Approximation and/or construction of curves by minimization methods with or without constraints

M. Bercovier; A. Jacobi

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1992)

  • Volume: 26, Issue: 1, page 211-232
  • ISSN: 0764-583X

How to cite

top

Bercovier, M., and Jacobi, A.. "Approximation and/or construction of curves by minimization methods with or without constraints." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 26.1 (1992): 211-232. <http://eudml.org/doc/193656>.

@article{Bercovier1992,
author = {Bercovier, M., Jacobi, A.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {Bézier curve; offset curve; approximate conversion; variational problem; finite-element method; Bernstein-Bézier basis; numerical examples},
language = {eng},
number = {1},
pages = {211-232},
publisher = {Dunod},
title = {Approximation and/or construction of curves by minimization methods with or without constraints},
url = {http://eudml.org/doc/193656},
volume = {26},
year = {1992},
}

TY - JOUR
AU - Bercovier, M.
AU - Jacobi, A.
TI - Approximation and/or construction of curves by minimization methods with or without constraints
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1992
PB - Dunod
VL - 26
IS - 1
SP - 211
EP - 232
LA - eng
KW - Bézier curve; offset curve; approximate conversion; variational problem; finite-element method; Bernstein-Bézier basis; numerical examples
UR - http://eudml.org/doc/193656
ER -

References

top
  1. [1] BABUSKA, B. A. SZABO & I. N. KATZ (1981), The p-version of the Finite Element Method, SIAM J. Numer. Anal, 18, pp. 515-545. Zbl0487.65059MR615529
  2. [2] A. BALL (1984), Reparametrization and Its Application in CAGD, Internat. J. Numer. Methods Engrg., Vol. 20, pp. 197-216, John Wiley & Sons. Zbl0539.65005
  3. [3] P. G. CIARLET (1982), Introduction à l'Analyse Numérique Matricielle et à l'Optimisation, Masson, Paris, English translation (1989), Cambridge University Press. Zbl0488.65001
  4. [4] L. DANNENBERG, H. NOWACKI (1985), Approximate Conversion of Surface Representations with Polynomials Bases, CAGD, 2, pp. 123-132. Zbl0577.65005MR828540
  5. [5] G. FARIN (1988), Curves and Surfaces for Computer Aided Geometric Design, A Practical Guide, Academic Press, Inc., Boston. Zbl0694.68004MR974109
  6. [6] R. J. GOULT (1990), Parametric Curves and Surface Approximation, in Mathematics of Surfaces III, éd. Handscomb, D. C, Oxford University Press. Zbl0718.41025
  7. [7] G. HÖLZLE (1983), Knot Placement for Piecewise Polynomial Approximation of Curves, Comput. Aided Design, 15, pp. 295-296. 
  8. [8] J. HOSCHEK (1985), Offset Curves in the Plane, Comput. Aided Design, 4, pp. 59-66. Zbl0645.65008MR898023
  9. [9] J. HOSCHEK (1987), Approximation Conversion of Spline Curves, Comput. Aided Geom. Design, 17, pp. 77-82. Zbl0645.65008MR898023
  10. [10] J. HOSCHEK (1988), Spline Approximation of Offset Curves, Comput. Aided Geom. Design, 5, pp. 33-40. Zbl0647.65007MR945304
  11. [11] J. HOSCHEK (1988), Intrinsic Parametrization for Approximation, Comput. Aided Geom. Design, 5, pp. 27-31. Zbl0644.65011MR945303
  12. [12] J. HOSCHEK, F. J. SCHNEIDER, P. WASSUM (1988), Optimal Approximation Conversion of Spline Surfaces, Comput. Aided Design, 20, pp. 457-483. Zbl0682.65005
  13. [13] M. A. LACHANCE (1988), Chebyshev Economisation for Parametric Surfaces, Comput. Aided Geom. Design, 5, pp. 195-208. Zbl0709.65012MR959604
  14. [14] L. D. LANDAU, E. M. LIFSHITZ (1959), Mechanics, Pergamon Press, Oxford, Ed. 3. Zbl0081.22207MR475051
  15. [15] N. LUSCHER (1988), The Bernstein-Bézier Technique in the Finite Element Method, Exemplary for the Univariate Case, Technical Report from the University of Braunschweig. 
  16. [16] H. NOWACKI, L. DINGYUAN, L. XINMIN (1990), Fairing Bézier Curves With Constraints, Comput. Aided Geom. Design, 7, pp. 43-55. Zbl0755.65018MR1074598
  17. [17] C. ZIENKIEWICZ (1977), The Finite Element Method in Engineering Science, McGraw-Hill, London. Zbl0237.73071

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.