Optimal knots allocation in the cubic and bicubic spline interpolation problems

2019 ◽  
Vol 164 ◽  
pp. 131-145 ◽  
Author(s):  
H. Idais ◽  
M. Yasin ◽  
M. Pasadas ◽  
P. González
Keyword(s):  
Spline Interpolation ◽  
Bicubic Spline ◽  
Interpolation Problems

scholarly journals BUILDING 3D SURFACES OF LAND STORAGE VERTICAL CYLINDRICAL STEEL TANK USING BICUBIC SPLINE INTERPOLATION

2019 ◽  
Vol 45 (2) ◽  
pp. 85-91
Author(s):  
Kostyantyn Burak ◽  
Vitaliy Kovtun ◽  
Mary Nychvyd
Keyword(s):  
Information Content ◽  
Spline Interpolation ◽  
Geometric Parameters ◽  
Practical Significance ◽  
Bicubic Spline ◽  
3D Surface ◽  
Nominal Capacity ◽  
Steel Tank ◽  
Steel Tanks ◽  
Cylindrical Steel

The purpose of this work is to increase the accuracy, quality and information content of geodetic surveys of vertical steel tanks by using modern geodetic equipment and creating algorithms for data processing of these observations. Method. In order to increase the information content of data for straightening, it is proposed to calculate the geometric parameters of vertical steel tanks not only in places where data are directly obtained through instrumental observations, but also at any point of the 3D surface of the tank. The paper describes an algorithm for creating a 3D surface of a tank by bicubic spline interpolation (BSI). Results on the basis of the conducted research, it was established that the developed algorithm could be used and the 3D-surface spatial coordinates were determined. The method of determining the geometric parameters of vertical steel tanks by using BSI is improved. Scientific novelty and practical significance. Bicubic spline interpolation (BSI) was used for the first time. It greatly increases the accuracy and informality of the results of the control. The practical significance is confirmed by the control of the geometric parameters of a vertical cylindrical steel tank with a nominal capacity of 75.000 m3 with a floating roof and a double wall of the LODS “Brody” company.

Solvability of cardinal spline interpolation problems

1983 ◽  
Vol 95 (1-2) ◽  
pp. 39-57
Author(s):  
T. N. T. Goodman
Keyword(s):  
Incidence Matrix ◽  
Bounded Solution ◽  
Spline Interpolation ◽  
Piecewise Polynomial ◽  
Piecewise Polynomials ◽  
Cardinal Spline ◽  
Interpolation Problems ◽  
Bounded Data ◽  
Derivatives Of ◽  
Cardinal Spline Interpolation

SynopsisWe consider interpolation by piecewise polynomials, where the interpolation conditions are on certain derivatives of the function at certain points of a periodic vector x, specified by a periodic incidence matrix G. Similarly, we allow discontinuity of certain derivatives of the piecewise polynomial at certain points of x, specified by a periodic incidence matrix H. This generalises the well-known cardinal spline interpolation of Schoenberg. We investigate conditions on G, H and x under which there is a unique bounded solution for any given bounded data.

Bicubic Spline Interpolation

1962 ◽  
Vol 41 (1-4) ◽  
pp. 212-218 ◽  
Author(s):  
Carl de Boor
Keyword(s):  
Spline Interpolation ◽  
Bicubic Spline

scholarly journals A new gridding method for zonal travel activity and emissions using bicubic spline interpolation

2004 ◽  
Vol 38 (8) ◽  
pp. 751-766 ◽  
Author(s):  
Yi Zheng ◽  
Bo Wang ◽  
H.Michael Zhang ◽  
Debbie Niemeier
Keyword(s):  
Spline Interpolation ◽  
Bicubic Spline
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