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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

DOI: 10.12677/AAM.2021.1010378, PP. 3582-3591

Keywords: 四次DP曲线,形状参数,圆锥曲线,逼近
Quartic DP Curve
, Shape Parameters, Conic Section, Approximation

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Abstract:

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.

References

[1]  Delgado, J. and Pe?a, J.M. (2003) A Shape Preserving Representation with an Evaluation Algorithm of Linear Complexity. Computer Aided Geometric Design, 20, 1-10.
https://doi.org/10.1016/S0167-8396(02)00190-5
[2]  陈杰, 王国瑾. 一类带形状参数的DP-NTP 曲线及其应用[J]. 计算机辅助设计与图形学学报, 2011, 23(6): 1055-1060.
[3]  陈福来, 吴晓勤, 朱秀云. 广义三次DP曲线[J]. 计算机科学, 2012, 39(12): 264-267.
[4]  彭兴璇, 蒋新昕, 谢宇迪. 一类带形状参数的三次DP曲线[J]. 计算机辅助设计与图形学学报, 2018, 30(9): 1712-1718.
[5]  张迪, 查东东, 刘华勇. 三次DP曲线定义区间的扩展及其形状优化[J]. 浙江大学学报(理学版), 2020, 47(2): 178-190.
[6]  Floater, M.S. (1997) An O(h2n) Hermite Approximation for Conic Sections. Computer Aided Geometric Design, 14, 135- 151.
https://doi.org/10.1016/S0167-8396(96)00025-8
[7]  Ahn, Y.J. (2010) Approximation of Conic Sections by Curvature Continuous Quartic Bézier Curves. Computers and Mathematics with Applications, 6, 1986-1993.
https://doi.org/10.1016/j.camwa.2010.07.032
[8]  Hu, Q.Q. (2012) Approximating Conic Sections by Constrained Bézier Curves of Arbitrary Degree. Journal of Computational and Applied Mathematics, 236, 2813-2821.
https://doi.org/10.1016/j.cam.2012.01.017
[9]  Bakhshesh, D. and Davoodi, M. (2014) Approximating of Conic Sections by DP Curves with Endpoint Interpolation. International Journal of Computer Mathematics, 92, 1-14.
https://doi.org/10.1080/00207160.2014.889293
[10]  张伟红, 蔡亦青, 冯玉瑜. 圆弧的五次PH曲线等弧长逼近[J]. 计算机辅助设计与图形学学报, 2010, 22(7): 1082-1086.

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