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On Quadratic Splines and Their CAD-Application

  • Ferenc Fenyves
  • George Kovács
Conference paper

Abstract

One of the important tasks of computer aided engineering design in geometric modeling. Because of theoretical and computational reasons most practical CAD-systems use parametric curves and surfaces (most commonly parametric cubic segments) in geometric modeling. Most basic ideas involved are presented in the survey paper [3] of Böhm, Farin and Kahmann, 1984. Our paper deals with quadratic splines and their application for curve and surface representation. The basic problem is to present a method for obtaining a smooth bivariate function which takes on certain prescribed values. The collection of these values is assumed to be on a rectangular grid, that is, for every point (xi, yj) on the rectangular grid {xi} i=0 n × {yj} j=0 m there is a given value zij.

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References

  1. [1]
    Ahlberg, J.H. — Nilson, E.N. — Walsh, J.L., (1967). The theory of splines and their applications. Academic Press, New York.zbMATHGoogle Scholar
  2. [2]
    de Boor, C., (1978). Apractical guide to splines. Springer-Verlag, New York-Heidelberg-Berlin.CrossRefGoogle Scholar
  3. [3]
    Böhm, W. — Farin, G. — Kahmann, J., (1984). A survey of curve and surface methods in CAGD. Computer Aided Geometric Design, Vol. 1. pp. 1–60.CrossRefzbMATHGoogle Scholar
  4. [4]
    Fenyves, F. — Licskó, I. — Kovács, G., (1983). Translation-surfaces in the 3D subsystem of the COMECON NC programming system. Proceeding of ICED,83, Kobenhavn (WDK 10) Vol.1. pp.105–112.Google Scholar
  5. [5]
    Forrest, A.R., (1972). On Coons and other methods for the representation of curved surfaces. Computer Graphics and Image Processing. Vol.1. pp. 341–359.CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  • Ferenc Fenyves
    • 1
  • George Kovács
    • 1
  1. 1.Computer and Automation InstituteHungarian Academy of SciencesBudapestHungary

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