Bezier curves and surfaces based on modified bernstein polynomials

• Main Authors: Khan, Khalid, Lobiyal, D.K., Kilicman, Adem
• Format: Article
• Language: English
• Published: Institute of Mathematics and Mechanics of Azerbaijan 2019
• Online Access: http://psasir.upm.edu.my/id/eprint/80805/1/BEZIER.pdf; http://psasir.upm.edu.my/id/eprint/80805/; https://arxiv.org/abs/1511.06594

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].