Optimization of the parameters of surfaces by interpolating variational bicubic splines

2014 ◽  
Vol 102 ◽  
pp. 76-89 ◽  
Author(s):  
A. Kouibia ◽  
M. Pasadas
Keyword(s):  
Bicubic Splines

Asymmetric Lens Design Using Bicubic Splines: Application to the Color TV Lighthouse

1971 ◽  
Vol 10 (11) ◽  
pp. 2513 ◽  
Author(s):  
T. P. Vogl ◽  
A. K. Rigler ◽  
B. R. Canty
Keyword(s):  
Lens Design ◽  
Bicubic Splines

scholarly journals Optimal Approximation of Biquartic Polynomials by Bicubic Splines

2018 ◽  
Vol 173 ◽  
pp. 03012
Author(s):  
Viliam Kačala ◽  
Csaba Török
Keyword(s):  
Optimal Approximation ◽  
First Derivative ◽  
Polynomial Coefficients ◽  
Spline Curves ◽  
Spline Surfaces ◽  
Chebyshev Norm ◽  
Quartic Polynomial ◽  
Hermite Spline ◽  
Open Question ◽  
Bicubic Splines

Recently an unexpected approximation property between polynomials of degree three and four was revealed within the framework of two-part approximation models in 2-norm, Chebyshev norm and Holladay seminorm. Namely, it was proved that if a two-component cubic Hermite spline’s first derivative at the shared knot is computed from the first derivative of a quartic polynomial, then the spline is a clamped spline of classC2and also the best approximant to the polynomial.Although it was known that a 2 × 2 component uniform bicubic Hermite spline is a clamped spline of classC2if the derivatives at the shared knots are given by the first derivatives of a biquartic polynomial, the optimality of such approximation remained an open question.The goal of this paper is to resolve this problem. Unlike the spline curves, in the case of spline surfaces it is insufficient to suppose that the grid should be uniform and the spline derivatives computed from a biquartic polynomial. We show that the biquartic polynomial coefficients have to satisfy some additional constraints to achieve optimal approximation by bicubic splines.

3D fuzzy data approximation by fuzzy smoothing bicubic splines

2019 ◽  
Vol 164 ◽  
pp. 94-102 ◽  
Author(s):  
P. González ◽  
H. Idais ◽  
M. Pasadas ◽  
M. Yasin
Keyword(s):  
Fuzzy Data ◽  
Data Approximation ◽  
Bicubic Splines

Generalizing bicubic splines for modeling and IGA with irregular layout

2016 ◽  
Vol 70 ◽  
pp. 23-35 ◽  
Author(s):  
Kȩstutis Karčiauskas ◽  
Thien Nguyen ◽  
Jörg Peters
Keyword(s):  
Bicubic Splines

Approximation of fuzzy functions by fuzzy interpolating bicubic splines: 2018 CMMSE conference

2018 ◽  
Vol 57 (5) ◽  
pp. 1252-1267
Author(s):  
P. González ◽  
H. Idais ◽  
M. Pasadas ◽  
M. Yasin
Keyword(s):  
Bicubic Splines
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