Previous |  Up |  Next

Article

Title: On one approach to local surface smoothing (English)
Author: Dikoussar, Nikolay
Author: Török, Csaba
Language: English
Journal: Kybernetika
ISSN: 0023-5954
Volume: 43
Issue: 4
Year: 2007
Pages: 533-546
Summary lang: English
.
Category: math
.
Summary: A bicubic model for local smoothing of surfaces is constructed on the base of pivot points. Such an approach allows reducing the dimension of matrix of normal equations more than twice. The model enables to increase essentially the speed and stability of calculations. The algorithms, constructed by the aid of the offered model, can be used both in applications and the development of global methods for smoothing and approximation of surfaces. (English)
Keyword: data smoothing
Keyword: least squares and related methods
Keyword: linear regression
Keyword: approximation by polynomials
Keyword: interpolation
Keyword: computer aided design (modeling of curves and surfaces)
Keyword: surface approximation
MSC: 41A10
MSC: 62J05
MSC: 65D17
MSC: 93E14
MSC: 93E24
idZBL: Zbl 1139.65009
idMR: MR2377931
.
Date available: 2009-09-24T20:26:41Z
Last updated: 2012-06-06
Stable URL: http://hdl.handle.net/10338.dmlcz/135795
.
Reference: [1] Ahlberg J. H., Nilson E. N. L.Walsh J.: The Theory of Splines and Their Applications.Academic Press, New York 1967 Zbl 0238.65001, MR 0239327
Reference: [2] Davydov O., Zeilfelder F.: Scattered data fitting by direct extension of local polynomials with bivariate splines.Adv. Comp. Math. 21 (2004), 223–271 MR 2073142
Reference: [3] Boor C. de: Bicubic spline interpolation.J. Math. Phys. 41 (1962), 212–218 Zbl 0108.27103, MR 0158512
Reference: [4] Dikoussar N. D.: Function parametrization by using 4-point transforms.Comput. Phys. Comm. 99 (1997), 235–254 Zbl 0927.65009
Reference: [5] Dikoussar N. D.: Adaptive projective filters for track finding.Comput. Phys. Comm. 79 (1994), 39–51
Reference: [6] Dikoussar N. D., Török, Cs.: Automatic knot finding for piecewise-cubic approximation.Math. Model. T-18 (2006), 3, 23–40 Zbl 1099.65014, MR 2255951
Reference: [8] Farin G. E.: Triangular Bernstein–Bezier patches.Comput. Aided Geom. Design 3 (1986), 2, 83–127 MR 0867116
Reference: [9] Farin G.: History of curves and surfaces in CAGD.In: Handbook of CAGD (G. Farin, M. S. Kim and J. Hoschek, eds.), North Holland, Amsterdam 2002 MR 1928534
Reference: [10] Härdle W.: Applied Nonparametric Regression.Cambridge University Press, Cambridge 1990 Zbl 0851.62028, MR 1161622
Reference: [11] Loader C.: Smoothing: Local regression techniques In: Handbook of Computational Statistics (J.E. Gentle et al., eds.), Springer–Verlag, Berlin 2004 MR 2090154
Reference: [12] Mallat S.: A Wavelet Tour of Signal Processing.Academic Press, New York 1999 Zbl 1170.94003, MR 2479996
Reference: [13] Riplay B. D.: Pattern Recognition and Neural Networks.Cambridge University Press, Cambridge 1996 MR 1438788
Reference: [14] Seber G. A.: Linear Regression Analysis.Wiley, New York 1977 Zbl 1029.62059, MR 0436482
Reference: [15] Török, Cs.: 4-point transforms and approximation.Comput. Phys. Comm. 125 (2000), 154–166
Reference: [16] Török, Cs., Dikoussar N. D.: Approximation with discrete projective transformation.Comput. Math. Appl. 38 (1999), 211–220 Zbl 1058.65506, MR 1718884
Reference: [17] Török, Cs., Kepič T.: Data compression based on auto-tracking piecewise cubic approximation and wavelets.In: SICAM Plovdiv 2005, p. 274
Reference: [18] Wahba G.: Spline Models for Observational Data.SIAM, Philadelphia 1990 Zbl 0813.62001, MR 1045442
.

Files

Files Size Format View
Kybernetika_43-2007-4_14.pdf 1.246Mb application/pdf View/Open
Back to standard record
Partner of
EuDML logo