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Recent Advances in Remeshing of Surfaces

  • Pierre Alliez
  • Giuliana Ucelli
  • Craig Gotsman
  • Marco Attene
Part of the Mathematics and Visualization book series (MATHVISUAL)

Remeshing is a key component of many geometric algorithms, including modeling, editing, animation and simulation. As such, the rapidly developing field of geometry processing has produced a profusion of new remeshing techniques over the past few years. In this paper we survey recent developments in remeshing of surfaces, focusing mainly on graphics applications. We classify the techniques into five categories based on their end goal: structured, compatible, high quality, feature and error-driven remeshing.We limit our description to the main ideas and intuition behind each technique, and a brief comparison between some of the techniques. We also list some open questions and directions for future research.

Keywords

Voronoi Diagram Polygonal Mesh Geometry Image Geometry Processing Base Mesh 
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.
    M. Alexa. Merging polyhedral shapes with scattered features. In Proceedings of the International Conference on Shape Modeling and Applications (SMI-99), pages 202-210, 1999.Google Scholar
  2. 2.
    M. Alexa. Recent advances in mesh morphing. Computer Graphics Forum, 21(2):173-196,2002.CrossRefGoogle Scholar
  3. 3.
    P. Alliez and C. Gotsman. Recent advances in compression of 3d meshes. In Proceedings of the Symposium on Multiresolution in Geometric Modeling, 2003.Google Scholar
  4. 4.
    P. Alliez, N. Laurent, H. Sanson, and F. Schmitt. Mesh approximation using a volumebased metric. In Proceedings of the 7th Pacific Conference on Computer Graphics and Applications 1999, pages 292-301, Los Alamitos, 1999. IEEE Computer Society.Google Scholar
  5. 5.
    P. Alliez, M. Meyer, and M. Desbrun. Interactive geometry remeshing. Acm Transactions on Graphics, 21(3):347-354, 2002.Google Scholar
  6. 6.
    Pierre Alliez, David Cohen-Steiner, Olivier Devillers, Bruno Levy, and Mathieu Desbrun. Anisotropic polygonal remeshing. ACM.Transactions on Graphics, 22:485-493, 2003.CrossRefGoogle Scholar
  7. 7.
    Pierre Alliez, Eric Colin de Verdiere, Olivier Devillers, and Martin Isenburg. Isotropic surface remeshing. In M.S. Kim, editor, SMI ’03: Proceedings of Shape Modeling International 2003, pages 49-58, Los Alamitos, 2003. IEEE Computer Society.CrossRefGoogle Scholar
  8. 8.
    N. Amenta, M. Bern, and M. Kamvysselis. A new voronoi-based surface reconstruction algorithm. Computer graphics proceedings, annual conference series: SIGGRAPH conference proceedings, pages 415-422, Jul 1998.Google Scholar
  9. 9.
    M. Attene, B. Falcidieno, J. Rossignac, and M. Spagnuolo. Edge-sharpener: recovering sharp features in triangulations of non-adaptively re-meshed surfaces. In Proceedings of the Eurographics/ACM SIGGRAPH Symposium on Geometry Processing 2003, pages 62-69. ACM Press, 2003.Google Scholar
  10. 10.
    M. Attene, B. Falcidieno, M. Spagnuolo, and J. Rossignac. Swingwrapper: Retiling triangle meshes for better edgebreaker compression. Acm Transactions on Graphics, 22(4):982-996, 2003.CrossRefGoogle Scholar
  11. 11.
    M. Attene, B. Falcidieno, M. Spagnuolo, and G. Wyvill. A mapping-independent primitive for the triangulation of parametric surfaces. Graphical Models, 65(5):260-273, 2003.zbMATHCrossRefGoogle Scholar
  12. 12.
    J. D. Boissonnat and S. Oudot. Provably good surface sampling and approximation. In Proc. of Symp. on Geo. Processing, pages 9-18, 2003.Google Scholar
  13. 13.
    Houman Borouchaki, Frederic Hecht, and J.Frey Pascal. Mesh gradation control. In Proceedings of 6th International Meshing Roundtable, pages 131-141. Sandia National Laboratories, 1997.Google Scholar
  14. 14.
    Mario Botsch and Leif Kobbelt. A remeshing approach to multiresolution modeling. In R. Scopigno and D. Zorin, editors, Proceedings of 2nd Eurographics Symposium on Geometry Processing, pages 189-196. Eurographics, 2004.Google Scholar
  15. 15.
