In this paper, we present a new class of sextic trigonometric Bernstein (ST-Bernstein, for short) basis functions with two shape parameters along with their geometric properties which are similar to the classical Bernstein basis functions. A sextic trigonometric Bézier (ST-Bézier, for short) curve with two shape parameters and their geometric characteristics is also constructed. The continuity constraints for the connection of two adjacent ST-Bézier curves segments are discussed. Shape control parameters can provide an opportunity to modify the shape of curve as designer desired. Some open and closed curves are also part of this study.

中文翻译：

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一类具有两个形状参数的六边形三角贝塞尔曲线

在本文中，我们提出了一类新的六分三角伯恩斯坦（简称 ST-Bernstein）基函数，它具有两个形状参数及其与经典伯恩斯坦基函数相似的几何特性。还构造了具有两个形状参数及其几何特征的六分三角贝塞尔（简称ST-Bézier）曲线。讨论了两个相邻 ST-Bézier 曲线段连接的连续性约束。形状控制参数可以提供根据设计者的需要修改曲线形状的机会。一些开放和闭合曲线也是本研究的一部分。