Advertisement

Harmonic Variation of Edge Size in Meshing CAD Geometries from IGES Format

  • Maharavo Randrianarivony
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5102)

Abstract

We shall describe a mesh generation technique on a closed CAD surface composed of a few parametric surfaces. The edge size function is a fundamental entity in order to be able to apply the process of generalized Delaunay triangulation with respect to the first fundamental form. Unfortunately, the edge size function is not known a-priori in general. We describe an approach which invokes the Laplace-Beltrami operator to determine it. We will discuss theoretically the functionality of our methods. Our approach is illustrated by numerical results from the harmonicity of triangulations of some CAD objects. The IGES format is used in order to acquire the initial geometries.

Keywords

Geometric modeling IGES mesh generation CAD models edge size Delaunay 

References

  1. 1.
    Borouchaki, H., George, P.: Aspects of 2-D Delaunay Mesh Generation. Int. J. Numer. Methods Eng. 40(11), 1957–1975 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Bossen, F., Heckbert, P.: A Pliant Method for Anisotropic Mesh Generation. In: 5th International Meshing Roundtable Sandia National Laboratories, pp. 63–76 (1996)Google Scholar
  3. 3.
    Brunnett, G.: Geometric Design with Trimmed Surfaces. Computing Supplementum 10, 101–115 (1995)Google Scholar
  4. 4.
    Edelsbrunner, H., Tan, T.: An Upper Bound for Conforming Delaunay Triangulations. Discrete Comput. Geom. 10, 197–213 (1993)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Farin, G.: Curves and Surfaces for Computer Aided Geometric Design: A Practical Guide. Academic Press, Boston (1997)zbMATHGoogle Scholar
  6. 6.
    Frey, P., Borouchaki, H.: Surface Mesh Quality Evaluation. Int. J. Numer. Methods Eng. 45(1), 101–118 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Graham, I., Hackbusch, W., Sauter, S.: Discrete Boundary Element Methods on General Meshes in 3D. Numer. Math. 86(1), 103–137 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Kolingerova, I.: Genetic Approach to Triangulations. In: 4th International Conference on Computer Graphics and Artificial Intelligence, France, pp. 11–23 (2000)Google Scholar
  9. 9.
    O’Rourke, J.: Computational Geometry in C. Cambridge Univ. Press, Cambridge (1998)zbMATHGoogle Scholar
  10. 10.
    Randrianarivony, M.: Geometric Processing of CAD Data and Meshes as Input of Integral Equation Solvers. PhD thesis, Technische Universität Chemnitz (2006)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Maharavo Randrianarivony
    • 1
  1. 1.Institute of Computer ScienceChristian-Albrecht University of KielKielGermany

Personalised recommendations