| 摘要: |
| 通过在三角基函数中引入两个指数函数，构造了一种具有四个形状参数的有理二次三角Bézier曲线,它与有理二次Bézier曲线有着相类似的性质.给定控制顶点，该曲线可通过改变形状参数和权因子而调整形状.适当选取控制顶点、形状参数和权因子时，一些二次曲线可以被精确的表示.讨论了连接两条曲线所满足C0，C1和C2的连续条件，并给出了一些例子. |
| 关键词: 二次三角基函数 有理二次三角Bézier曲线 形状参数 指数函数 |
| DOI：10.3969/J.ISSN.100-5137.2017.03.009 |
| 分类号: |
| 基金项目:This research was supported by Natural Science Foundation of China (11271289, 11502141);the Fundamental Research Funds for the Central Universities;the Key Program of NSFC-Guangdong Joint Fund of China (U1135003) |
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| Rational quadratic trigonometric Bézier curve based on new basis with exponential functions |
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Wu Beibei1,2, Yin Junfeng1, Li Chunjing1, Jin Meng1
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1.School of Mathematical Science, Tongji University, Shanghai 200092, China;2.School of Mathematics and Physics, Shanghai University of Electric Power, Shanghai 200090, China
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| Abstract: |
| We construct a rational quadratic trigonometric Bézier curve with four shape parameters by introducing two exponential functions into the trigonometric basis functions in this paper. It has the similar properties as the rational quadratic Bézier curve. For given control points, the shape of the curve can be flexibly adjusted by changing the shape parameters and the weight. Some conics can be exactly represented when the control points, the shape parameters and the weight are chosen appropriately. The C0, C1 and C2 continuous conditions for joining two constructed curves are discussed. Some examples are given. |
| Key words: quadratic trigonometric basis functions rational quadratic trigonometric Bézier curve shape parameters exponential functions |
