Skip to main content
SpringerLink
Log in

A general framework for analysis and comparison of surface mesh optimization techniques

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

Abstract

Many different algorithms for surface mesh optimization (including smoothing, remeshing, simplification and subdivision), each giving different results, have recently been proposed. All these approaches affect vertices of the mesh. Vertex coordinates are modified, new vertices are added and some original ones are removed, with the result that the shape of the original surface is changed. The important question is how to evaluate the differences in shape between the input and output models. In this paper, we present a novel and versatile framework for analysis of various mesh optimization algorithms in terms of shape preservation. We depart from the usual strategy by measuring the changes in the approximated smooth surfaces rather than in the corresponding meshes. The proposed framework consists of two error metrics: normal-based and physically based. We demonstrate that our metrics allow more subtle changes in shape to be captured than is possible with some commonly used measures. As an example, the proposed tool is used to compare three different techniques, reflecting basic ideas on how to solve the surface mesh improvement problem.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

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. Strang G, Fix GJ (1973) An analysis of the finite element method. Prentice Hall, Englewood Cliffs

    MATH  Google Scholar 

  2. Hoppe H, Duchamp T, McDonald J, Stuetzle W (1993) Mesh optimization. In: Computer graphics (SIGGRAPH’93) pp 19–26

  3. Surazhsky V, Gotsman C (2003) Explicit surface remeshing. In: Proceedings of eurographics symposium on geometry processing, pp 17–28

  4. Alboul L, van Damme R (1997) Polyhedral metrics in surface reconstruction: tight triangulations, the mathematics of surfaces VII. Clarendon Press, Oxford, pp 309–336

    Google Scholar 

  5. Dyn N, Hormann K, Kim S-J, Levin D (2001) Optimizing 3D triangulations using discrete curvature analysis, mathematical methods for curves and surfaces. Vanderbilt University Press, Innovations in Applied Mathematics Series, pp 135–146

  6. Garimella RV, Shashkov MJ, Knupp PM (2004) Triangular and quadrilateral surface mesh quality optimization using local parameterization, Comput Meth Appl Mech Eng 193(9–11):913–928

    Article  MATH  Google Scholar 

  7. Frey P, Borouchaki H (1998) Geometric surface mesh optimization. Computer and Visualization in Science, pp 113–121

  8. Knupp PM (2000) Achieving finite element mesh quality via optimization of the Jacobian matrix norm and associated quantities. Int J Numer Meth Eng 48:401–420

    Article  MATH  Google Scholar 

  9. Heckbert PS, Garland M (1997) Survey of polygonal surface simplification algorithms. In: SIGGRAPH’97 course notes: multiresolution surface modeling

  10. Loop C (1987) Smooth subdivision surfaces based on triangles. Master’s thesis. University of Utah, Department of Mathematics

  11. Dyn N, Levin D, Gregory JA (1990) A butterfly subdivision scheme for surface interpolation with tension control. ACM Trans Graph 9(2):160–169

    Article  MATH  Google Scholar 

  12. Zorin D, Schroder P, Sweldens W (1996) Interpolating subdivision for meshes with arbitrary topology. In: SIGGRAPH’96, conference proceedings, pp 189–192

  13. Cignoni P, Rocchini C, Scopigno R (1998) Metro: measuring error on simplified surfaces. Comput Graph Forum 17(2):167–174

    Article  Google Scholar 

  14. Belyaev A, Ohtake Y (2003) A comparison of mesh smoothing methods. In: Israel-Korea bi-national conference modeling and computer graphics, pp 83–87

  15. Karbacher S, Seeger S, Hausler G (2000) A non-linear subdivision scheme for triangle meshes. In: Vision, modeling and visualization 2000, pp 163–170

  16. Karbacher S, Seeger S, Hausler G (2001) Refining triangle meshes by non-linear subdivision. In: Proceedings of 3rd international conference on 3D digital imaging and modeling, IEEE Computer Society, pp 270–277

  17. Anoshkina EV, Belyaev AG, Seidel H-P (2002) Asymptotic analysis of three-point approximations of vertex normals and curvatures. In: Vision, modeling, and visualization 2002, pp 211–216

  18. Vlachos A, Peters J, Boyd C, Mitchell JL (2001) Curved PN triangles, In: Symposium on interactive 3D graphics, pp 159–166

  19. Floater MS (1997) Parameterization and smooth approximation of surface triangulation. Comput Aid Geomet Des 14:231–250

    Article  MATH  MathSciNet  Google Scholar 

  20. Hormann K, Lasik U, Greiner G (2001) Remeshing triangulated surface with optimal parameterization. Comput Aid Des 33(11):779–788

    Article  Google Scholar 

  21. Canann SA, Tristano JR, Staten ML (1998) An approach to combined Laplacian and optimization-based smoothing for triangular, quadrilateral, and quad-dominant meshes. In: Proceedings of the 7th international meshing roundtable, pp 479–494

  22. Semenova I, Savchenko V, Hagiwara I (2004) Two techniques to improve mesh quality and preserve surface characteristics. In: Proceedings in 13th international meshing roundtable, pp 277–288

  23. Semenova I, Savchenko V, Hagiwara I (2004) Improvement of triangular and quadrilateral surface meshes. In: Proceedings in the 14th international conference on computer graphics and vision (GraphiCon’2004), pp 79–87

Download references

Author information

Authors and Affiliations

  1. Department of Mech. Sciences and Eng., Tokyo Institute of Technology, Tokyo, Japan

    Irina Semenova, Nikita Kozhekin & Ichiro Hagiwara

  2. Faculty of Computer and Information Sciences, Hosei University, Tokyo, Japan

    Vladimir Savchenko

Authors
  1. Irina Semenova
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Nikita Kozhekin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Vladimir Savchenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ichiro Hagiwara
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Irina Semenova.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Semenova, I., Kozhekin, N., Savchenko, V. et al. A general framework for analysis and comparison of surface mesh optimization techniques. Engineering with Computers 21, 91–100 (2005). https://doi.org/10.1007/s00366-005-0305-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00366-005-0305-y

Keywords

Search

Navigation