Geometry in Design: The Bezier Method

  • Gerald Farin
Part of the The IMA Volumes in Mathematics and Its Applications book series (IMA, volume 14)


The Bezier method for the representation of polynomial curves and surfaces is outlined, with emphasis on a geometric viewpoint. Several examples are given to underline the usefulness of the geometric approach to curve and surface design.


Bernstein Polynomial Spline Curve Bezier Curve Control Polygon Auxiliary Point 


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  1. P. Alfeld (1987): A case study of multivariate piecewise polynomials, in: Geometric Mod-ding, G. Farin (ed.), SIAM, 149–159.Google Scholar
  2. C. de Boor (1987): B-form basics, in: Geometric Modeling, G. Farin (ed.), SIAM, 131–148.Google Scholar
  3. R. Bartels, J. Beatty, B. Barsky (1987): An Introduction to the Use of Splines in Computer Graphics, Morgan-Kaufmann.Google Scholar
  4. W. Boehm (1977): Cubic B-spline curves and surfaces in CAGD, Computing 19, 29–34.MathSciNetCrossRefMATHGoogle Scholar
  5. W. Boehm(1987): Smooth curves and surfces, in: Geometric Modeling, G. Farin (ed.), SIAM, 175–184.Google Scholar
  6. W. Boehm, G. Farin, J. Kahmann (1984): A survey of curve and surface methods in CAGD, Computer Aided Geometric Design 1, 1–60.CrossRefMATHGoogle Scholar
  7. P. de Casteljau (1963): Courbes et surfaces à pôles; André Citroen, Paris.Google Scholar
  8. G. Farin (1982): Visually C2 cubic splines, Computer Aided Design 14, 137–139.CrossRefGoogle Scholar
  9. G. Farin (1986): Triangular Bernstein-Bezier patches, CAGD 3, 83–128.MathSciNetGoogle Scholar
  10. G. Farin (1987): The commutativity of tensor product and Boolean surface schemes. Being revised.Google Scholar
  11. R. Farouki and V. Rajan (1987): On the numerical condition of Bernstein polynomials, to appear in CAGD.Google Scholar
  12. R. Forrest (1972): Interactive interpolation and approximation by Bezier polynomials, The Computer Journal 15, 71–79.MathSciNetMATHGoogle Scholar
  13. W. Gordon and R. Riesenfeld (1974): B-spline curves and surfaces, in: Computer Aided Geometric Design, R. Barnhill and R. Riesenfeld (eds.), Academic Press, 95–126.Google Scholar
  14. G. Nielson (1974): Some piecewise polynomial alternatives to splines under tesnion, in: Computer Aided Geometric Design, R Barnhill and R. Riesenfeld (eds.), Academic Press, 209–235.Google Scholar
  15. I. Schoenberg (1946): Contributions to the problem of approximation of equidistant data by analytic functions, Quart. Appl. Math 4, 45–99.Google Scholar

Copyright information

© Springer-Verlag New York Inc. 1988

Authors and Affiliations

  • Gerald Farin
    • 1
  1. 1.Arizona State UniversityTempeUSA

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