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T-Bézier Curves Based on Algebraic and Trigonometric Polynomials

In this paper, a new basis, called T-Bezier basis, is constructed for the space Γ n= span{1,t,t 2,t 3,...,t n -4,sint,cost,sin2t,cos2t}. Properties of this basis are analyzed and T-Bezier curves are defined based on it. Then it is demonstrated that many valuable curves, such as algebraic curves and transcendental curves, can be expressed by T-Bezier curves.