Spherical Harmonics for Surface Parametrisation and Remeshing

Article English OPEN
Nortje, Caitlin R. ; Ward, Wil O. C. ; Neuman, Bartosz P. ; Bai, Li (2015)
  • Publisher: Hindawi Publishing Corporation
  • Journal: Mathematical Problems in Engineering (issn: 1024-123X, eissn: 1563-5147)
  • Related identifiers: doi: 10.1155/2015/582870
  • Subject: TA1-2040 | Mathematics | Engineering (General). Civil engineering (General) | QA1-939 | Article Subject
    arxiv: Statistics::Computation | Mathematics::Numerical Analysis | Computer Science::Numerical Analysis

This paper proposes a novel method for parametrisation and remeshing incomplete and irregular polygonal meshes. Spherical harmonics basis functions are used for parametrisation. This involves least squares fitting of spherical harmonics basis functions to the surface mesh. Tikhonov regularisation is then used to improve the parametrisation before remeshing the surface. Experiments show that the proposed techniques are effective for parametrising and remeshing polygonal meshes.
  • References (33)
    33 references, page 1 of 4

    [1] H. Borouchaki, P. Laug, and P.-L. George, “Parametric surface meshing using a combined advancing-front generalized delaunay approach,” International Journal for Numerical Methods in Engineering, vol. 49, no. 1-2, pp. 233-259, 2000.

    [2] Y. Zheng, N. P. Weatherill, and O. Hassan, “Topology abstraction of surface models for three-dimensional grid generation,” Engineering with Computers, vol. 17, no. 1, pp. 28-38, 2001.

    [3] D. L. Marcum, “Eficient generation of high-quality unstructured surface and volume grids,” Engineering with Computers, vol. 17, no. 3, pp. 211-233, 2001.

    [4] P. Laug and H. Borouchaki, “Interpolating and meshing 3D surface grids,” International Journal for Numerical Methods in Engineering, vol. 58, no. 2, pp. 209-225, 2003.

    [5] B. Le´vy, S. Petitjean, N. Ray, and J. Maillot, “Least squares conformal maps for automatic texture atlas generation,” ACM Transactions on Graphics, vol. 21, no. 3, pp. 362-371, 2002.

    [6] Y. Ito and K. Nakahashi, “Direct surface triangulation using stereolithography data,” AIAA Journal, vol. 40, no. 3, pp. 490- 496, 2002.

    [7] E. Be´chet, J.-C. Cuilliere, and F. Trochu, “Generation of a finite element MESH from stereolithography (STL) files,” ComputerAided Design, vol. 34, no. 1, pp. 1-17, 2002.

    [8] D. Wang, O. Hassan, K. Morgan, and N. Weatherill, “Enhanced remeshing from STL files with applications to surface grid generation,” Communications in Numerical Methods in Engineering, vol. 23, no. 3, pp. 227-239, 2007.

    [9] E. Marchandise, G. Compe`re, M. Willemet, G. Bricteux, C. Geuzaine, and J.-F. Remacle, “Quality meshing based on STL triangulations for biomedical simulations,” International Journal for Numerical Methods in Biomedical Engineering, vol. 26, no. 7, pp. 876-889, 2010.

    [10] D. M. B. de Siqueira, M. O. Freitas, J. B. Cavalcante-Neto, C. A. Vidal, and R. J. da Silva, “An adaptive parametric surface mesh generation method guided by curvatures,” in Proceedings of the 22nd International Meshing Roundtable, pp. 425-443, Springer, 2014.

  • Metrics
    No metrics available
Share - Bookmark