Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
Implicit Boundary and Adaptive Anisotropic Meshing Read chapter Read first chapter

2015 | OriginalPaper | Chapter

A Curvature-Adapted Anisotropic Surface Re-meshing Method

Authors : Franco Dassi, Hang Si

Published in: New Challenges in Grid Generation and Adaptivity for Scientific Computing

Publisher: Springer International Publishing

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

We present a method for re-meshing surfaces in order to follow the intrinsic anisotropy of the surfaces. In particular, we use the information related to the normals to the surfaces, and embed the surfaces into a higher dimensional space (here we embed the surfaces in a six-dimensional space). This allows us to settle an isotropic mesh optimization problem in this embedded space: starting from an initial mesh of a surface, we optimize the mesh by improving the mesh quality measured in the embedded space. The mesh is optimized by properly combining common local mesh operations, i.e., edge flipping, edge contraction, vertex smoothing, and vertex insertion. All operations are applied directly on the three-dimensional surface mesh and the resulting mesh is curvature adapted. This new method improves the approach proposed by Lévy and Bonneel (Variational anisotropic surface meshing with Voronoi parallel linear enumeration. In: Proceedings of the 21st International Meshing Roundtable, pp. 349–366. Springer, New York, 2013), by allowing to preserve sharp features. The reliability and robustness of the proposed re-meshing technique is shown via a number of examples.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
previous chapter Implicit Boundary and Adaptive Anisotropic Meshing
next chapter The Benefits of Anisotropic Mesh Adaptation for Brittle Fractures Under Plane-Strain Conditions
Literature
1.
Alliez, P., Cohen-Steiner, D., Devillers, O., Lévy, B., Desbrun, M.: Anisotropic polygonal remeshing. ACM Trans. Graph. 22(3), 485–493 (2003)CrossRef
2.
Alliez, P., De Verdire, E., Devillers, O., Isenburg, M.: Isotropic surface remeshing. In: Shape Modeling International, 2003, pp. 49–58. IEEE (2003)
3.
Alliez, P., Ucelli, G., Gotsman, C., Attene, M.: Recent advances in remeshing of surfaces. In: Shape Analysis and Structuring, pp. 53–82. Springer, New York (2008)
4.
Aurenhammer, F.: Voronoi diagrams a survey of a fundamental geometric data structure. ACM Comp. Surv. 23(3), 345–405 (1991)CrossRef
5.
Boissonnat, J.D., Wormser, C., Yvinec, M.: Locally uniform anisotropic meshing. In: Proceedings of the Twenty-Fourth Annual Symposium on Computational geometry, pp. 270–277. ACM, New York (2008)
6.
7.
Bossen, F.J., Heckbert, P.S.: A pliant method for anisotropic mesh generation. In: 5th International Meshing Roundtable, pp. 63–74. Citeseer (1996)
8.
Cañas, G.D., Gortler, S.J.: Surface remeshing in arbitrary codimensions. Vis. Comput. 22(9–11), 885–895 (2006)CrossRef
9.
Canas, G.D., Gortler, S.J.: Shape operator metric for surface normal approximation. In: Proceedings of the 18th International Meshing Roundtable, pp. 447–461. Springer, New York (2009)
10.
 Chen, L., Sun, P., Xu, J.: Optimal anisotropic meshes for minimizing interpolation errors in L p -norm. Math. Comput. 76(257), 179–204 (2007)CrossRefMATHMathSciNet
11.
Cheng, S.W., Dey, T.K., Ramos, E.A., Wenger, R.: Anisotropic surface meshing. In: Proceedings of the Seventeenth Annual ACM-SIAM Symposium on Discrete Algorithm, pp. 202–211. ACM, New York (2006)
12.
Cheng, S.W., Dey, T.K., Levine, J.A.: A practical Delaunay meshing algorithm for a large class of domains. In: Proceedings of the 16th International Meshing Roundtable, pp. 477–494. Springer, New York (2008)
13.
de Cougny, H.L., Shephard, M.S.: Surface meshing using vertex insertion. In: Proceedings of the 5th International Meshing Roundtable, pp. 243–256. Citeseer (1996)
14.
 Dobrzynski, C., Frey, P.: Anisotropic Delaunay mesh adaptation for unsteady simulations. In: Proceedings of the 17th International Meshing Roundtable, pp. 177–194. Springer, New York (2008)
15.
 Du, Q., Wang, D.: Anisotropic centroidal Voronoi tessellations and their applications. SIAM J. Sci. Comput. 26(3), 737–761 (2005)CrossRefMATHMathSciNet
