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Reconstructing high-order surfaces for meshing

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Abstract

We consider the problem of reconstructing a high-order surface from a given surface mesh. This problem is important for many meshing operations, such as generating high-order finite elements, mesh refinement, mesh smoothing, and mesh adaptation. We introduce two methods called Weighted Averaging of Local Fittings and Continuous Moving Frames. These methods are both based on weighted least squares polynomial fittings and guarantee C 0 continuity. Unlike existing methods for reconstructing surfaces, our methods are applicable to surface meshes composed of triangles and/or quadrilaterals, can achieve third and even higher order accuracy, and have integrated treatments for sharp features. We present the theoretical framework of our methods, their accuracy, continuity, experimental comparisons against other methods, and applications in a number of meshing operations.

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References

  1. Frey PJ, George PL (2000) Mesh generation: application to finite elements. Hermes, Lavoisier

    MATH  Google Scholar 

  2. Donea J, Huerta A, Ponthot J-P, Rodriguez-Ferran A (2004) Arbitrary Lagrangian–Eulerian methods. In: Stein E, de Borst R, Hughes TJ (eds) Encyclopedia of computational mechanics, chap. 14. Wiley, New York

  3. Jiao X, Colombi A, Ni X, Hart J (2010) Anisotropic mesh adaptation for evolving triangulated surfaces. Eng Comput 26:363–376

    Article  Google Scholar 

  4. Fleishman S, Cohen-Or D, Silva CT (2005) Robust moving least-squares fitting with sharp features. ACM Trans Comput Graph (TOG) 24(3):544–552

    Google Scholar 

  5. Walton D (1996) A triangular G1 patch from boundary curves. Comput Aid Des 28(2):113–123

    Article  Google Scholar 

  6. Hughes TJR, Cottrell JA, Bazilevs Y (2005) Isogeometric analysis: CAD, finite elements, NURBS, exact geometry, and mesh refinement. Comput Methods Appl Mech Eng 194:4135–4195

    Article  MathSciNet  MATH  Google Scholar 

  7. Jiao X, Wang D (2010) Reconstructing high-order surfaces for meshing. In: Proceedings of 19th International Meshing Roundtable, pp 143–160

  8. Jiao X, Zha H (2008) Consistent computation of first- and second-order differential quantities for surface meshes. In: ACM Solid and Physical Modeling Symposium, pp 159–170. ACM

  9. Wang D, Clark B, Jiao X (2009) An analysis and comparison of parameterization-based computation of differential quantities for discrete surfaces. Comput Aid Geometric Des 26(5):510–527

    Article  MathSciNet  MATH  Google Scholar 

  10. Heath MT (2002) Scientific computing: an introductory survey, 2nd edn. McGraw–Hill, New York

    Google Scholar 

  11. Golub GH, Van Loan CF (1996) Matrix computation 3rd edn. Johns Hopkins, Baltimore

    Google Scholar 

  12. Lancaster P, Salkauskas K (1986) Curve and Surface Fitting: An Introduction. Academic Press, London

    MATH  Google Scholar 

  13. Levin D (1998) The approximation power of moving least-squares. Math Comput 67:1517–1531

    Article  MATH  Google Scholar 

  14. Frey PJ (2001) Yams: a fully automatic adaptive isotropic surface remeshing procedure. Tech. rep. INRIA (2001). RT-0252

  15. Frey PJ (2000) About surface remeshing. In: Proceedings of 9th International Meshing Roundtable, pp 123–136

  16. Jiao X (2006) Volume and feature preservation in surface mesh optimization. In: Proceedings of 15th International Meshing Roundtable

  17. Jiao X, Bayyana N (2008) Identification of C 1 and C 2 discontinuities for surface meshes in CAD. Comput Aid Des 40:160–175

    Article  Google Scholar 

  18. Garimella R (2004) Triangular and quadrilateral surface mesh quality optimization using local parametrization. Comput Meth Appl Mech Eng 193(9–11):913–928

    Article  MATH  Google Scholar 

  19. Semenova IB, Savchenko VV, Hagiwara I (2004) Two techniques to improve mesh quality and preserve surface characteristics. In: Proceedings of 13th International Meshing Roundtable, pp 277–288

  20. Jiao X, Wang D, Zha H (2008) Simple and effective variational optimization of surface and volume triangulations. In: Proceedings of 17th International Meshing Roundtable, pp 315–332

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Acknowledgments

This work was supported by National Science Foundation under award number DMS-0809285. The first author is also supported by DOE NEUP program under contract #DE-AC07-05ID14517 and by DoD-ARO under contract #W911NF0910306. We thank Navamita Ray for her help with testing the oscillation safeguards presented in this paper.

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Authors and Affiliations

  1. Department of Applied Mathematics, Stony Brook University, Stony Brook, NY, 11794, USA

    Xiangmin Jiao & Duo Wang

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  1. Xiangmin Jiao
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  2. Duo Wang
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Correspondence to Xiangmin Jiao.

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Jiao, X., Wang, D. Reconstructing high-order surfaces for meshing. Engineering with Computers 28, 361–373 (2012). https://doi.org/10.1007/s00366-011-0244-8

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  • DOI: https://doi.org/10.1007/s00366-011-0244-8

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