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A Class of Trigonometric Bernstein-Type Basis Functions with Four Shape Parameters

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  • Yuanpeng Zhu
  • Zhuo Liu

Abstract

In this work, a family of four new trigonometric Bernstein-type basis functions with four shape parameters is constructed, which form a normalized basis with optimal total positivity. Based on the new basis functions, a kind of trigonometric Bézier-type curves with four shape parameters, analogous to the cubic Bézier curves, is constructed. With appropriate choices of control points and shape parameters, the resulting trigonometric Bézier-type curves can represent exactly any arc of an ellipse or parabola. The four shape parameters have tension control roles on adjusting the shape of resulting curves. Moreover, a new corner cutting algorithm is also proposed for calculating the trigonometric Bézier-type curves stably and efficiently.

Suggested Citation

  • Yuanpeng Zhu & Zhuo Liu, 2019. "A Class of Trigonometric Bernstein-Type Basis Functions with Four Shape Parameters," Mathematical Problems in Engineering, Hindawi, vol. 2019, pages 1-16, April.
    • Handle: RePEc:hin:jnlmpe:9026187
    DOI: 10.1155/2019/9026187
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    Cited by:

    1. Yunyi Fu & Yuanpeng Zhu, 2021. "A Generalized Quasi Cubic Trigonometric Bernstein Basis Functions and Its B-Spline Form," Mathematics, MDPI, vol. 9(10), pages 1-25, May.

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