Skip to main content
SpringerLink
Log in

Smooth-curve interpolation: A generalized spline-fit procedure

  • Published:
BIT Numerical Mathematics Aims and scope Submit manuscript

Abstract

A method is presented for finding the smoothest curve through a set of data points. “Smoothest” refers to the equilibrium, or minimum-energy configuration of an ideal elastic beam constrained to pass through the data points. The formulation of the smoothest curve is seen to involve a multivariable boundary-value minimization problem which makes use of a numerical solution of the beam non-linear differential equation. The method is shown to offer considerable improvement over the spline technique for smooth-curve interpolation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Theilheimer, F. and W. Starkweather,The Fairing of Ship Lines on a High-Speed Computer, Math. Comp., 15, pp. 338–355, 1961.

    Google Scholar 

  2. Asker, B.,The Spline Curve, A Smooth Interpolation Function Used in Numerical Design of Ship-Lines, BIT 2, pp. 76–82, 1962.

    Article  Google Scholar 

  3. Walsh, J. L., Ahlberg, J. H., and Nilson, E. N.,Best Approximation Properties of the Spline Fit, J. Math. Mech. 11, pp. 225–234, 1962.

    Google Scholar 

  4. Greville, T. N. E.,Numerical Procedures for Interpolation by Spline Functions, Mathematics Research Center, University of Wisconsin, Technical Summary Report No. 450, January 1964 (Madison, Wis.).

  5. Mehlum, E.,A Curve-Fitting Method Based on a Variational Criterion, BIT 4, pp. 213–223, 1964.

    Google Scholar 

  6. Holladay, J. C.,A Smoothest Curve Approximation, Math. Comp. 11, pp. 233–243, 1957.

    Google Scholar 

  7. Glass, J. M.,A Criterion for the Quantization of Line-Drawing Data, Technical Report 400-112, Laboratory for Electroscience Research, Department of Electrical Engineering, New York University, New York 10453, N. Y., 1965.

    Google Scholar 

  8. Freeman, H. and Glass J. M.,On the Quantization of Line-Drawing Data, to be published.

  9. Fox, L.,The Numerical Solution of Two-Point Boundary Problems in Ordinary Differential Equations, Oxford University Press, London, 1957.

    Google Scholar 

  10. Curry, H. B.,The Method of Steepest Descent for Nonlinear Minimization Problems, Q. of Appl. Math. 2, pp. 258–261, 1944.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Applied Research Laboratory Sylvania Electronic Systems, Waltham, Massachusetts

    J. M. Glass

Authors
  1. J. M. Glass
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Glass, J.M. Smooth-curve interpolation: A generalized spline-fit procedure. BIT 6, 277–293 (1966). https://doi.org/10.1007/BF01966089

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01966089

Key words

Search

Navigation