Least-squares B-spline curve approximation with arbitrary end derivatives

Engineering with Computers

Volumn 16, Issue 2, 2000, Pages 109-116

  Piegl, L A ^a   Tiller, W ^b  

^a University of South Florida   (United States)

^b GeomWare Inc   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; CONSTRAINT THEORY; DATA PROCESSING;

B SPLINE APPROXIMATION; CURVE APPROXIMATION;

LEAST SQUARES APPROXIMATIONS;

EID: 0034469029     PISSN: 01770667     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00007188     Document Type: Article

References (27)

1. Cohen, E., O'Dell, C.L. (1989) A data dependent parametrisation for spline approximation. In: Lyche, T., Schumaker, L.L. (Editors), Mathematical Methods in Computer Aided Geometric Design. Academic Press, New York, 155-166
2. Cox, M.G. (1971) Curve fitting with piecewise polynomials. J Inst Maths Applics, 8, 36-52
3. Cox, M.G., Harris, P.M., Jones, H.M. (1987) Strategies for knot placement in least-squares data fitting by splines. DITC 101/87, NPL, Teddington, UK
4. Cox, M.G., Harris, P.M., Jones, H.M. (1990) A knot placement strategy for least-squares spline fitting based on the use of local polynomial approximations. In: Cox, M.G., Mason, J.C. (Editors), Algorithms for Approximation. Chapman & Hall, London, 37-45
5. Davis, P.J. (1975) Interpolation and Approximation. Dover Publications, New York, NY
6. De Boor, C., Rice, J.R. (1968) Least-squares cubic spline approximation I - fixed knots. CSD TR 20, Purdue University
7. De Boor, C., Rice, J.R. (1968) Least-squares cubic spline approximation II - variable knots. CSD TR 21, Purdue University
8. De Boor, C. (1974) Good approximation by splines with variable knots II. In: Watson, G.A. (Editor), Numerical Solution of Differential Equations - Lecture Notes in Mathematics No. 363. Springer-Verlag, New York, NY, 12-20
9. De Boor, C. (1978) A Practical Guide to Splines. Springer-Verlag, New York, NY
10. Foley, T.A., Nielson, G.M. (1989) Knot selection for parametric spline interpolation. In: Lyche, T., Schumaker, L.L. (Editors), Mathematical Methods in Computer Aided Geometric Design. Academic Press, New York, NY, 261-271
11. Forrest, A.R. (1990) Interactive interpolation and approximation by Bézier polynomials. Computer-Aided Design, 22, 527-537
12. Hartley, P.J., Judd, C.J. (1980) Parametrisation and shape of B-spline curves for CAD. Computer-Aided Design, 12, 235-238
13. Hayes, J.G. (Editor) (1970) Numerical Approximation to Functions and Data. Athlone Press, London
14. Hölzle, G.E. (1983) Knot placement for piecewise polynomial approximation of curves. Computer-Aided Design, 15, 295-296
15. Hoschek, J. (1988) Intrinsic parametrisation for approximation. Computer Aided Geometric Design, 5, 27-31
16. Hoschek, J., Schneider, F.-J. (1990) Spline conversion for trimmed rational Bézier and B-spline surfaces, Computer-Aided Design, 22, 580-590
17. Ichida, K., Yoshimoto, F., Kiyono, T. (1976) Curve fitting by a piecewise cubic polynomial. Computing, 16, 329-338
18. McConalogue, D.J. (1970) A quasi-intrinsic scheme for passing a smooth curve through a discrete set of points. The Computer Journal, 13, 392-396
19. Piegl, L., Tiller, W. (1997) The NURBS Book. Second Edition, Springer-Verlag, New York, NY
20. Renner, G. (1982) A method of shape description for mechanical engineering practice. Computers in Industry, 3, 137-142
21. Rogers, D.F., Fog, N.G. (1989) Constrained B-spline curve and surface fitting. Computer-Aided Design, 21, 641-648
22. Epstein, M.P. (1976) On the influence of parametrization in parametric interpolation. SIAM J Numer Anal, 13, 261-268
23. Grossman, M. (1971) Parametric curve fitting. The Computer Journal, 17, 169-172
24. Lee, E.T.Y. (1989) Choosing nodes in parametric curve interpolation. Computer-Aided Design, 21, 363-370
25. Plass, M., Stone, M. (1983) Curve-fitting with piece-wise parametric cubics. Computer Graphics, 17, 229-239
26. Akima, H. (1970) A new method of interpolation and smooth curve fitting based on local procedures. Journal ACM, 17, 589-602
27. Manning, J.R. (1974) Continuity conditions for spline curves. The Computer Journal, 17, 181-186