Skip to main content
Springer Nature Link
Log in

Applications of heat-diffusion equation for surface wrapping: hole detection and normal orientation

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

Abstract

This paper presents a method for detecting holes during the surface wrapping process which cause surface leaks into the volume parts that shall not be meshed. The method solves a heat-diffusion equation on the background octree mesh, which is generated based on user-defined parameters, and its resolution corresponds to the resolution of the wrapper surface mesh. The heat problem is posed with the constant heat source in the volume, and the holes are detected as regions of high temperature gradients. The method detects both holes with open-boundary edges and semantic holes due to some missing parts. The sensitivity of the method is controlled via user-adjustable parameter which represents the ratio between the volume that shall not be meshed and the area of the hole. In addition, it is demonstrated that the method can be used to correct the orientation of normals in the surface mesh by utilising the property that high temperature is always found inside the volume. The potential of the method is presented on complex engineering examples.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18

Similar content being viewed by others

Explore related subjects

Discover the latest articles and news from researchers in related subjects, suggested using machine learning.

References

  1. Bendels GH, Schnabel R, Klein R (2006) Detecting Holes in Point Set Surfaces. In: Proceedings of 14th International Conference in Central Europe on Computer Graphics, Visualization and Computer Vision

  2. Branch J, Prieto F, Boulanger P (2006) A Hole-Filling Algorithm for Triangular Meshes Using Local Radial Basis Function. In: Proceedings of 15th International Meshing Roundtable, pp 411–431

  3. Carr JC, Beatson RK, Cherrie JB, Mitchell TJ, Fright WR, McCallum BC, Evans TR (2001) Reconstruction and representation of 3D objects with Radial Basis Functions. In: Proceedings of SIGRAPH 2001: Proceedings of the 28th annual conference on Computer graphics and interactive techniques, pp 67–76

  4. Davidson L (1996) A pressure correction methods for unstructured meshes with arbitrary control volumes. Int J Numer Methods Fluids 22:265–281

    Article  MATH  Google Scholar 

  5. Davis J, Marschner S, Garr M, Levoy M (2002) Filling holes in complex surfaces using volumetric diffusion. In: Proceedings of First International Symposium on 3D Data Processing, Visualization and Transmission, vol 11

  6. Dinh HQ, Turk G, Slabaugh G (2001) Reconstructing surfaces using anisotropic basis functions. In: Proceedings of International Conference on Computer Vision, pp 606–613

  7. Escobar JM, Rodriguez E, Montenegro R, Montero G, Gonzalez-Yuste JM (2003) Simultaneous untangling and smoothing of tetrahedral meshes. Comput Methods Appl Mech Eng 192:2775–2787

    Article  MATH  Google Scholar 

  8. Ferziger J, Perić M (1996) Computational Methods for Fluid Dynamics. Springer, Berlin

    Book  MATH  Google Scholar 

  9. Garimella RV, Swartz BK (2003) Curvature estimation for unstructured triangulations of surfaces. In: Technical Report LA-UR-03-8240, Los Alamos National Laboratory

  10. Garimella RV, Shashkov MJ, Knupp PM (2002) Optimization of surface mesh quality using local parametrization. In: Proceedings of 11th International Meshing Roundtable, pp 41–52

  11. Incropera FP, DeWitt DP (2001) Fundamentals of heat and mass transfer, 5th edn. Wiley, New York (ISBN: 978-0-471-20448-0)

  12. Jasak H (1996) Error analysis and estimation in the finite volume method with applications to fluid flows. In: PhD Thesis, Imperial College, University of London, London

  13. Kobbelt LP, Vorsatz J, Labsik U, Seidel HP (1999) A shrink wrapping approach to remeshing polygonal surfaces. Comput Graph Forum 18:119–130

    Article  Google Scholar 

  14. Kumar A, Shih AM (2011) Hybrid approach for repair of geometry with complex topology. In: Proceedings of 20th International Meshing Roundtable, pp 387–403

  15. Lee YK, Lim CK, Ghazilam H, Vardhan H, Eklund E (2006) Surface mesh generation for dirty geometries by shrink wrapping using Cartesian grid approach. In: Proceedings of 15th International Meshing Roundtable, pp 393–410

  16. Lindstrom P (2000) Out-of-core simplification of large polygonal models. In: Proceedings of SIGGRAPH 2000, pp 259–262

  17. Lorensen WE, Cline HE (1987) Marching cubes: a high resolution 3D surface construction algorithm. Comput Graph 21:163–169

    Article  Google Scholar 

  18. Rosen D (2008) Seamless Intersection Between Triangle Meshes. In Proceedings: Senior Conference on Computational Geometry, pp 1–8

  19. Sanchez GT, Branch JW, Atencio P (2010) A metric for automatic hole characterization. In: Proceedings of 19th International Meshing Roundtable, pp 195–208

  20. Schilling A, Bidmon K, Sommer O, Ertl T (2008) Filling arbitrary holes in finite element models. In: Proceedings of 17th International Meshing Roundtable, pp 231–248

  21. Schroeder WJ, J. A. Zarge JA, Lorensen WE. (1992) Decimation of triangle meshes. In: Proceedings of SIGGRAPH 1992, pp 65–70

  22. Shapira Y (2003) Matrix-based multigrid: theory and applications. Springer, Berlin (ISBN 1402074859)

  23. Veleba D, Felkel P (2007) Survey of errors in surface representation and their detection and correction, WSCG 07. In: Proceedings of the 15th International Conference in Central Europe on Computer Graphics, Visualization and Computer Vision, Plzen-Bory, Czech Republic

  24. Vollmer J, Mencl R, Muller H (1999) Improved Laplacian smoothing of noisy surface meshes. Comput Graph Forum 131–138

  25. Wang ZJ, Srinivasan K (2002) An adaptive Cartesian grid generation method for ’Dirty’ geometry. Int J Numer Methods Fluids 39:703–717

    Article  MATH  Google Scholar 

  26. Whitaker RT (1998) A Level-set approach to 3D reconstruction from range data. Int J Comput Vision 29:203–231

    Article  Google Scholar 

  27. Zhao HK, Osher S, Fedkiw R (2001) Fast surface reconstruction using the level set method. In: Proceedings of IEEE Workshop on Variational and Level Set Methods in Computer Vision (VLSM 2001), pp 194–201

Download references

Author information

Authors and Affiliations

  1. AVL-AST d.o.o, Avenija Dubrovnik 10/III, 10020, Zagreb, Croatia

    Franjo Juretić

  2. AVL GmbH, Alte Poststrasse 152, Graz, Austria

    Norbert Putz

Authors
  1. Franjo Juretić
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Norbert Putz
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Franjo Juretić.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Juretić, F., Putz, N. Applications of heat-diffusion equation for surface wrapping: hole detection and normal orientation. Engineering with Computers 30, 363–374 (2014). https://doi.org/10.1007/s00366-012-0304-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00366-012-0304-8

Keywords