Citation
Khan, Khalid and Lobiyal, D.K. and Kilicman, Adem
(2019)
Bezier curves and surfaces based on modified bernstein polynomials.
Azerbaijan Journal of Mathematics, 9 (1).
3,6,7,8,9,14,15,16,17,18,19,20,21.
ISSN 2218-6816
Abstract
In this paper, B´ezier curves and surfaces have been constructed based on modified Bernstein bases functions with shifted knots for t ∈αn+β,n+αn+β. Various properties of these modified Bernstein bases are studied. A de Casteljau type algorithm has been developed to compute B´ezier curves and surfaces with shifted knots. Furthermore, some fundamental properties of B´ezier curves and surfaces with modified Bernstein bases are also discussed. Introduction of parameters α and β enable us to shift Bernstein bases functions over subintervals of [0, 1]. These new curves have some properties similar to classical B´ezier curves. We get B´ezier curves defined on [0, 1] when we set the parameters α, β to the value 0. Simulation study is performed through MATLAB R2010a. It has been concluded that B´ezier curves that are generated over any subinterval of [0, 1] based on modified Bernstein bases functions are similar to the B´ezier curves that are generated based on classical Bernstein bases functions over the interval [0, 1].
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Additional Metadata
Item Type: |
Article
|
Divisions: |
Faculty of Science |
Publisher: |
Institute of Mathematics and Mechanics of Azerbaijan |
Keywords: |
Degree elevation; Degree reduction; de Casteljau algorithm;
Bernstein blending functions with shifted knots; B´ezier curve; Tensor product; Shape preserving |
Depositing User: |
Ms. Nuraida Ibrahim
|
Date Deposited: |
15 Oct 2020 22:00 |
Last Modified: |
15 Oct 2020 22:00 |
URI: |
http://psasir.upm.edu.my/id/eprint/80805 |
Statistic Details: |
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