    L. Paul Chew. Guaranteed-quality mesh generation for curved surfaces. In Proceedings of the ninth annual symposium on Computational geometry, pages 274-280. ACM Press, 1993.Google Scholar
  16. 16.
    D. Cohen-Steiner, P. Alliez, and M. Desbrun. Variational shape approximation. Computer graphics proceedings, annual conference series: SIGGRAPH conference proceedings, 2004.Google Scholar
  17. 17.
    T.K. Dey and R. Wenger. Reconstructing curves with sharp corners. Computational Geometry Theory and Applications, 19:89-99, 2001.zbMATHMathSciNetGoogle Scholar
  18. 18.
    S. Dong, S. Kircher, and M. Garland. Harmonic functions for quadrilateral remeshing of arbitrary manifolds. Computer Aided Geometric Design, 2005. To appear.Google Scholar
  19. 19.
    Q. Du, V. Faber, and M. Gunzburger. Centroidal Voronoi Tesselations: Applications and Algorithms. SIAM review, 41(4):637-676, 1999.zbMATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    M. Eck, T. De Rose, T. Duchamp, H. Hoppe, M.Lounsbery, and W. Stuetzle. Multiresolution analysis of arbitrary meshes. Computer graphics proceedings, annual conference series: SIGGRAPH conference proceedings, pages 173-182, 1995.Google Scholar
  21. 21.
    H. Edelsbrunner and D. Guoy. Sink-insertion for mesh improvement. In Proceedings of the seventeenth annual symposium on Computational geometry, pages 115-123. ACM Press, 2001.Google Scholar
  22. 22.
    M.S. Floater and K. Hormann. Surface Parameterization: a Tutorial and Survey. Springer, 2004.Google Scholar
  23. 23.
    P. J. Frey and H. Borouchaki. Geometric surface mesh optimization. Computing and Visualization in Science, 1:113-121, 1998.zbMATHCrossRefGoogle Scholar
  24. 24.
    Pascal J. Frey. About surface remeshing. In Proceedings of the 9th International Meshing Roundtable, pages 123-136. Sandia National Laboratories, 2000.Google Scholar
  25. 25.
    M. Garland. Multiresolution modeling: Survey & future opportunities. In Eurographics ’99, State of the Art Report (STAR), pages 111-131. Eurographics, 2000.Google Scholar
  26. 26.
    A. Gersho. Asymptotically optimal block quantization. IEEE Transactions on Information Theory, IT-25(4):373-380, July 1979.zbMATHCrossRefMathSciNetGoogle Scholar
  27. 27.
    C. Gotsman, X.F. Gu, and A. Sheffer. Fundamentals of spherical parameterization for 3d meshes. Acm Transactions on Graphics, 22(3):358-363, 2003.CrossRefGoogle Scholar
  28. 28.
    C. Gotsman, S. Gumhold, and L. Kobbelt. Simplification and compression of 3D-meshes. 2002.Google Scholar
  29. 29.
    X. Gu, S.J. Gortler, and H. Hoppe. Geometry images. Computer graphics proceedings, annual conference series: SIGGRAPH conference proceedings, pages 355-361, 2002.Google Scholar
  30. 30.
    I. Guskov, K. Vidimce, W. Sweldens, and P. Schroeder. Normal meshes. Computer graphics proceedings, annual conference series: SIGGRAPH conference proceedings, pages 95-102, 2000.Google Scholar
  31. 31.
    E. Hartmann. A marching method for the triangulation of surfaces. the Visual Computer, 14(3):95-108, 1998.zbMATHGoogle Scholar
  32. 32.
    P. Heckbert and M. Garland. Survey of polygonal surface simplification algorithms, 1997.Google Scholar
  33. 33.
    H. Hoppe. Progressive meshes. Computer graphics proceedings, annual conference series: SIGGRAPH conference proceedings, pages 99-108, 1996.Google Scholar
  34. 34.
    Hugues Hoppe, Tony De Rose, Tom Duchamp, John McDonald, and Werner Stuetzle. Mesh optimization. Computer graphics proceedings, annual conference series: SIGGRAPH conference proceedings, pages 19-26, 1993.Google Scholar
  35. 35.
    K. Hormann and G. Greiner. Quadrilateral remeshing. In Proceedings of Vision, Modeling, and Visualization 2000, pages 153-162, 2000.Google Scholar
  36. 36.
