Visualization of Constrained Data Using Trigonometric Splines

2017 ◽  
Author(s):  
Farheen Ibraheem ◽  
Malik Zawwar Hussain
Keyword(s):  
Trigonometric Splines

Ternary approximating non-stationary subdivision schemes for curve design

2014 ◽  
Vol 4 (4) ◽  
Author(s):  
Shahid Siddiqi ◽  
Muhammad Younis
Keyword(s):  
Trigonometric Polynomials ◽  
Asymptotic Equivalence ◽  
Conic Sections ◽  
Subdivision Schemes ◽  
Linear Spaces ◽  
Curve Design ◽  
Trigonometric Splines ◽  
Stationary Subdivision

AbstractIn this paper, an algorithm has been introduced to produce ternary 2m-point (for any integer m ≥ 1) approximating non-stationary subdivision schemes which can generate the linear spaces spanned by {1; cos(α.); sin(α.)}. The theory of asymptotic equivalence is being used to analyze the convergence and smoothness of the schemes. The proposed algorithm can be consider as the non-stationary counter part of the 2-point and 4-point existing ternary stationary approximating schemes, for different values of m. Moreover, the proposed algorithm has the ability to reproduce or regenerate the conic sections, trigonometric polynomials and trigonometric splines.

scholarly journals Method of phantom nodes in the interpolation problem trigonometric splines

2013 ◽  
Vol 4 (44) ◽  
Author(s):  
В. П. Денисюк ◽  
Л. В. Рибачук ◽  
О. В. Негоденко
Keyword(s):  
Interpolation Problem ◽  
Trigonometric Splines

scholarly journals Approximation by the Third-Order Splines on Uniform and Non-uniform Grids and Image Processing

2020 ◽  
Vol 19 ◽  
Keyword(s):  
Order Approximation ◽  
Approximation Error ◽  
Polynomial Splines ◽  
Third Order ◽  
The Third ◽  
Uniform Grids ◽  
Trigonometric Splines ◽  
Image Enlargement ◽  
Third Order Approximation ◽  
Approximation Polynomial

This work is one of a series of papers that is devoted to the further investigation of polynomial splines and trigonometric splines of the third order approximation. Polynomial basis splines are better known and therefore more commonly used. However, the use of trigonometric basis splines often provides a smaller approximation error. In some cases, the use of the trigonometric approximations is preferable to the polynomial approximations. Here we continue to compare these two types of approximation. The Lebesgue functions and constants are discussed for the polynomial splines and the trigonometric splines. The examples of the applications of the splines to image enlargement are given.

scholarly journals A Marsden Type Identity for Periodic Trigonometric Splines

1993 ◽  
Vol 75 (3) ◽  
pp. 248-265 ◽  
Author(s):  
J.M. Carnicer ◽  
J.M. Pena
Keyword(s):  
Type Identity ◽  
Trigonometric Splines

scholarly journals Image Compression and Enlargement Algorithms

2021 ◽  
Vol 15 ◽  
pp. 836-846
Author(s):  
I. G. Burova ◽  
Yu. K. Demyanovich ◽  
A. N. Terekhov ◽  
A. Yu. Altynova ◽  
A. D. Satanovskiy ◽  
...  
Keyword(s):  
Image Compression ◽  
Order Of Approximation ◽  
Polynomial Splines ◽  
Third Order ◽  
Main Method ◽  
Local Polynomial ◽  
Trigonometric Splines ◽  
Speed Up ◽  
Image Compression Algorithm ◽  
Approximation Polynomial

In some cases, there are problems associated with the compression and enlargement of images. The use of splines is quite effective in some cases. In this paper, a new image compression algorithm is presented. The features of increasing the size of an image when using local polynomial or non-polynomial splines are considered. The main method for enlarging an image is based on the use of splines of the second and third order of approximation. Polynomial and trigonometric splines are considered. To speed up the process of enlarging the image, we used the parallelization techniques

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