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Controllable highly regular triangulation

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Abstract

This paper presents a novel algorithm for generating a highly regular triangle mesh under various user requirements. Three scalar fields are first computed on the input mesh. Then, the intersections of their isocontours with one another are used to construct the highly regular mesh result. The proposed algorithm uses the N-symmetry direction field to guide the edge orientation. Size control is achieved by using a density function on the surface. All user requirements are incorporated into an energy optimization framework of the scalar fields, and then the isocontours of the generated scalar fields are used to construct a high quality result that satisfies all requirements. The experimental results show that the proposed method can successfully handle various user requirements and complex shapes.

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References

  1. Shewchuk J R. What is a good linear element? Interpolation, conditioning and quality measures. In: 11th Int Meshing Rountable, 2002. 115–126

  2. Zorin D, Schröder P, Sweldens W. Interactive multiresolution mesh editing. In: Proceedings of ACM SIGGRAPH 97. Citeseer, 1997. 259–268

  3. Khodakovsky A, Schroder P, Sweldens W. Progressive geometry compression. In: Proceedings of ACM SIGGRAPH 2000, Citeseer, 2000. 271–278

  4. Alliez P, Meyer M, Desbrun M. Interactive Geometry Remeshing. ACM Trans Graph (Special issue for SIGGRAPH Conference), 2002, 21: 347–354

    Google Scholar 

  5. Alliez P, de Verdi`ere É C, Olivier D, et al. Isotropic surface remeshing. In: Proceedings of Shape Modeling International, Seoul, Korea, 2003. 49–58

  6. Surazhsky V, Alliez P, Gotsman C. Isotropic remeshing of surfaces: a local parameterization approach. In: Proceedings of 12th International Meshing Roundtable, Sandia National Laboratories, 2003. 215–224

  7. Alliez P, Ucelli G, Gotsman C, et al. Recent advances in remeshing of surfaces. In: de Floriani L, Spagnuolo M, eds. Shape Analysis and Structuring, Mathematics and Visualization. Berlin: Springer, 2008. 53–82

    Chapter  Google Scholar 

  8. Ick M, DeRose T, Duchamp T, et al. Multiresolution analysis of arbitrary meshes. In: Proceedings of the 22nd Annual Conference on Computer Graphics and Interactive Techniques, Los Angeles, California, USA, 1995. 173–182

  9. Aaron W, Lee F, Sweldens W, et al. Maps: multiresolution adaptive parameterization of surfaces. In: Proceedings of SIGGRAPH, Orlando, FL, USA, 1998. 95–104

  10. Khodakovsky A, Litke N, Schroder P. Globally smooth parameterizations with low distortion. ACM Trans Graph, 2003, 22: 350–357

    Article  Google Scholar 

  11. Hoppe H. Progressive meshes. In: Computer Graphics (SIG-GRAPH’ 96 Proceedings), New York, USA, 1996. 99–108

  12. Garland M, Heckbert P S. Surface simplification using quadric error metrics. In: Proceedings of ACM SIGGRAPH 1997, Los Angeles, CA, USA, 1997. 209–216

  13. Hormann K, Labsik U, Günther G. Remeshing triangulated surfaces with optimal parameterizations. Comput-Aid Des, 2001, 33: 779–788

    Article  MATH  Google Scholar 

  14. Wood Z J, Schröder P, Breen D, et al. Semi-regular mesh extraction from volumes. In: Proceedings of the conference on Visualization’00. Los Alamitos, California: IEEE Computer Society Press, 2000. 275–282

    Google Scholar 

  15. Szymczak A, Rossignac J, King D. Piecewise regular meshes: Construction and compression. Graph Models, 2002, 64: 183–198

    Article  MATH  Google Scholar 

  16. Surazhsky V, Gotsman C. Explicit surface remeshing. In: Proceedings of Eurographics Symposium on Geometry Processing, Aachen, Germany, 2003. 17–28

  17. Ray N, Li W C, Lévy B. Periodic global parameterization. ACM Trans Graph, 2006, 25: 1460–1485

    Article  Google Scholar 

  18. Palacios J, Zhang E. Rotational symmetry field design on surfaces. ACM Trans Graph, 2007, 26: 1–55

    Article  Google Scholar 

  19. Bommes D, Zimmer H, Kobbelt L. Mixed-integer quadrangulation. ACM Trans Graph, 2009, 28: 1–10

    Article  Google Scholar 

  20. Ray N, Vallet B, Li W C, et al. N-symmetry direction field design. ACM Trans Graph, 2008, 27: 1–13

    Article  Google Scholar 

  21. Davis T A. A column pre-ordering strategy for the unsymmetric-pattern multifrontal method. ACM Trans Math Softw, 2004, 30: 165–195

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. CAD&CG State Key Lab of Zhejiang University, Hangzhou, 310058, China

    Jin Huang, MuYang Zhang, WenJie Pei, Wei Hua & HuJun Bao

Authors
  1. Jin Huang
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  2. MuYang Zhang
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  3. WenJie Pei
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  4. Wei Hua
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  5. HuJun Bao
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Correspondence to Wei Hua.

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Huang, J., Zhang, M., Pei, W. et al. Controllable highly regular triangulation. Sci. China Inf. Sci. 54, 1172–1183 (2011). https://doi.org/10.1007/s11432-011-4261-4

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  • DOI: https://doi.org/10.1007/s11432-011-4261-4

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