    T. Ju, F. Losasso, S. Schaefer, and J. Warren. Dual contouring of hermite data. Computer graphics proceedings, annual conference series: SIGGRAPH conference proceedings, pages 339-346, 2002.Google Scholar
  37. 37.
    T. Kanai, H. Suzuki, and F. Kimura. Metamorphosis of arbitrary triangular meshes. Ieee Computer Graphics and Applications, 20:62-75, 2000.CrossRefGoogle Scholar
  38. 38.
    A. Khodakovsky and I. Guskov. Compression of Normal Meshes. Springer-Verlag, 2003.Google Scholar
  39. 39.
    A. Khodakovsky, N. Litke, and P. Schr öder. Globally smooth parameterizations with low distortion. ACM.Transactions on Graphics, 22:350-357, 2003.CrossRefGoogle Scholar
  40. 40.
    A. Khodakovsky, P. Schroeder, and W. Sweldens. Progressive geometry compression. Computer graphics proceedings, annual conference series: SIGGRAPH conference proceedings, pages 271-278, 2000.Google Scholar
  41. 41.
    L. Kobbelt, S. Bischoff, M. Botsch, K. Kahler, C. R össl, R. Schneider, and J. Vorsatz. Geometric modeling based on polygonal meshes. In Euroraphics 2000 Tutorial, 2000.Google Scholar
  42. 42.
    L. Kobbelt and M. Botsch. Feature sensitive mesh processing. In SCCG ’03: Proceedings of the 19th Spring Conference on Computer Graphics, pages 17-22. ACM Press, 2003.Google Scholar
  43. 43.
    L. Kobbelt, J. Vorsatz, U. Labsik, and H.-P. Seidel. A shrink wrapping approach to remeshing polygonal surfaces. Computer Graphics Forum, 18:119-130, 1999.CrossRefGoogle Scholar
  44. 44.
    L.P. Kobbelt, M. Botsch, U. Schwanecke, and H.P. Seidel. Feature sensitive surface extraction from volume data. Computer graphics proceedings, annual conference series: SIGGRAPH conference proceedings, pages 57-66, Aug 2001.Google Scholar
  45. 45.
    V. Kraevoy and A. Sheffer. Cross-parameterization and compatible remeshing of 3d models. Computer graphics proceedings, annual conference series: SIGGRAPH conference proceedings, 2004.Google Scholar
  46. 46.
    A. Lee, D. Dobkin, W. Sweldens, and P. Schr öder. Multiresolution mesh morphing. In Siggraph 1999, Computer Graphics Proceedings, pages 343-350, 1999.Google Scholar
  47. 47.
    A.W.F. Lee, W. Sweldens, P. Schroeder, L. Cowsar, and D. Dobkin. Maps: Multiresolution adaptive parameterization of surfaces. Computer Graphics, 32:95-104, 1998.Google Scholar
  48. 48.
    J. L. Lin, J. H. Chuang, C. C. Lin, and C. C. Chen. Consistent parametrization by quinary subdivision for remeshing and mesh metamorphosis. In GRAPHITE ’03: Proceedings of the 1th International Conference on Computer Graphics and Interactive Techniques in Austalasia and South East Asia 2003, pages 151-158. ACM Press, 2003.Google Scholar
  49. 49.
    M.l Lindenbaum, M. Porat, Y. Y. Zeevi, and Y. Eldar. The farthest point strategy for progressive image sampling, 1996.Google Scholar
  50. 50.
    S. Lloyd. Least square quantization in PCM. IEEE Trans. Inform. Theory, 28:129-137, 1982.zbMATHCrossRefMathSciNetGoogle Scholar
  51. 51.
    W.E. Lorensen and H.E. Cline. Marching cubes: a high resolution 3d surface reconstruc- tion algorithm. Computer Graphics, 21:163-169, 1987.CrossRefGoogle Scholar
  52. 52.
    D. Luebke. A developer’s survey of polygonal simplification algorithms. Ieee Computer Graphics and Applications, 2001.Google Scholar
  53. 53.
    D. Luebke, M. Reddy, J. Cohen, A. Varshney, B. Watson, and R. Huebner. Level of Detail for 3D Graphics. Morgan-Kaufmann, San Francisco, 2002.Google Scholar
  54. 54.
    M. Marinov and L. Kobbelt. Direct anisotropic quad-dominant remeshing. In Proceedings of the 12th Pacific Conference on Computer Graphics and Applications, pages 207-216, 2004.Google Scholar
  55. 55.
