Skip to main content
Top
Published in: Engineering with Computers 2/2013

01-04-2013 | Original Article

A local adaptation-based generation method of medial axis for efficient engineering analysis

Authors: Yusheng Liu, Chuhua Xian, Ming Li, Haibin Xia, Shuming Gao

Published in: Engineering with Computers | Issue 2/2013

Log in

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

search-config
loading …

Abstract

Currently engineering analysis is regarded as an integrated part of design process and medial axis (MA) is often utilized. However, the generation of MA of complicated models is computation intensive since it is always generated from scratch even if a tiny modification is imposed. A novel local adaptation-based approach to generating the MA for efficient engineering analysis is proposed in this study. With this method, the MA of a resultant model constructed from two other models via a Boolean operation or parameter modification is generated by adapting the MAs of the operand models in a certain way, instead of regenerating the MA from scratch. First, several new properties of the MA which are the fundamental basis of the proposed method are investigated. Then, the boundaries that will vanish from or be added into the resultant model during the Boolean operation or parameter modification are found, and the region in which the MA segments (MASs) need to be regenerated is determined. Finally, the new MASs are generated for the region using an improved tracing method. The final MA of the resultant model is thus constructed by combining the newly generated MASs with the reserved MASs of the operated model(s). Some examples are given to illustrate the high computational efficiency of the proposed method for engineering analysis.

