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Accurate and Fast Algorithm for the Plotting of Contours Using Eight Node Quadrilateral Meshes

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Abstract

A fast algorithm for plotting of contours using eight-node quadrilateral elements is described in this communication. The contours are accurately generated over each element using the interpolation functions. The exactness of the contours matches that of the finite element analysis. The contour joining algorithm discussed here is considerably faster than the existing technique.

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References

  1. O.C. Zienkiewicz, The Finite Element Method (Tata McGraw Hill, New Delhi, 2002)

    Google Scholar 

  2. D.F. Wiley, H.R. Childs, B. Hamann, K.I. Joy, N.L. Max, Best quadratic spline approximation for hierarchical visualization, in Data Visualization 2002, Proceedings of VisSym 2002, 133–140, 2002

  3. D.L. Logan, Finite Element Method (Cengage Learning India Pvt. Ltd., New Delhi, 2008)

    Google Scholar 

  4. J.L. Meek, G. Beer, Contour plotting of data using isoparametric element representation. Int. J. Numer. Methods Eng. 10(1), 954–957 (1976)

    Article  Google Scholar 

  5. J.E. Akin, W.H. Gray, Contouring on isoparametric surfaces. Int. J. Numer. Methods Eng. 11, 1893–1897 (1977)

    Article  Google Scholar 

  6. W.H. Gray, J.E. Akin, An improved method for contouring on isoparametric surfaces. Int. J. Numer. Methods Eng. 14, 451–472 (1979)

    Article  Google Scholar 

  7. J.F. Lyness, L. Asquith, A simple contour plotting program for finite element output. Adv. Eng. Softw. 5(1), 23–31 (1983)

    Article  Google Scholar 

  8. G.D. Kontopidis, D.E. Limbert, A predictor-corrector contouring algorithm for isoparametric 3D elements. Int. J. Numer. Methods Eng. 19, 995–1004 (1983)

    Article  MATH  Google Scholar 

  9. M.F. Yeo, An interactive contour plotting program. Eng. Comput. 1, 273–279 (1984)

    Article  Google Scholar 

  10. S. Rajasekaran, A note on plotting curves. Comput. Struct. 19, 497–500 (1984)

    Article  Google Scholar 

  11. A. Preusser, Computing contours by successive solution of quintic polynomial equations. ACM Trans. Math. Softw. 10(4), 463–472 (1984)

    Article  MathSciNet  Google Scholar 

  12. G. Farin, Triangular bernstein-bezier patches. Comput. Aided Geom. Des. 3, 83–128 (1986)

    Article  MathSciNet  Google Scholar 

  13. W.E. Lorensen, H.E. Cline, Marching cubes: a high resolution 3D surface construction algorithm. Comput. Graph. 21(4), 163–169 (1987)

    Article  Google Scholar 

  14. S.R. Yates, Contur: a fortran algorithm for two-dimensional high quality contouring. Comput. Geosci. 13(1), 61–76 (1987)

    Article  Google Scholar 

  15. J.F. Stelzer, R. Welzel, Plotting of contours in a natural way. Int. J. Numer. Methods Eng. 24, 1757–1796 (1987)

    Article  MATH  Google Scholar 

  16. R.R. Dickinson, R.H. Bartels, A.H. Vermeulen, The interactive editing and contouring of empirical fields. IEEE Comput. Graph. Appl. 9(3), 34–43 (1989)

    Article  Google Scholar 

  17. A.J. Worsey, G. Farin, Contouring a bivariate quadratic polynomial over a triangle. Comput. Aided Geom. Des. 7(1–4), 337–352 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  18. K.J. Berry, Parametric finite element contour mapping. Comput. Struct. 35(3), 249–257 (1990)

    Article  MATH  Google Scholar 

  19. C. Singh, Comments on a simple algorithm for the plotting of contours. Commun. Appl. Numer. Methods 6(3), 191–195 (1990)

    Article  MATH  Google Scholar 

  20. C. Singh, D. Sarkar, A simple and fast algorithm for the plotting of contours using quadrilateral meshes. Finite Elem. Anal. Des. 7, 217–228 (1990)

    Article  Google Scholar 

  21. M.J. Twu, B.P. Wang, A new method for contour plotting in finite element analysis. Comput. Struct. 45, 1097–1102 (1992)

    Article  Google Scholar 

  22. T.C. Gopalakrishnan, M. Korttom, An algorithm for contouring and interpolation of data using bilinear finite elements. Finite Elem. Anal. Des. 14, 37–54 (1993)

    Article  MATH  Google Scholar 

  23. S. Rajasekaran, K.G. Venkatesan, A new contouring algorithm. Comput. Struct. 54(5), 953–977 (1995)

    Article  MATH  Google Scholar 

  24. B. Hamann, I.J. Trotts, G. Farin, On approximating contours of the piecewise trilinear interpolant using triangular rational-quadratic bézier patches. IEEE Trans. Vis. Comput. Graph. 3(3), 215–227 (1997)

    Article  Google Scholar 

  25. D.F. Wiley, H.R. Childs, B.F. Gregorski, B. Hamann, K.I. Joy, Contouring curved quadratic elements, in Joint Eurographics-IEEE TCVG Symposium on Visualization, 167–177, 2003

  26. E.L. Bradbury, W.H. Enright, Fast contouring of solutions to partial differential equations. ACM Trans. Math. Softw. 29(4), 418–439 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  27. I. Jaworska, An effective contour plotting method for presentation of the postprocessed results. Computer Vision and Graphics. Comput. Imaging Vis. Ser. 32: 1112–1117, 2006

  28. C. Singh, J. Singh, Accurate contour plotting using 6-node triangular elements in 2D. Finite Elem. Anal. Des. 45, 81–93 (2009)

    Article  Google Scholar 

  29. D. Hearn, M.P. Baker, Computer Graphics with OpenGL (Pearson Education, India, 2009)

    Google Scholar 

  30. R. Subramanian, Strength of Materials (Oxford University Press, India, 2005)

    Google Scholar 

  31. S. Sadhu, Strength of Materials (Khanna Publishers, India, 2008)

    Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical Engineering, Thapar University, Patiala, 147004, Punjab, India

    Jaswinder Singh Saini

  2. Department of Computer Science, Punjabi University, Patiala, 147 002, Punjab, India

    Chandan Singh

Authors
  1. Chandan Singh
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  2. Jaswinder Singh Saini
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Correspondence to Jaswinder Singh Saini.

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Singh, C., Saini, J.S. Accurate and Fast Algorithm for the Plotting of Contours Using Eight Node Quadrilateral Meshes. J. Inst. Eng. India Ser. B 96, 311–325 (2015). https://doi.org/10.1007/s40031-014-0151-7

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  • DOI: https://doi.org/10.1007/s40031-014-0151-7

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