    T. Michikawa, T. Kanai, M. Fujita, and H. Chiyokura. Multiresolution interpolation meshes. In Proceedings of the 9th Pacific Conference on Computer Graphics and Applications 2001, pages 60-69, Los Alamitos, 2001. IEEE Computer Society.CrossRefGoogle Scholar
  56. 56.
    G. L. Miller. A time efficient delaunay refinement algorithm. In Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms, pages 400-409. Society for Industrial and Applied Mathematics, 2004.Google Scholar
  57. 57.
    C. Moenning and N. A. Dodgson. Fast marching farthest point sampling. Technical Report UCAM-CL-TR-562, University of Cambridge, Computer Laboratory, 2003.Google Scholar
  58. 58.
    V. Ostromoukhov. A Simple and Efficient Error-Diffusion Algorithm. In Proceedings of SIGGRAPH, pages 567-572, 2001.Google Scholar
  59. 59.
    V. Ostromoukhov, C. Donohue, and P. M. Jodoin. Fast hierarchical importance sampling with blue noise properties new york, ny, usa. ACM.Transactions on Graphics, 23, Aug 2004.Google Scholar
  60. 60.
    F. Payan and M. Antonini. 3d mesh wavelet coding using efficient model-based bit allocation. In Proceedings of the 1st International Symposium on 3D Data Processing Visualization and Transmission 2002, pages 391-394, 2002.Google Scholar
  61. 61.
    P. P. Pebay and T. J. Baker. A comparison of triangle quality measures. In Proceedings, 10th International Meshing Roundtable, pages 327-340, 2001.Google Scholar
  62. 62.
    G. Peyr é and L. Cohen. Surface Segmentation Using Geodesic Centroidal Tesselation. In Proceedings of 2nd International Symposium on 3D Data Processing, Visualization, and Transmission, pages 995-1002, 2004.Google Scholar
  63. 63.
    Gabriel Peyre and Laurent Cohen. Geodesic remeshing using front propagation. In Proceedings of 2nd IEEE Workshop on Variational, Geometric and Level Set Methods in Computer Vision 2003, pages 33-40, Los Alamitos, 2003. IEEE Computer Society.Google Scholar
  64. 64.
    E. Praun and H. Hoppe. Spherical parametrization and remeshing. Computer graphics proceedings, annual conference series: SIGGRAPH conference proceedings, pages 340- 349,2003.Google Scholar
  65. 65.
    E. Praun, W. Sweldens, and P. Schr öder. Consistent mesh parameterizations. Computer graphics proceedings, annual conference series: SIGGRAPH conference proceedings, pages 179-184, 2001.Google Scholar
  66. 66.
    A. Rassineux, P. Villon, J.M. Savignat, and O. Stab. Surface remeshing by local hermite diffuse interpolation. International Journal for Numerical Methods in Engineering, 49:31-49, 2000.zbMATHCrossRefGoogle Scholar
  67. 67.
    C. Rocchini, P. Cignoni, F. Ganovelli, C. Montani, P. Pingi, and R. Scopigno. Marching intersections: an efficient resampling algorithm for surface management. In Proceedings of the International Conference on Shape Modeling and Applications, pages 296-305, 2001.Google Scholar
  68. 68.
    J. Ruppert. A delaunay refinement algorithm for quality 2-dimensional mesh generation. Journal of Algorithms, 18(3):548-585, 1995.zbMATHCrossRefMathSciNetGoogle Scholar
  69. 69.
    P. Sander, S. Gortler, J. Snyder, and H. Hoppe. Signal-specialized parametrization. In EGWR ’02: 13th Eurographics Workshop on Rendering 2002. Eurographics, 2002.Google Scholar
  70. 70.
    P. Sander, Z. Wood, S. Gortler, J. Snyder, and H. Hoppe. Multi-chart geometry images. In Proceedings of the Eurographics/ACM SIGGRAPH Symposium on Geometry Processing 2003, pages 246-255. ACM Press, 2003.Google Scholar
  71. 71.
    J. Schreiner, A. Asirvatham, E. Praun, and H. Hoppe. Inter-surface mapping. Computer graphics proceedings, annual conference series: SIGGRAPH conference proceedings, 2004.Google Scholar
  72. 72.
    P. Schr öder. Subdivision for modeling and animation, 1998.Google Scholar
  73. 73.
    J. Sethian. Level Sets Methods and Fast Marching Methods. Cambridge University Press, 2nd edition, 1999.Google Scholar
  74. 74.