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 Blum H (1967) A transformation for extracting new descriptors of shape. Models for the Perception of Speech and Visual Form. MIT Press, Weinant Wathen-Dunn, pp 362–381 Blum H (1967) A transformation for extracting new descriptors of shape. Models for the Perception of Speech and Visual Form. MIT Press, Weinant Wathen-Dunn, pp 362–381
2.
go back to reference Ramanathan M, Gurumoorthy B (2002) Constructing medial axis transform of planar domains with curved boundaries. Comput Aided Des 35:619–632CrossRef Ramanathan M, Gurumoorthy B (2002) Constructing medial axis transform of planar domains with curved boundaries. Comput Aided Des 35:619–632CrossRef
3.
go back to reference Patrikalakis NM, Maekawa T (2002) Shape interrogation for computer aided design and manufacturing. Springer, BerlinMATH Patrikalakis NM, Maekawa T (2002) Shape interrogation for computer aided design and manufacturing. Springer, BerlinMATH
4.
go back to reference Hesselink WH, Roerdink JBTM (2008) Euclidean skeletons of digital image and volume data in linear time by the integer medial axis transform. IEEE Trans PAMI 30(12):2204–2217 Hesselink WH, Roerdink JBTM (2008) Euclidean skeletons of digital image and volume data in linear time by the integer medial axis transform. IEEE Trans PAMI 30(12):2204–2217
5.
6.
go back to reference Held M (2001) VRONI. An engineering approach to the reliable and efficient computation of Voronoi diagrams of points and line segments. Comput Geom 18:95–123MathSciNetMATHCrossRef Held M (2001) VRONI. An engineering approach to the reliable and efficient computation of Voronoi diagrams of points and line segments. Comput Geom 18:95–123MathSciNetMATHCrossRef
7.
go back to reference Lee DT (1982) Medial axis transformation of a planar shape. IEEE Pattern Anal Mach Intell 4:363–369MATHCrossRef Lee DT (1982) Medial axis transformation of a planar shape. IEEE Pattern Anal Mach Intell 4:363–369MATHCrossRef
8.
9.
go back to reference Aichholzer O, Aigner W, Aurenhammer F et al (2009) Medial axis computation for planar free_form shapes. Comput Aided Des 41:339–349CrossRef Aichholzer O, Aigner W, Aurenhammer F et al (2009) Medial axis computation for planar free_form shapes. Comput Aided Des 41:339–349CrossRef
10.
go back to reference Nackman LR (1982) Curvature relations in three-dimensional symmetric axes. Comput Graph Image Process 20:43–57MATHCrossRef Nackman LR (1982) Curvature relations in three-dimensional symmetric axes. Comput Graph Image Process 20:43–57MATHCrossRef
11.
go back to reference Bookstein FL (1979) The line skeleton. Comput Graph Image Process 11:123–137CrossRef Bookstein FL (1979) The line skeleton. Comput Graph Image Process 11:123–137CrossRef
12.
go back to reference Scott GL, Turner SC, Zisserman A (1989) Using a mixed wave diffusion process to elicit the symmetry set. Image Vis Comput 7(1):63–70CrossRef Scott GL, Turner SC, Zisserman A (1989) Using a mixed wave diffusion process to elicit the symmetry set. Image Vis Comput 7(1):63–70CrossRef
13.
go back to reference Siddiqi K, Bouix S, Tannenbaum A, et al. (1999) The Hamilton-Jacobi skeleton. In: International Conference on Computer Vision (ICCV), pp 828–834 Siddiqi K, Bouix S, Tannenbaum A, et al. (1999) The Hamilton-Jacobi skeleton. In: International Conference on Computer Vision (ICCV), pp 828–834
14.
15.
go back to reference Hoff KE, Keyser J, Lin M, et al (1999) Fast computation of generalized Voronoi diagrams using graphics hardware. Comput Graph 33(Annual Conference Series):277–286 Hoff KE, Keyser J, Lin M, et al (1999) Fast computation of generalized Voronoi diagrams using graphics hardware. Comput Graph 33(Annual Conference Series):277–286
16.
go back to reference Vleugels J, Overmars M (1995) Approximating generalized Voronoi diagrams in any dimension. Technical Report UU-CS-95-14, Department of computer science, Utrecht University Vleugels J, Overmars M (1995) Approximating generalized Voronoi diagrams in any dimension. Technical Report UU-CS-95-14, Department of computer science, Utrecht University
17.
go back to reference Foskey M, Lin M, Manocha D (2003) Efficient computation of a simplified MA. In: CD proceedings of the ACM symposium on solid and physical modeling Foskey M, Lin M, Manocha D (2003) Efficient computation of a simplified MA. In: CD proceedings of the ACM symposium on solid and physical modeling
19.
go back to reference Lee DT (1982) MA transformation of a planar shape. IEEE Trans Pattern Anal Mach Intell 4(4):363–369MATHCrossRef Lee DT (1982) MA transformation of a planar shape. IEEE Trans Pattern Anal Mach Intell 4(4):363–369MATHCrossRef
20.
go back to reference Srinivasan V, Nackman LR (1987) Voronoi diagram for multiply connect polygonal domains, I: algorithm. IBM J Res Dev 31(3):361–372MathSciNetCrossRef Srinivasan V, Nackman LR (1987) Voronoi diagram for multiply connect polygonal domains, I: algorithm. IBM J Res Dev 31(3):361–372MathSciNetCrossRef
21.
go back to reference Gursoy HN, Patrikalakis NM (1991) Automated interrogation and adaptive subdivision of shape using MA transform. Adv Eng Softw Workstn 13(5/6):287–302CrossRef Gursoy HN, Patrikalakis NM (1991) Automated interrogation and adaptive subdivision of shape using MA transform. Adv Eng Softw Workstn 13(5/6):287–302CrossRef
22.
go back to reference Gursoy HN, Patrikalakis NM (1992) An automated coarse and fine surface mesh generation scheme based on MA transform, part I: algorithms. Eng Comput 8(3):121–137CrossRef Gursoy HN, Patrikalakis NM (1992) An automated coarse and fine surface mesh generation scheme based on MA transform, part I: algorithms. Eng Comput 8(3):121–137CrossRef
23.
go back to reference Gursoy HN, Patrikalakis NM (1992) An automated coarse and fine surface mesh generation scheme based on MA transform, part II: implementation. Eng Comput 8(4):179–196CrossRef Gursoy HN, Patrikalakis NM (1992) An automated coarse and fine surface mesh generation scheme based on MA transform, part II: implementation. Eng Comput 8(4):179–196CrossRef
24.
