Research Article
Year 2017,
Volume: 5 Issue: 1, 56 - 67, 01.04.2017
Abstract
References
- [1] Farin, G., Curves and Surfaces for Computer AidedGeometric Design, A Practical Guide, 3rd Edition, Academic Press Inc., San Diego, 1993.
- [2] Do Carmo, M.P., Differential Geometry Curves and Surfaces, Prentice Hall, Englewood Cliffs, 1976.
- [3] Joy, Kenneth I. Bernstein polynomials. Visualization and Graphics Research Group Department of Computer Science University of California, 1996.
- [4] Doha, E. H., Bhrawy A.H., Saker M.A., On the derivatives of Bernstein polynomials: an application for the solution of high even-order differential equations BVP-Boundary Value Problems Vol:24 (2011), 1-16.
- [5] Gergen, J. J., Diessel, G. and Purcell, W. H., Convergence of Extended Bernstein Polynomials in the Complex plane, Vol 13, No.4, 1963, 1171-1180.
- [6] George M. Phillips,Bernstein Polynomials Interpolation and Approximation by Polynomials, CMS Books in Mathematics, 247-290, 2003.
- [7] Rida T. Farouki, The Bernstein polynomial basis:a centennial retrospective Department of Mechanical and Aerospace Engineering, University of California, Davis, CA 95616, 2012.
- [8] Kandasamy, W.B.V., and Smarandache, F., Dual Numbers, Zip Publishing, Ohio, 2012.
- [9] Study, E., Die Geometrie der Dynamen, Leibzig, 1903.
- [10] Veldkamp, G. R., On the Use of Dual Numbers, Vectors and Matrices in Instantaneous Spatial Kinematics, Mechanisms and Machine Theory, Vol:11 (1976), 141-156.
- [11] Messelmi, F. Analysis of dual functions Annual Review of Chaos Theory, Bifurcations and Dynamical Systems Vol:4 (2013): 37-54.
Year 2017,
Volume: 5 Issue: 1, 56 - 67, 01.04.2017
Abstract
Bernstein polynomials are used in computer graphics for Computer Aided Geometric Design (CAGD). In this paper, we introduce the concept of the generalized dual-variable Bernstein polynomials and give its some properties. In particular, we investigate the limit and derivation equations of the dual-variable Bernstein polynomials.
References
- [1] Farin, G., Curves and Surfaces for Computer AidedGeometric Design, A Practical Guide, 3rd Edition, Academic Press Inc., San Diego, 1993.
- [2] Do Carmo, M.P., Differential Geometry Curves and Surfaces, Prentice Hall, Englewood Cliffs, 1976.
- [3] Joy, Kenneth I. Bernstein polynomials. Visualization and Graphics Research Group Department of Computer Science University of California, 1996.
- [4] Doha, E. H., Bhrawy A.H., Saker M.A., On the derivatives of Bernstein polynomials: an application for the solution of high even-order differential equations BVP-Boundary Value Problems Vol:24 (2011), 1-16.
- [5] Gergen, J. J., Diessel, G. and Purcell, W. H., Convergence of Extended Bernstein Polynomials in the Complex plane, Vol 13, No.4, 1963, 1171-1180.
- [6] George M. Phillips,Bernstein Polynomials Interpolation and Approximation by Polynomials, CMS Books in Mathematics, 247-290, 2003.
- [7] Rida T. Farouki, The Bernstein polynomial basis:a centennial retrospective Department of Mechanical and Aerospace Engineering, University of California, Davis, CA 95616, 2012.
- [8] Kandasamy, W.B.V., and Smarandache, F., Dual Numbers, Zip Publishing, Ohio, 2012.
- [9] Study, E., Die Geometrie der Dynamen, Leibzig, 1903.
- [10] Veldkamp, G. R., On the Use of Dual Numbers, Vectors and Matrices in Instantaneous Spatial Kinematics, Mechanisms and Machine Theory, Vol:11 (1976), 141-156.
- [11] Messelmi, F. Analysis of dual functions Annual Review of Chaos Theory, Bifurcations and Dynamical Systems Vol:4 (2013): 37-54.
There are 11 citations in total.
Details
| Subjects | Engineering |
|---|---|
| Journal Section | Articles |
| Authors | |
| Publication Date | April 1, 2017 |
| Submission Date | June 6, 2016 |
| Acceptance Date | December 17, 2016 |
| Published in Issue | Year 2017 Volume: 5 Issue: 1 |
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