| 有理Bézier曲线的全正性与形状调控 |
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| 引用本文： | 孙建泉.有理Bézier曲线的全正性与形状调控[J].南京航空航天大学学报,1993(5). |
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| 作者姓名： | 孙建泉 |
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| 作者单位： | 南京航空航天大学数理力学系 |
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| 摘 要： | 本文证明了有理Bézier曲线的全正性,并由此推出有向角性质与变差减缩性质,还提出了对曲线形状进行调整与控制的几种方法。
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| 关 键 词： | 应用数学 样条函数 矩阵分析 有理Bézier曲线 全正性 |
Total Positivity of Rational Bezier Curves and Adjustment and Control of Its Shape |
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| Sun Jianquan.Total Positivity of Rational Bezier Curves and Adjustment and Control of Its Shape[J].Journal of Nanjing University of Aeronautics & Astronautics,1993(5). |
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| Authors: | Sun Jianquan |
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| Abstract: | This paper proves that the collocation matrix of Rational Bezier curves is totally positive by using the total positivity of Vandermonde matrix. The total positivity of Rational Bezier curves is then proved. The properties of direct angle and Variation-Diminish are proved by the total positivity. The methods which adjust the curve shapes are provided, that contain the change of the curve while one or two points of the curve are adjusted. Lastly the methods which control the shape of the curve wholly are provided,i. e. ,when (n + 1) points of the curve are given,the n+1 characteristic top points and weighting fac- tors may be found. |
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| Keywords: | applied mathematics spline functions matrix analysis rational Bezier curves total positivity |
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