go back to reference Culver T, Keyser J, Manocha D (1998) Accurate computation of MA of a polyhedron. Technical Report TR98-034, UNC-Chapel Hill Culver T, Keyser J, Manocha D (1998) Accurate computation of MA of a polyhedron. Technical Report TR98-034, UNC-Chapel Hill
26.
go back to reference Choset H (1997) Incremental construction of the generalized Voronoi diagram, the generalized Voronoi graph, and the hierarchical generalized Voronoi graph. In: 1st CGC workshop on computation geometry Choset H (1997) Incremental construction of the generalized Voronoi diagram, the generalized Voronoi graph, and the hierarchical generalized Voronoi graph. In: 1st CGC workshop on computation geometry
27.
go back to reference Chiang C-S (1992) The Euclidean distance transform. Ph.D. thesis, Department of Computer Science, Purdue University, West Lafayette, Report CSD-TR 92-050 Chiang C-S (1992) The Euclidean distance transform. Ph.D. thesis, Department of Computer Science, Purdue University, West Lafayette, Report CSD-TR 92-050
28.
go back to reference Sherbrooke EC, Patrikalakis NM, Brisson E (1995) Computation of MA transform of 3-D polyhedral. In: ACM solid modeling, pp 187–199 Sherbrooke EC, Patrikalakis NM, Brisson E (1995) Computation of MA transform of 3-D polyhedral. In: ACM solid modeling, pp 187–199
29.
go back to reference Reddy JM, Turkiyyah GM (1995) Computation of 3D skeletons using a generalized Delaunay triangulations technique. Comput Aided Des 27(9):677–694MATHCrossRef Reddy JM, Turkiyyah GM (1995) Computation of 3D skeletons using a generalized Delaunay triangulations technique. Comput Aided Des 27(9):677–694MATHCrossRef
30.
go back to reference Dutta D, Hoffmann CM (1990) A geometric investigation of the skeleton of CSG objects. UM-MEAM-90-02 Dutta D, Hoffmann CM (1990) A geometric investigation of the skeleton of CSG objects. UM-MEAM-90-02
31.
go back to reference Cao L, Jia Z, Liu J (2009) Computation of medial axis and offset curves of curved boundaries in planar domains based on the Cesaro’s approach. Comput Aided Geom Des 26:444–454MathSciNetMATHCrossRef Cao L, Jia Z, Liu J (2009) Computation of medial axis and offset curves of curved boundaries in planar domains based on the Cesaro’s approach. Comput Aided Geom Des 26:444–454MathSciNetMATHCrossRef
32.
go back to reference Cao T, Tang K, Mohamed A, Tan T (2010) Parallel banding algorithm to compute exact distance transform with the GPU. In: Proceedings of the ACM SIGGRAPH symposium on interactive 3D graphics and games (I3D). New York, 19–21 Feb 2010 Cao T, Tang K, Mohamed A, Tan T (2010) Parallel banding algorithm to compute exact distance transform with the GPU. In: Proceedings of the ACM SIGGRAPH symposium on interactive 3D graphics and games (I3D). New York, 19–21 Feb 2010
33.
go back to reference Lavender D, Bowyer A, Davenport J et al (1992) Voronoi diagrams of set-theoretic solid models. IEEE Comp Graph Appl 12(5):69–77CrossRef Lavender D, Bowyer A, Davenport J et al (1992) Voronoi diagrams of set-theoretic solid models. IEEE Comp Graph Appl 12(5):69–77CrossRef
34.
go back to reference Brandt JW (1994) Convergence and continuity criteria for discrete approximations of the continuous planar skeleton. CVGIP: Image Underst 59(1):116–124CrossRef Brandt JW (1994) Convergence and continuity criteria for discrete approximations of the continuous planar skeleton. CVGIP: Image Underst 59(1):116–124CrossRef
35.
go back to reference Dey TK, Woo H, Zhao W (2003) Approximate MA for CAD models. In: Proceedings of the solid and physical modeling 2003, Seattle, Washington, 16–20 June, 2003 Dey TK, Woo H, Zhao W (2003) Approximate MA for CAD models. In: Proceedings of the solid and physical modeling 2003, Seattle, Washington, 16–20 June, 2003
36.
go back to reference Sheehy DJ, Armstrong CG, Robinson DJ (1996) Numerical computation of medial surface vertices. In: Mullineux G (ed) The mathematics of Surfaces VI. IMA, Oxford University Press, Oxford Sheehy DJ, Armstrong CG, Robinson DJ (1996) Numerical computation of medial surface vertices. In: Mullineux G (ed) The mathematics of Surfaces VI. IMA, Oxford University Press, Oxford
37.
go back to reference Etzion M, Rappoport A (1999) Computing the Voronoi diagram of a 3D polyhedron by separate computation of its symbolic and geometric parts. in W. F. Bronsvoort and D. C. Anderson, editors. In: Proceedings of fifth symposium on solid molid modeling and applications, Ann Arbor, ACM, pp 167–168 Etzion M, Rappoport A (1999) Computing the Voronoi diagram of a 3D polyhedron by separate computation of its symbolic and geometric parts. in W. F. Bronsvoort and D. C. Anderson, editors. In: Proceedings of fifth symposium on solid molid modeling and applications, Ann Arbor, ACM, pp 167–168
38.
go back to reference Ramamurthy R, Farouki T (1999) Voronoi diagram and medial axis algorithm for planar domains with curved boundaries I: Theoretical foundations. J Comput Appl Math 102:119–141MathSciNetMATHCrossRef Ramamurthy R, Farouki T (1999) Voronoi diagram and medial axis algorithm for planar domains with curved boundaries I: Theoretical foundations. J Comput Appl Math 102:119–141MathSciNetMATHCrossRef
39.
go back to reference Joachim G, Balint M, Mark P (2007) Medial axis approximation of planar shapes from union of balls: a simpler and more robust algorithm. In: Canadian Conf. on Computational Geometry, Ottawa, Canada, 20–22 Aug, 2007 Joachim G, Balint M, Mark P (2007) Medial axis approximation of planar shapes from union of balls: a simpler and more robust algorithm. In: Canadian Conf. on Computational Geometry, Ottawa, Canada, 20–22 Aug, 2007
Metadata
Title
A local adaptation-based generation method of medial axis for efficient engineering analysis
Authors
Yusheng Liu
Chuhua Xian
Ming Li
Haibin Xia
Shuming Gao
Publication date
01-04-2013
Publisher
Springer-Verlag
Published in
Engineering with Computers / Issue 2/2013
Print ISSN: 0177-0667
Electronic ISSN: 1435-5663
DOI
https://doi.org/10.1007/s00366-012-0256-z

Other articles of this Issue 2/2013

Engineering with Computers 2/2013 Go to the issue