Skip to main content
Top
Published in: Engineering with Computers 3/2018

06-12-2017 | Original Article

Curvature-adapted remeshing of CAD surfaces

Authors: Franco Dassi, Andrea Mola, Hang Si

Published in: Engineering with Computers | Issue 3/2018

Log in

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

search-config
loading …

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.

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

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!

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!

Literature
1.
go back to reference Alliez P, Ucelli G, Gotsman C, Attene Marco (2008) Recent advances in remeshing of surfaces. In: Shape analysis and structuring, mathematics and visualization. Springer 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.
go back to reference Boissonnat J-D, Shi K-L, Tournois J, Yvinec M (2015) Anisotropic delaunay meshes of surfaces. ACM Trans Graph 34(2):14:1–14:11CrossRefMATH Boissonnat J-D, Shi K-L, Tournois J, Yvinec M (2015) Anisotropic delaunay meshes of surfaces. ACM Trans Graph 34(2):14:1–14:11CrossRefMATH
3.
go back to reference 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 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.
go back to reference Hiltebeitel AM, Gauss CF, Morehead JC (1902) General investigations of curved surfaces of 1827 and 1825. The Princeton university library, Princeton Hiltebeitel AM, Gauss CF, Morehead JC (1902) General investigations of curved surfaces of 1827 and 1825. The Princeton university library, Princeton
5.
go back to reference Cañas GD, Gortler SJ (2006) Surface remeshing in arbitrary codimensions. Vis Comput 22(9–11):885–895CrossRef Cañas GD, Gortler SJ (2006) Surface remeshing in arbitrary codimensions. Vis Comput 22(9–11):885–895CrossRef
6.
go back to reference 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 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.
go back to reference 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 19–41MATH 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 19–41MATH
8.
go back to reference 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 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.
go back to reference Field David A (1988) Laplacian smoothing and Delaunay triangulations. Commun Appl Numer Methods 4(6):709–712CrossRefMATH Field David A (1988) Laplacian smoothing and Delaunay triangulations. Commun Appl Numer Methods 4(6):709–712CrossRefMATH
10.
go back to reference Michael S (2005) Floater and Kai Hormann. Advances in multiresolution for geometric modelling, Berlin Michael S (2005) Floater and Kai Hormann. Advances in multiresolution for geometric modelling, Berlin
11.
go back to reference Frey PJ, Borouchaki H (1998) Geometric surface mesh optimization. Comput Vis Sci 1(3):113–121CrossRefMATH Frey PJ, Borouchaki H (1998) Geometric surface mesh optimization. Comput Vis Sci 1(3):113–121CrossRefMATH
12.
go back to reference Heckbert Paul S, Garland Michael (1999) Optimal triangulation and quadric-based surface simplification. Comput Geometry 14(13):49–65MathSciNetCrossRefMATH Heckbert Paul S, Garland Michael (1999) Optimal triangulation and quadric-based surface simplification. Comput Geometry 14(13):49–65MathSciNetCrossRefMATH
13.
go back to reference Hoppe H (1996) Progressive meshes. In: Proceedings of the 23rd annual conference on Computer graphics and interactive techniques, ACM, pp 99–108 Hoppe H (1996) Progressive meshes. In: Proceedings of the 23rd annual conference on Computer graphics and interactive techniques, ACM, pp 99–108
14.
go back to reference 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 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.
go back to reference Jiao X, Colombi A, Ni X, Hart J (2010) Anisotropic mesh adaptation for evolving triangulated surfaces. Eng Comput 26(4):363–376CrossRef Jiao X, Colombi A, Ni X, Hart J (2010) Anisotropic mesh adaptation for evolving triangulated surfaces. Eng Comput 26(4):363–376CrossRef
16.
go back to reference Kim H-S, Kim H-S (2009) New computation of normal vector and curvature. W Trans Comp 8(10):1661–1670MATH Kim H-S, Kim H-S (2009) New computation of normal vector and curvature. W Trans Comp 8(10):1661–1670MATH
17.
go back to reference 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):34–45CrossRef 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):34–45CrossRef
18.
go back to reference 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):34–45CrossRef 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):34–45CrossRef
19.
go back to reference Laug P, Borouchaki H (2012) Proceedings of the 20th International Meshing Roundtable. Berlin, Heidelberg Laug P, Borouchaki H (2012) Proceedings of the 20th International Meshing Roundtable. Berlin, Heidelberg
20.
go back to reference Lawson CL (1977) Software for C1 surface interpolation. In: Rice JR (ed) Mathematical Software III. Academic Press, New York, pp 161–194CrossRef Lawson CL (1977) Software for C1 surface interpolation. In: Rice JR (ed) Mathematical Software III. Academic Press, New York, pp 161–194CrossRef
21.
go back to reference 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 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.
go back to reference Medioni G (2000) Tensor voting: theory and applications Medioni G (2000) Tensor voting: theory and applications
23.
go back to reference Mola A, Heltai L, DeSimone A (2014) A fully nonlinearpotential model for ship hydrodynamics directly interfaced with CAD data structures Mola A, Heltai L, DeSimone A (2014) A fully nonlinearpotential model for ship hydrodynamics directly interfaced with CAD data structures
24.
go back to reference 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 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
26.
go back to reference 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 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
Metadata
Title
Curvature-adapted remeshing of CAD surfaces
Authors
Franco Dassi
Andrea Mola
Hang Si
Publication date
06-12-2017
Publisher
Springer London
Published in
Engineering with Computers / Issue 3/2018
Print ISSN: 0177-0667
Electronic ISSN: 1435-5663
DOI
https://doi.org/10.1007/s00366-017-0558-2

Other articles of this Issue 3/2018

Engineering with Computers 3/2018 Go to the issue