| 平面三次Pythagorean-Hodograph Hyperbolic曲线 |
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| 引用本文： | 郝永霞,廖莲星. 平面三次Pythagorean-Hodograph Hyperbolic曲线[J]. 数学研究及应用, 2022, 42(2): 206-220 |
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| 作者姓名： | 郝永霞 廖莲星 |
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| 作者单位： | 江苏大学数学科学学院, 江苏 镇江 212000 |
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| 基金项目： | 国家自然科学基金(Grant No.11801225),江苏省教育厅高校自然科学项目(Grant No.18KJB11005),江苏大学高级人才科研启动项目(Grant No.14JDG034). |
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| 摘 要： | 本文基于Pythagorean-hodograph (PH)曲线和代数双曲线的良好几何特性,构造了Pythagorean-Hodograph Hyperbolic (PH-H)曲线,并给出了PH-H曲线的定义以及相应性质.同时,分别利用Hyperbolic基函数和Algebraic Hyperbolic (AH) B''ezier基函数,得到了平面三次AH B''ezier曲线为PH曲线的两个不同的充要条件.此外,三次PH-H曲线也被用于求解具有确定解的$G^1$ Hermite插值问题.文中给出了具体实例来说明我们的方法.
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| 关 键 词： | Pythagorean-hodograph曲线 代数双曲B''ezier曲线 $G^1$ Hermite插值 |
| 收稿时间： | 2021-03-02 |
| 修稿时间： | 2021-09-04 |
Planar Cubic Pythagorean-Hodograph Hyperbolic Curves |
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| Yongxia HAO,Lianxing LIAO. Planar Cubic Pythagorean-Hodograph Hyperbolic Curves[J]. Journal of Mathematical Research with Applications, 2022, 42(2): 206-220 |
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| Authors: | Yongxia HAO Lianxing LIAO |
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| Affiliation: | School of Mathematical Sciences, Jiangsu University, Jiangsu 212000, P. R. China |
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| Abstract: | The purpose of this paper is to develop a method to construct the Pythagorean-hodograph hyperbolic (PH-H) curves based on the good geometric properties of PH curves and algebraic hyperbolic curves. The definition of Pythagorean-hodograph hyperbolic curves is given and their properties are examined. By using hyperbolic basis functions and algebraic B''{e}zier basis functions respectively, two different necessary and sufficient conditions for a planar cubic algebraic hyperbolic B''{e}zier curve to be a PH curve are obtained. Moreover, cubic PH-H curves are applied in the problem of $G^{1}$ Hermite interpolation with determined closed form solutions. Several examples serve to illustrate our method. |
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| Keywords: | Pythagorean-hodograph curve algebraic hyperbolic B''{e}zier curve $G^{1}$ Hermite interpolation |
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