四次带参数PH曲线的构造方法
Construction Approach of Quartic PH Curves with Parameter
摘要: 针对四次带参数PH曲线，讨论其几何特征和几何构造方法。首先，定义了一类含一个形状参数的四次m-Bernstein基函数，进而得到四次m-Bézier曲线。然后通过引入辅助控制顶点给出四次m-Bézier曲线成为PH曲线的几何特征条件，最后提出一种新的四次带参数PH曲线的几何构造方法，并给出误差分析，通过数值例子，验证了方法的有效性和可行性。
Abstract: The geometric characteristics and the geometric construction method of quartic PH curve with parameter are discussed. First, we define a class of quartic m-Bernstein basis function with a shape parameter. Then the quartic m-Bézier curve is obtained. By introducing the auxiliary control vertex, the geometric characteristic conditions for quartic m-Bézier curve becoming PH curve is given. We propose a new geometric construction approach of quartic PH curve with parameter. And the error analysis is given. The validity and feasibility of the study are verified by numerical examples.
文章引用：杨雪, 彭兴璇, 段卓. 四次带参数PH曲线的构造方法[J]. 理论数学, 2023, 13(3): 395-404. https://doi.org/10.12677/PM.2023.133043

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