16.
 Du, Q., Faber, V., Gunzburger, M.: Centroidal Voronoi tessellations: applications and algorithms. SIAM Rev. 41(4), 637–676 (1999)CrossRefMATHMathSciNet
17.
 Edelsbrunner, H.: Geometry and Topology for Mesh Generation. Cambridge University Press, Cambridge (2001)CrossRefMATH
18.
19.
 El-Hamalawi, A.: Mesh generation—application to finite elements. Eng. Constr. Archit. Manag. 8(3), 234–235 (2001)CrossRef
20.
Field, D.A.: Laplacian smoothing and Delaunay triangulations. Commun. Appl. Numer. Methods 4(6), 709–712 (1988)CrossRefMATH
21.
22.
Frey, P.J., Alauzet, F.: Anisotropic mesh adaptation for CFD computations. Comput. Methods Appl. Mech. Eng. 194(48), 5068–5082 (2005)CrossRefMATHMathSciNet
23.
Frey, P.J., Borouchaki, H.: Geometric surface mesh optimization. Comput. Vis. Sci. 1(3), 113–121 (1998)CrossRefMATH
24.
Heckbert, P.S., Garland, M.: Optimal triangulation and quadric-based surface simplification. Comput. Geol. 14(1), 49–65 (1999)CrossRefMATHMathSciNet
25.
Hoppe, H.: Progressive meshes. In: Proceedings of the 23rd Annual Conference on Computer Graphics and Interactive Techniques, pp. 99–108. ACM, New York (1996)
26.
Hoppe, H., DeRose, T., Duchamp, T., McDonald, J., Stuetzle, W.: Mesh optimization. In: Proceedings of the 20th Annual Conference on Computer Graphics and Interactive Techniques, pp. 19–26. ACM, New York (1993)
27.
28.
Jiao, X., Colombi, A., Ni, X., Hart, J.: Anisotropic mesh adaptation for evolving triangulated surfaces. Eng. Comput. 26(4), 363–376 (2010)CrossRef
29.
Kimmel, R., Malladi, R., Sochen, N.: Images as embedded maps and minimal surfaces: movies, color, texture, and volumetric medical images. Int. J. Comput. Vis. 39(2), 111–129 (2000)CrossRefMATH
30.
31.
 Labelle, F., Shewchuk, J.R.: Anisotropic Voronoi diagrams and guaranteed-quality anisotropic mesh generation. In: Proceedings of the Nineteenth Annual Symposium on Computational Geometry, pp. 191–200. ACM, New York (2003)
32.
Lai, Y.K., Zhou, Q.-Y., Hu, S.-M., Wallner, J., Pottmann, D., et al.: Robust feature classification and editing. IEEE Trans. Vis. Comput. Graph. 13(1), 34–45 (2007)CrossRef
33.
Lawson, C.L.: Software for C 1 surface interpolation. In: Mathematical Software III, pp. 164–191. Academic, New York (1977)
34.
Lévy, B., Bonneel, N.: Variational anisotropic surface meshing with Voronoi parallel linear enumeration. In: Proceedings of the 21st International Meshing Roundtable, pp. 349–366. Springer, New York (2013)
35.
Lévy, B., Liu, Y.: l p centroidal Voronoi tessellation and its applications. ACM Trans. Graph. 29(4), 119 (2010)
36.
Liu, Y., Wang, W., Lévy, B., Sun, F., Yan, D.-M., Lu, L., Yang, C.: On centroidal Voronoi tessellation energy smoothness and fast computation. ACM Trans. Graph. 28(4), 101 (2009)CrossRef
37.
Loseille, A., Alauzet, F.: Continuous mesh framework part I: well-posed continuous interpolation error. SIAM J. Numer. Anal. 49(1), 38–60 (2011)CrossRefMATHMathSciNet
38.
Loseille, A., Alauzet, F.: Continuous mesh framework part II: validations and applications. SIAM J. Numer. Anal. 49(1), 61–86 (2011)CrossRefMATHMathSciNet
39.
Mirebeau, J.M.: Optimally adapted meshes for finite elements of arbitrary order and W 1, p norms. Numer. Math. 120, 271–305 (2012)
40.
Owen, S.J., White, D.R., Tautges, T.J.: Facet-based surfaces for 3d mesh generation. In: IMR, pp. 297–311 (2002)
41.
Pottmann, H., T. Steiner, T., Hofer, M., Haider, C., Hanbury, A.: The Isophotic Metric and its Application to Feature Sensitive Morphology on Surfaces. Springer, New York (2004)
42.
43.
Shewchuk, J.R.: What is a good linear element? Interpolation, conditioning, and quality measures. In: Proceedings of 11th International Meshing Roundtable, pp. 115–126 (2002)
44.
Zhong, Z., Guo, X., Wang, W., Lévy, B., Sun, F., Liu, Y., Mao, W.: Particle-based anisotropic surface meshing. ACM Trans. Graph. 32(4), 99 (2013)CrossRef
Metadata
Title
A Curvature-Adapted Anisotropic Surface Re-meshing Method
Authors
Franco Dassi
Hang Si
Copyright Year
2015
Book
New Challenges in Grid Generation and Adaptivity for Scientific Computing

Print ISBN: 978-3-319-06052-1

Electronic ISBN: 978-3-319-06053-8

Copyright Year: 2015

DOI
https://doi.org/10.1007/978-3-319-06053-8_2

Premium Partner

    Image Credits