Advertisement

Spline Curve Fitting for an Interactive Design Environment

  • Christine Vercken
  • Christine Potier
  • Sylvie Vignes
Conference paper
Part of the NATO ASI Series book series (volume 40)

Abstract

In many graphical applications, it is necessary to build a geometrical curve model by fitting a set of data points such as the input of a digitizing tablet or a scanner. We propose an interactive spline smoothing method, particularly efficient when the data set is large, that have been implemented on a “graphic-mouse” microcomputer.

The user has to choose some parameters, such as the order of the curve and its continuity, and a spline curve is automatically fitted with as few control points as possible. By tuning the values of the different parameters, the user can compare different curves and select the most appropriate one that he can easily modify locally if necessary. The resulting curve has an analytical representation in the B-spline basis,device independent, and an approximate polygonal representation, based on the subdivision of its control polygon, whose accuracy is controlled by a parameter which can reflect the device definition. We present an algorithm to select a curve, which is pointed to with the mouse on the screen, using a hierarchical data structure, derived from the polygonal approximation.

Keywords

Control Point Spline Curve Polygonal Domain Bezier Curve Control Polygon 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. D.H. Ballard, Strip trees: A hierarchical representation for curves. Communication of ACM, 24, 5, may 1981, p. 320–321.CrossRefGoogle Scholar
  2. P. Bézier, Courbes et Surfaces, Mathématiques et CAO, vol. 4, Hermès, 1986.Google Scholar
  3. W. Böhm, G. Farin and J. Kahmann, A survey of curve and surface methods in CAGD, Computer Aided Geometric Design, 1, 1984, p. 1–60.CrossRefMATHGoogle Scholar
  4. C. De Boor, A Practical Guide to Splines, Springer-Verlag, 1978.CrossRefMATHGoogle Scholar
  5. E. Cohen, T. Lyche and R. Riesenfeld Discrete B-splines and subdivision techniques in computer-aided geometric design and computer graphics, Computers Graphics and Image Processing, 14, 1980, p. 87–111.CrossRefGoogle Scholar
  6. P. Dierckx, Algorithms for smoothing data with periodic and parametric splines, Computer Graphics and Image Processing, 20, 1982, p. 171–184.CrossRefMATHGoogle Scholar
  7. I.D. Faux and M.J. Pratt, Computational geometry for design and manufacture, Ellis Horwood, 1979.MATHGoogle Scholar
  8. M. Plass and M. Stone, Curve fitting with piecewise parametric cubics, Computer Graphics, vol 17, n° 3, juillet 83, p. 229–239.Google Scholar
  9. C. Potier and C. Vercken, Lissage de surfaces par éléments finis, L’Echo des Recherches, n° 122, 1985, p. 51–58.Google Scholar
  10. M.J.D. Powell, Curve fitting by splines in one variable, J.G. Hayes ed., Numerical approximation to functions and data, The Institute of Mathematics and its applications, the Athlone Press, 1970, p. 65–83.Google Scholar
  11. F.P. Preparata and M.I. Shamos, Computational Geometry An Introduction, Springer-Verlag New-York, 1985.Google Scholar
  12. H. Samet, The quadtree and related hierarchical data structure, Computing Surveys, Vol.16, n°2, 1984.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • Christine Vercken
    • 1
  • Christine Potier
    • 1
  • Sylvie Vignes
    • 1
  1. 1.École Nationale Supérieure des TélécommunicationsParis-Cedex 13France

Personalised recommendations