带形状参数的四次DP曲线的构造与应用  

Construction and Application of the Quartic DP Curve with Shape Parameters

作　　者：王研 宋九锡 秦凌云 沈洋 彭兴璇[1] 

机构地区：[1]辽宁师范大学数学学院,辽宁 大连

出　　处：《应用数学进展》2021年第10期3582-3591,共10页Advances in Applied Mathematics

摘　　要：本文将四次DP基函数进行推广,构造出带形状参数的四次DP基函数,分析了带形状参数的四次DP基函数的性质。然后基于这组基函数定义了带形状参数的四次DP曲线,讨论了形状参数的几何意义。最后利用最小二乘法将端点插值的带形状参数的四次DP曲线进行圆锥曲线逼近,求出带形状参数的四次DP曲线的控制顶点,并展示了实例。In this paper, the quartic DP basis functions are extended, the quartic DP basis functions with shape parameters are constructed, the properties of the quartic DP basis functions with shape parameters are analyzed. Then, based on the basis functions, the quartic DP curve with shape parameters is defined, the geometrical meanings of the shape parameters are discussed. Finally, we use the least squares method and approximate conic sections by the quartic DP curve with shape parameters with endpoint interpolation, find the control points of the quartic DP curve with shape parameters, and examples are shown.

关 键 词：四次DP曲线 形状参数 圆锥曲线 逼近 

分 类 号：G63[文化科学—教育学]