1993, 19–26.

    Google Scholar 

  27. H. Hoppe. Progressive meshes. SIGGRAPH 1996, 99–108.

    Google Scholar 

  28. H. Hoppe. Efficient implementation of progressive meshes. Computers and Graphics 22.1, 1998, 27–36.

    Google Scholar 

  29. H. Hoppe. New quadric metric for simplifying meshes with appearance attributes. Proc. IEEE Vis., 1999, 59–66.

    Google Scholar 

  30. D. A. Huffman. A method for the construction of minimum-redundancy codes. Proc. Inst. Radio Eng., 1952, 1098–1101.

    Google Scholar 

  31. M. Isenburg and J. Snoeyink. Spirale reversi: reverse decoding of the Edge-Breaker encoding. 12th Can. Conf. on Comp. Geom., 2000, 247–256.

    Google Scholar 

  32. M. Isenburg and J. Snoeyink. Face Fixer: Compressing polygon meshes with properties. SIGGRAPH 2000, 263–270.

    Google Scholar 

  33. Z. Kami and C. Gotsman. Spectral coding of mesh geometry. SIGGRAPH 2000, 279–286.

    Google Scholar 

  34. Z. Kami and C. Gotsman. 3D mesh compression using fixed spectral bases. Proc. Graph. Interf., 2001, 1–8.

    Google Scholar 

  35. G. Karypis and V. Kumar. MeTiS: A software package for partitioning unstructured graphs, partitioning meshes, and computing fill-reducing orderings of sparse matrices. Version 4.0, Univ. of Minnesota, Dept. of Computer Science, 1998. Available at www-users.cs.umn.edu/karypis/metis/metis.html.

    Google Scholar 

  36. D. King and J. Rossignac. Guaranteed 3.67v bit encoding of planar triangle graphs. 11th Can. Conf. on Comp. Geom., 1999, 146–149.

    Google Scholar 

  37. D. King, J. Rossignac, and A. Szymczak. Connectivity compression for irregular quadrilateral meshes. Tech. Rep. TR-99–36,GVU, Georgia Tech, 1999.

    Google Scholar 

  38. R. Klein, G. Liebich, and W. Straßer. Mesh reduction with error control. Proc. IEEE Vis., 1996, 311–318.

    Google Scholar 

  39. L. Kobbelt, S. Campagna, and H.-P. Seidel. A general framework for mesh decimation. Proc. Graph. Interf., 1998, 43–50.

    Google Scholar 

  40. L. Kobbelt, S. Campagna, J. Vorsatz, and H.-P. Seidel. Interactive multi-resolution modeling on arbitrary meshes. SIGGRAPH 1998, 105–114.

    Google Scholar 

  41. L. Kobbelt, J. Vorsatz, U. Labsik, and H.-P. Seidel. Shrink wrapping approach to remeshing polygonal surfaces. Computer Graphics Forum, 1999, 119–130.

    Google Scholar 

  42. L. Kobbelt, J. Vorsatz, and H.-P. Seidel. Multiresolution hierarchies on unstructured triangle meshes. Computational Geometry 14, 1999, 5–24.

    Article  MathSciNet  MATH  Google Scholar 

  43. B. Kronrod and C. Gotsman. Efficient coding of non-triangular meshes. Proc. 8-th Pacific Graphics, 2000, 235–242.

    Google Scholar 

  44. A. Lee, W. Sweldens, P. Schröder, L. Cowsar, and D. Dobkin. MAPS: Multiresolution adaptive parameterization of surfaces. SIGGRAPH 1998, 95–104.

    Google Scholar 

  45. E. Lee and H. Ko. Vertex data compression for triangular meshes. Proc. Pacific Graphics, 2000, 225–234.

    Google Scholar 

  46. P. Lindstrom and G. Turk. Fast and memory efficient polygonal simplification. Proc. IEEE Vis., 1998, 279–286.

    Google Scholar 

  47. P. Lindstrom and G. Turk. Evaluation of memoryless simplification. Proc. IEEE Trans. on Vis. and Comp. Graph., 1999, 98–115.

    Google Scholar 

  48. P. Lindstrom. Out-Of-Core simplification of large polygonal models. SIGGRAPH 2000, 259–262.

    Google Scholar 

  49. P. Lindstrom and G. Turk. Image-Driven Simplification. ACM Trans. on Graph., 2000, 204–241.

    Google Scholar 

  50. M. Mäntylä. An Introduction to Solid Modeling. Computer Science Press, Rockville, MD, 1988.

    Google Scholar 

  51. R. Pajarola and J. Rossignac. Compressed Progressive Meshes. IEEE Trans. on Vis. and Comp. Graph. 6.1, 2000, 79–93.

    Article  Google Scholar 

  52. J. Rossignac and P. Borrel. Multi-resolution 3D approximation for rendering complex scenes. 2nd Conf. on Geom. Model. in Comp. Graph., 1993, 453–465.

    Google Scholar 

  53. J. Rossignac. EdgeBreaker: Connectivity compression for triangle meshes. IEEE Trans. on Vis. and Comp. Graphics, 1999, 47–61.

    Google Scholar 

  54. J. Rossignac and D. Cardoze. Matchmaker: Manifold Breps for non-manifold r-sets. Tech. Rep. GIT-GVU-99–03 GVU Center, Georgia Inst. of Tech., 1998.

    Google Scholar 

  55. W. Schroeder, J. Zarge, and W. Lorensen. Decimation of triangle meshes. SIG-GRAPH 1992, 65–70.

    Google Scholar 

  56. W. Schroeder. A topology modifying progressive decimation algorithm. Proc. IEEE Vis., 1997, 205–212.

    Google Scholar 

  57. D. S. Scott. LAS02 Documentation. Technical Report, Computer Science Dept., University of Texas at Austin, 1980.

    Google Scholar 

  58. A. Szymczak, D. King, and J. Rossignac. An EdgeBreaker-based efficient compression scheme for regular meshes. Preprint, 2000.

    Google Scholar 

  59. G. Taubin and J. Rossignac. Geometric compression through topological surgery. ACM Trans. on Graphics 17.2, 1998, 84–115.

    Article  Google Scholar 

  60. G. Taubin, A. Gueziec, W. Horn, and F. Lazarus. Progressive forest split compression. SIGGRAPH 1998, 123–132.

    Google Scholar 

  61. C. Tourna and C. Gotsman. Triangle mesh compression. Proc. Graph. Interf., 1998, 26–34.

    Google Scholar 

  62. G. Turan. Succinct representations of graphs. Discrete Appl. Math. 8, 1984, 289–294.

    Article  MathSciNet  MATH  Google Scholar 

  63. G. Turk. Re-tiling polygonal surfaces. SIGGRAPH 1992, 55–64.

    Google Scholar 

  64. W. Tutte. A census of planar triangulations. Can. Journ. of Math. 14, 1962, 21–38.

    Article  MathSciNet  MATH  Google Scholar 

  65. I. H. Witten, R. M. Neal and J. G. Cleary. Arithmetic coding for data compression. Comm. of the ACM 30(6), 1987, 520–540.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Gotsman, C., Gumhold, S., Kobbelt, L. (2002). Simplification and Compression of 3D Meshes. In: Iske, A., Quak, E., Floater, M.S. (eds) Tutorials on Multiresolution in Geometric Modelling. Mathematics and Visualization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04388-2_12

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-04388-2_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-07819-4

  • Online ISBN: 978-3-662-04388-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics