四次带参数PH曲线的构造方法  

Construction Approach of Quartic PH Curves with Parameter

作　　者：杨雪 彭兴璇[1] 段卓 

机构地区：[1]辽宁师范大学数学学院,辽宁 大连

出　　处：《理论数学》2023年第3期395-404,共10页Pure Mathematics

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。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.

关 键 词：m-Bézier曲线 形状参数 PH曲线 几何特征 

分 类 号：G63[文化科学—教育学]