Hu Gang, Bo Cuicui, Qin Xinqiang
Department of Applied Mathematics, Xi'an University of Technology, Xi'an, 710054 P.R. China.
J Inequal Appl. 2017;2017(1):115. doi: 10.1186/s13660-017-1390-3. Epub 2017 May 16.
As a new method of representing curves, Q-Bézier curves not only exhibit the beneficial properties of Bézier curves but also allow effective shape adjustment by changing multiple shape parameters. In order to resolve the problem of not being able to construct complex curves using a single curve, we study the geometric continuity conditions for Q-Bézier curves of degree . Following the analysis of basis functions and terminal properties of Q-Bézier curves of degree , the continuity conditions of [Formula: see text] and [Formula: see text] between two adjacent Q-Bézier curves are proposed. In addition, we discuss the specific steps of smooth continuity for Q-Bézier curves and analyze the influence rules of shape parameters for Q-Bézier curves. The modeling examples show that the proposed method is effective and easy to achieve, making it useful for constructing complex curves for engineering design.
作为一种表示曲线的新方法，Q - 贝塞尔曲线不仅具有贝塞尔曲线的有益特性，还能通过改变多个形状参数实现有效的形状调整。为了解决无法用单一曲线构造复杂曲线的问题，我们研究了n次Q - 贝塞尔曲线的几何连续性条件。在分析了n次Q - 贝塞尔曲线的基函数和端点性质之后，提出了两条相邻Q - 贝塞尔曲线之间[公式：见原文]和[公式：见原文]的连续性条件。此外，我们讨论了Q - 贝塞尔曲线光滑连续性的具体步骤，并分析了Q - 贝塞尔曲线形状参数的影响规律。建模实例表明，所提出的方法有效且易于实现，对工程设计中复杂曲线的构造具有实用价值。
