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2016•DEStech Transactions on Engineering and Technology ResearchRequires access

A New Set of Bernstein Basis Functions with Multiparameter and Applications

Caiyong Wang, Ying Zeng, Xiaoming Zeng

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Abstract

In this paper, a new set of Bernstein type basis functions with 3 parameters is introduced. The properties of these basis functions are studied. A new kind of Bezier like curves with 3 parameters is defined based on the new basis functions. The new curve not only holds many practical geometrical properties of Bezier curve, but also its shape can be adjusted totally or locally by changing values of the parameters. Finally, some application examples of the new curve are presented.

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What this paper is about

In this paper, a new set of Bernstein type basis functions with 3 parameters is introduced. The properties of these basis functions are studied. A new kind of Bezier like curves with 3 parameters is defined based on the new basis functions. The new curve not only holds many practical geometrical properties of Bezier curve, but also its shape can be adjusted totally or locally by changing values of the parameters. Finally, some application examples of the new curve are presented.

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Available abstract

In this paper, a new set of Bernstein type basis functions with 3 parameters is introduced. The properties of these basis functions are studied. A new kind of Bezier like curves with 3 parameters is defined based on the new basis functions. The new curve not only holds many practical geometrical properties of Bezier curve, but also its shape can be adjusted totally or locally by changing values of the parameters. Finally, some application examples of the new curve are presented.

Key concepts: Basis (linear algebra), Set (abstract data type), Bernstein polynomial, Applied mathematics, Basis function, Mathematics, Computer science, Mathematical analysis

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