Bezier curves and surfaces based on modified bernstein polynomials
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 surface...
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| Format: | Article |
| Language: | English |
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Institute of Mathematics and Mechanics of Azerbaijan
2019
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| Online Access: | http://psasir.upm.edu.my/id/eprint/80805/ http://psasir.upm.edu.my/id/eprint/80805/1/BEZIER.pdf |
| _version_ | 1848858958810316800 |
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| author | Khan, Khalid Lobiyal, D.K. Kilicman, Adem |
| author_facet | Khan, Khalid Lobiyal, D.K. Kilicman, Adem |
| author_sort | Khan, Khalid |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | 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]. |
| first_indexed | 2025-11-15T12:21:43Z |
| format | Article |
| id | upm-80805 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T12:21:43Z |
| publishDate | 2019 |
| publisher | Institute of Mathematics and Mechanics of Azerbaijan |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-808052020-10-15T22:00:24Z http://psasir.upm.edu.my/id/eprint/80805/ Bezier curves and surfaces based on modified bernstein polynomials Khan, Khalid Lobiyal, D.K. Kilicman, Adem 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]. Institute of Mathematics and Mechanics of Azerbaijan 2019 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/80805/1/BEZIER.pdf 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 https://arxiv.org/abs/1511.06594 |
| spellingShingle | Khan, Khalid Lobiyal, D.K. Kilicman, Adem Bezier curves and surfaces based on modified bernstein polynomials |
| title | Bezier curves and surfaces based on modified bernstein polynomials |
| title_full | Bezier curves and surfaces based on modified bernstein polynomials |
| title_fullStr | Bezier curves and surfaces based on modified bernstein polynomials |
| title_full_unstemmed | Bezier curves and surfaces based on modified bernstein polynomials |
| title_short | Bezier curves and surfaces based on modified bernstein polynomials |
| title_sort | bezier curves and surfaces based on modified bernstein polynomials |
| url | http://psasir.upm.edu.my/id/eprint/80805/ http://psasir.upm.edu.my/id/eprint/80805/ http://psasir.upm.edu.my/id/eprint/80805/1/BEZIER.pdf |