Skip to main content
Log in

Curvature-adapted remeshing of CAD surfaces

  • Original Article
  • Published:
Engineering with Computers Aims and scope Submit manuscript

Abstract

A common representation of surfaces with complicated topology and geometry is through composite parametric surfaces. This is the case for most CAD modelers. The majority of these models focus on having a good approximation of the surface itself, but they are usually built without taking into account a subsequent mesh generation. Indeed they are often characterized by too many patches which are not logically connected and make a standard mesh generator fail. In this work, we present a novel mesh generation strategy that can handle such “bad” input data and produces an anisotropic curvature-adapted surface mesh. There are two main ingredients to achieve this goal. First of all, we define a new and fast way to project point on an input model which overcomes the presence of non-connected patches. Then we consider the higher embedding strategy to build the final anisotropic surface mesh.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  1. Alliez P, Ucelli G, Gotsman C, Attene Marco (2008) Recent advances in remeshing of surfaces. In: Shape analysis and structuring, mathematics and visualization. Springer

  2. Boissonnat J-D, Shi K-L, Tournois J, Yvinec M (2015) Anisotropic delaunay meshes of surfaces. ACM Trans Graph 34(2):14:1–14:11

    Article  MATH  Google Scholar 

  3. Bossen Frank J, Heckbert Paul S (1996) A pliant method for anisotropic mesh generation. In: Proceedings of the 5th International Meshing Roundtable, pp 63–74, Albuquerque, NM, Sandia National Laboratories

  4. Hiltebeitel AM, Gauss CF, Morehead JC (1902) General investigations of curved surfaces of 1827 and 1825. The Princeton university library, Princeton

    Google Scholar 

  5. Cañas GD, Gortler SJ (2006) Surface remeshing in arbitrary codimensions. Vis Comput 22(9–11):885–895

    Article  Google Scholar 

  6. Cheng S-W, Dey Tamal K, Ramos Edgar A, Wenger R (2006) Anisotropic surface meshing. In: Proceedings of the Seventeenth Annual ACM-SIAM Symposium on Discrete Algorithm, SODA ’06, pages 202–211, Philadelphia, PA, USA. Society for Industrial and Applied Mathematics

  7. Dassi Franco, Si Hang (2015) New challenges in grid generation and adaptivity for scientific computing, chapter A curvature-adapted anisotropic surface re-meshing method. Springer International Publishing, Cham, pp 19–41

    MATH  Google Scholar 

  8. de Cougny Hugues L, Shephard Mark S (1996) Surface meshing using vertex insertion. In: Proceedings of the 5th International Meshing Roundtable, Citeseer, pp 243–256

  9. Field David A (1988) Laplacian smoothing and Delaunay triangulations. Commun Appl Numer Methods 4(6):709–712

    Article  MATH  Google Scholar 

  10. Michael S (2005) Floater and Kai Hormann. Advances in multiresolution for geometric modelling, Berlin

    Google Scholar 

  11. Frey PJ, Borouchaki H (1998) Geometric surface mesh optimization. Comput Vis Sci 1(3):113–121

    Article  MATH  Google Scholar 

  12. Heckbert Paul S, Garland Michael (1999) Optimal triangulation and quadric-based surface simplification. Comput Geometry 14(13):49–65

    Article  MathSciNet  MATH  Google Scholar 

  13. Hoppe H (1996) Progressive meshes. In: Proceedings of the 23rd annual conference on Computer graphics and interactive techniques, ACM, pp 99–108

  14. Hoppe H, DeRose T, Duchamp T, McDonald J, Stuetzle W (1993) Mesh optimization. In: Proceedings of the 20th annual conference on Computer graphics and interactive techniques, ACM, pp 19–26

  15. Jiao X, Colombi A, Ni X, Hart J (2010) Anisotropic mesh adaptation for evolving triangulated surfaces. Eng Comput 26(4):363–376

    Article  Google Scholar 

  16. Kim H-S, Kim H-S (2009) New computation of normal vector and curvature. W Trans Comp 8(10):1661–1670

    MATH  Google Scholar 

  17. Lai Y-K, Zhou Q-Y, Shi-Min Hu, Wallner J, Pottmann Helmut (2007) Robust feature classification and editing. IEEE Trans Vis Comput Gr 13(1):34–45

    Article  Google Scholar 

  18. Lai Y-K, Zhou Q-Y, Shi-Min Hu, Wallner J, Pottmann Helmut (2007) Robust feature classification and editing. IEEE Trans Vis Comp Gr 13(1):34–45

    Article  Google Scholar 

  19. Laug P, Borouchaki H (2012) Proceedings of the 20th International Meshing Roundtable. Berlin, Heidelberg

  20. Lawson CL (1977) Software for C1 surface interpolation. In: Rice JR (ed) Mathematical Software III. Academic Press, New York, pp 161–194

    Chapter  Google Scholar 

  21. Lévy B, Bonneel N (2013) Variational anisotropic surface meshing with voronoi parallel linear enumeration. In: Proceedings of the 21st International Meshing Roundtable, Springer, pp 349–366

  22. Medioni G (2000) Tensor voting: theory and applications

  23. Mola A, Heltai L, DeSimone A (2014) A fully nonlinearpotential model for ship hydrodynamics directly interfaced with CAD data structures

  24. Owen Steven J, White David R, Tautges Timothy J (2002) Facet-based surfaces for 3d mesh generation. In: Proc. 11 th Int. Meshing Roundtable, pp 297–311

  25. Open Cascade S.A.S. Open cascade technology, 3d modeling & numerical simulation, 2010. http://www.opencascade.org

  26. Surazhsky V, Gotsman C (2003) Explicit surface remeshing. In: Proceedings of the 2003 Eurographics/ACM SIGGRAPH Symposium on Geometry Processing, SGP ’03, Aire-la-Ville, Switzerland, Switzerland, Eurographics Association, pp 20–30

Download references

Acknowledgements

The work of Franco Dassi was supported under the “Leibniz - DAAD Research Fellowship 2014”. The work of Andrea Mola was carried out in the context of the project OpenViewSHIP, “Sviluppo di un ecosistema computazionale per la progettazione idrodinamica del sistema elica-carena”, supported by Regione FVG - PAR FSC 2007-2013, Fondo per lo Sviluppo e la Coesione.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Franco Dassi.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dassi, F., Mola, A. & Si, H. Curvature-adapted remeshing of CAD surfaces. Engineering with Computers 34, 565–576 (2018). https://doi.org/10.1007/s00366-017-0558-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00366-017-0558-2

Keywords

Navigation