| Bezier曲线的全正性及其应用 |
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| 引用本文： | 孙建泉.Bezier曲线的全正性及其应用[J].南京航空航天大学学报,1987(1). |
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| 作者姓名： | 孙建泉 |
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| 摘 要： | 本文首先提出了Bézier曲线的全正性问题,通过揭示Vandermonde矩阵的一个重要性质,证明了系数矩阵的全正性,从而阐明了Bézier曲线的全正性。继而用全正性证明了Bézier曲线的有向角性质与变差减缩性质。最后探讨了Bézier曲面的全正性的概念。
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| 关 键 词： | 应用数学 样条函数 曲线 曲面 矩阵分析 |
The Total Positivity of Bezier Curves |
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| Sun Jianquan.The Total Positivity of Bezier Curves[J].Journal of Nanjing University of Aeronautics & Astronautics,1987(1). |
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| Authors: | Sun Jianquan |
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| Institution: | Sun Jianquan |
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| Abstract: | In this paper, the total positivity of Bezier curves is first dealt with By enunciating an important property of Vandermonde matrix, it is proved that the collocation matrix is total posifive, hence the total positivity of Bezier curves.Then the properties of directed angle and Variation-Diminish of Bezier curves are proved by the total positivity. Lastly the conception of the total positivity of Bezier surface is discussed |
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| Keywords: | applied mathematics spline function curves surface matrix analysis |
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