    J. R. Shewchuk. What is a good linear element? interpolation, conditioning, and quality measures. In Proceedings of 11th International Meshing Roundtable, 2002.Google Scholar
  75. 75.
    K. Shimada and J. Liao. Quadrilateral Meshing with Directionality Control through the Packing of Square Cells. In 7th Intl. Meshing Roundtable, pages 61-76, oct 1998.Google Scholar
  76. 76.
    Oren Sifri, Alla Sheffer, and Craig Gotsman. Geodesic-based surface remeshing. In Proceedings of 12th International Meshing Roundtable, pages 189-199. Sandia National Laboratories, 2003.Google Scholar
  77. 77.
    V. Surazhsky and C. Gotsman. Explicit surface remeshing. In Proceedings of the Eurographics/ACM SIGGRAPH Symposium on Geometry Processing 2003, pages 20-30. ACM Press, 2003.Google Scholar
  78. 78.
    Vitaly Surazhsky, Pierre Alliez, and Craig Gotsman. Isotropic remeshing of surfaces: a local parameterization approach. In Proceedings of 12th International Meshing Round-table, pages 215-224. Sandia National Laboratories, 2003.Google Scholar
  79. 79.
    W. Sweldens and P. Schr öder, editors. Digital Geometry Processing. SIGGRAPH Conference course notes, 2001.Google Scholar
  80. 80.
    A. Szymczak, J. Rossignac, and D. King. Piecewise regular meshes: Construction and compression. Graphical.models., 2003.Google Scholar
  81. 81.
    G. Taubin. Geometric signal processing on polygonal meshes. In Euroraphics 2000: State of the Art Report (STAR). Eurographics, 2000.Google Scholar
  82. 82.
    J.R. Tristano, S.J. Owen, and S.A. Canann. Advancing Front Surface Mesh Generation in Parametric Space Using a Riemannian Surface Definition. In Proceedings of the 7th Int. Meshing Roundtable, 1998.Google Scholar
  83. 83.
    Greg Turk. Re-tiling polygonal surfaces. Computer graphics proceedings, annual conference series: SIGGRAPH conference proceedings, pages 55-64, 1992.Google Scholar
  84. 84.
    Sebastien Valette and Jean Marc Chassery. Approximated centroidal voronoi diagrams for uniform polygonal mesh coarsening. Computer Graphics Forum, 2004.Google Scholar
  85. 85.
    A. Vlachos, J. Peters, C. Boyd, and J. L. Mitchell. Curved PN triangles. In Symposium on Interactive 3D Graphics, pages 159-166, 2001.Google Scholar
  86. 86.
    J. Vorsatz, C. R össl, L. Kobbelt, and H.-P. Seidel. Feature sensitive remeshing. Computer Graphics Forum, pages 393-401, 2001.Google Scholar
  87. 87.
    J. Vorsatz, C. R össl, and H.-P. Seidel. Dynamic remeshing and applications. In SMA ’03: Proceedings of the 3th ACM Symposium on Solid Modeling and Applications 2003, pages 167-175. ACM Press, 2003.Google Scholar
  88. 88.
    D.J. Walton and D.S. Meek. A triangular G1 patch from boundary curves. Computer Aided Design, 28(2):113-123, 1996.CrossRefGoogle Scholar
  89. 89.
    Jianhua Wu and Leif Kobbelt. Structure recovery via hybrid variational surface approximation. Computer Graphics Forum, 24(3):277-284, 2005.Google Scholar
  90. 90.
    Soji Yamakawa and Kenji Shimada. Triangular/quadrilateral remeshing of an arbitrary polygonal surface via packing bubbles. In Proceedings of Geometric Modeling and Processing 2004, Los Alamitos, 2004. IEEE Computer Society.Google Scholar
  91. 91.
    Dong-Ming Yan, Yang Liu, and Wenping Wang. Quadric surface extraction by variational shape approximation. In Proceedings of Geometric Modeling and Processing 2006, 2006.Google Scholar
  92. 92.
    D. Zorin and P. Schr öder. Subdivision for modeling and animation. Computer graphics proceedings, annual conference series: SIGGRAPH conference proceedings, 2000.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Pierre Alliez
    • 1
  • Giuliana Ucelli
    • 2
  • Craig Gotsman
    • 3
  • Marco Attene
    • 4
  1. 1.INRIA, Sophia-AntipolisFrance
  2. 2.IGD / GraphiTechItaly
  3. 3.Technion - Israel Institute of TechnologyHaifaIsrael
  4. 4.IMATI-GE, CNRItaly

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