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Cubic Polynomial Curves and Surfaces

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Handbook of Computer Animation

Part of the book series: Springer Professional Computing ((SPC))

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Abstract

The purpose of this chapter is to introduce the reader to some of the most important concepts, mathematical techniques and algorithms relating to three-dimensional (3D) cubic polynomial curves and surfaces. These techniques are used in most current animation systems to represent the motion of computer-generated objects and to model their surfaces.

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Bibliography

  • Barsky, B.A., The beta-spline: a local representation based on shape parameters and fundamental geometric measures, PhD Dissertation, Dept of Computer Science, University of Utah, Salt Lake City, Utah 84112, 1981.

    Google Scholar 

  • Barsky, B.A., Computer Graphics and Geometric Modelling Using Beta-splines, Springer-Verlag, 1988.

    Google Scholar 

  • Barsky, B.A. and Beatty, J.C., Local control of bias and tension in beta-splines, ACM Transactions on Graphics, 2(2), 109–134, 1983.

    Article  MATH  Google Scholar 

  • Bartels, R.H., Beatty, J.C. and Barsky, B.A., An Introduction to Splines for use in Computer Graphics Modeling, Morgan-Kaufman, pp. 422–434, 1987.

    Google Scholar 

  • Bézier, P., Définition numérique de courbes et surfaces I, Automatisme, Vol. XI, pp. 625–632, 1966.

    Google Scholar 

  • Bézier, P., Définition numérique de courbes et surfaces II, Automatisme, Vol. XII, pp. 17–21, 1967.

    Google Scholar 

  • Bézier, P., The Mathematical Basis of the Unisurf CAD System, Butterworths, 1986.

    Google Scholar 

  • Coons, S.A., Surfaces for computer aided design, Technical Report, Project MAC-TR-41, MIT, Cambridge, Massachusetts 02139,1964.

    Google Scholar 

  • Coons, S.A., Surfaces for computer aided design of space forms, Technical Report, Project MAC-TR-41, MIT, Cambridge, Massachusetts 02139, 1967. (Available as AD-663-504 from the National Information Service, Springfield, Virginia 22161.)

    Google Scholar 

  • de Casteljau, P., Outillage Méthodes Calcul, Citröen, 1959.

    Google Scholar 

  • de Casteljau, P., Courbes et Surfaces à Pôles, Citröen, 1963.

    Google Scholar 

  • de Casteljau, P., Shape Mathematics and CAD, Kogan Page, 1986.

    Google Scholar 

  • Gordon, W., Spline-blended surface interpolation through curve networks, Journal of Mathematics and Mechanics, 18(10), 931–952, 1969.

    MATH  Google Scholar 

  • Kochanek, D.H.U. and Bartels, R.H., Interpolating splines with local tension, continuity and bias control, Computer Graphics, SIGGRAPH-84 Conference Proceedings, 18(3), 33–41, 1984.

    Article  Google Scholar 

  • Seroussi, G. and Barsky, B.A., An explicit derivation of discretely shaped beta-spline basis functions of arbitrary order, Mathematical Methods in Computer-Aided Geometric Design II (Proceedings of the 191-91 Conference on Curves, Surfaces, CAGD and Image Processing), Lyche, T. and Schumaker, L.L. (eds.), Academic Press, pp. 667–584, 1992.

    Google Scholar 

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© 2003 Springer-Verlag London

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Comninos, P. (2003). Cubic Polynomial Curves and Surfaces. In: Vince, J. (eds) Handbook of Computer Animation. Springer Professional Computing. Springer, London. https://doi.org/10.1007/978-1-4471-0091-1_5

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  • DOI: https://doi.org/10.1007/978-1-4471-0091-1_5

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-1106-1

  • Online ISBN: 978-1-4471-0091-1

  • eBook Packages: Springer Book Archive

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