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

Yuanpeng Zhu and Zhuo Liu

Mathematical Problems in Engineering, 2019, vol. 2019, 1-16

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.

Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:9026187

DOI: 10.1155/2019/9026187

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