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An Efficient Approach for Surface Creation

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Computational Science and Its Applications – ICCSA 2005 (ICCSA 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3482))

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Abstract

In this paper, we present an efficient method for generation of free from surfaces using the solution to a fourth order partial differential equation. In the interest of computational efficiency, the surface function is taken to be the combination of the boundary functions modulated by some unknown functions. Making use of the properties of boundary functions, the fourth order partial differential equation is transformed into a fourth order ordinary differential equation. To solve this equation, we further convert it to a set of one-dimensional finite difference equations where the number of unknowns is reduced significantly allowing fast surface generation.

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References

  1. Farin, G.: Curves and Surfaces for Computer Aided Geometric Design: A Practical Guide, 4th edn. Academic Press, London (1997)

    MATH  Google Scholar 

  2. Sederberg, T.W., Parry, S.R.: Free-form deformation of solid geometric models. In: SIGGRAPH 1986, vol. 20, pp. 151–160 (1986)

    Google Scholar 

  3. Coquillart, S.: Extended free-form deformation: A sculpturing tool for 3D geometric modelling. In: SIGGRAPH 1990, vol. 24(4), pp. 187–193 (1990)

    Google Scholar 

  4. Bloor, M.I.G., Wilson, M.J.: Using partial differential equations to generate free-form surfaces. Computer-Aided Design 22(4), 202–212 (1990)

    Article  MATH  Google Scholar 

  5. Bloor, M.I.G., Wilson, M.J.: Representing PDE surfaces in terms of B-splines. Computer-Aided Design 22(6), 324–331 (1990)

    Article  MATH  Google Scholar 

  6. Zhang, J.J., You, L.H.: PDE based surface representation—Vase design. Computers and Graphics 26, 89–98 (2002)

    Article  Google Scholar 

  7. You, L.H., Zhang, J.J., Comninos, P.: Blending surface generation using a fast and accurate analytical solution of a fourth order PDE with three shape control parameters. The Visual Computer 20, 199–214 (2004)

    Article  Google Scholar 

  8. Zhang, J.J., You, L.H.: Fast surface modelling using a 6th order PDE. Computer Graphics Forum 23(3), 311–320 (2004)

    Article  Google Scholar 

  9. Monterde, J., Ugail, H.: On harmonic and biharmonic Bzier surfaces. Computer Aided Geometric Design 21(7), 697–715 (2004)

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. National Centre for Computer Animation, Bournemouth University, UK

    L. H. You & Jian J. Zhang

Authors
  1. L. H. You
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  2. Jian J. Zhang
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Editor information

Editors and Affiliations

  1. Department of Mathematics and Computer Science, University of Perugia, via Vanvitelli, 1, I-06123, Perugia, Italy

    Osvaldo Gervasi

  2. Department of Computer Science, University of Calgary, 2500 University Drive N.W., T2N 1N4, Calgary, AB, Canada

    Marina L. Gavrilova

  3. William Norris Professor, Head of the Computer Science and Engineering, Department University of Minnesota, USA

    Vipin Kumar

  4. Department of Chemistry, University of Perugia, Via Elce di Sotto, 8, I-06123, Perugia, Italy

    Antonio Laganà

  5. Institute of High Performance Computing, IHCP, 1 Science Park Road, 01-01 The Capricorn, Singapore Science Park II, 117528, Singapore

    Heow Pueh Lee

  6. School of Computing, Soongsil University, Seoul, Korea

    Youngsong Mun

  7. Clayton School of IT, Monash University, 3800, Clayton, Australia

    David Taniar

  8. OptimaNumerics Ltd, Belfast, United Kingdom

    Chih Jeng Kenneth Tan

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© 2005 Springer-Verlag Berlin Heidelberg

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You, L.H., Zhang, J.J. (2005). An Efficient Approach for Surface Creation. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2005. ICCSA 2005. Lecture Notes in Computer Science, vol 3482. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11424857_22

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  • DOI: https://doi.org/10.1007/11424857_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-25862-9

  • Online ISBN: 978-3-540-32045-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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