Samsul Ariffin Abdul Karim 1,2,3,* , and Rakib Mustafa and Humaira Mustanira Tariq and Ghulam Mustafa and Rabia Hameed and Sidra Razaq (2023) The Generalized Classes of Linear Symmetric Subdivision Schemes Free from Gibbs Oscillations and Artifacts in the Fitting of Data. Symmetry, 15. pp. 1-28.
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Abstract
This paper presents the advanced classes of linear symmetric subdivision schemes for the fitting of data and the creation of geometric shapes. These schemes are derived from the Bspline and Lagrange’s blending functions. The important characteristics of the derived schemes, including continuity, support, and the impact of parameters on the magnitude of the artifact and Gibbs oscillations are discussed. Schemes additionally generalize various subdivision schemes. Linear symmetric subdivision schemes can produce Gibbs oscillations when the initial data is taken from discontinuous functions. Additionally, these schemes may generate unwanted artifacts in the limit curve that do not exist in the original polygon. One solution is to use non-linear schemes, but this approach increases the computational complexity of the scheme. An alternative approach is proposed that involves modifying the linear symmetric schemes by introducing parameters into the linear rules. The suitable values of these parameters reduce or eliminate Gibbs oscillations and artifacts while still using linear symmetric schemes. Our approach provides a balance between reducing or eliminating Gibbs oscillations and artifacts while maintaining computational efficiency. In the second half, the piecewise parametric polynomial curves by using the blending polynomials used in the symmetric schemes are also presented. The majority of the properties of uniform quadratic and cubic B-splines with G² geometric continuities are inherited by these polynomial curves. These curves can also be used for local interpolation of the control points with G² continuity. Furthermore, by adjusting the value of the shape parameter, uniform cubic and quadratic B-spline curves can also be produced. These polynomial curves also satisfy the shape preserving properties of initial data.
| Item Type: | Article |
|---|---|
| Keyword: | symmetric schemes, Linear subdivision scheme, Geometric shapes, Curve fitting, Discontinuous functions, Data fitting, Piecewise polynomial, Uniform B-spline with shape parameters |
| Subjects: | Q Science > QA Mathematics > QA1-939 Mathematics > QA71-90 Instruments and machines > QA75.5-76.95 Electronic computers. Computer science > QA76.75-76.765 Computer software |
| Department: | FACULTY > Faculty of Computing and Informatics |
| Depositing User: | SITI AZIZAH BINTI IDRIS - |
| Date Deposited: | 19 Jul 2024 16:08 |
| Last Modified: | 19 Jul 2024 16:08 |
| URI: | https://eprints.ums.edu.my/id/eprint/39222 |
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