| 容许参数变换下曲线和曲面的几何不变量 |
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| 引用本文： | 王恒斌,郭亚梅.容许参数变换下曲线和曲面的几何不变量[J].安阳师范学院学报,2013(5):25-29. |
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| 作者姓名： | 王恒斌 郭亚梅 |
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| 作者单位： | 安阳师范学院数学与统计学院; |
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| 摘 要： | 空间曲线和曲面的几何量的计算均依赖于所选参数.本文从参数变换的角度,较详细讨论了曲线的弧长、曲率、挠率及曲面上两方向的夹角、曲面的面积、曲面的曲率等都与坐标参数的选取无关.这反映了曲线与曲面的几何性质不依赖于参数的选取.
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| 关 键 词： | 参数变换 曲线 曲面 曲率 挠率 |
Geometrical Invariant of Curve and Surface in Admissible Parameters |
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| Institution: | WANG Heng - bin, GUO Ya - mei ( School of Mathematics and Statistics, Anyang Normal University, Anyang 455000, China ) |
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| Abstract: | Calculation for geometric quantities of Space curve and surface are depended on parameters. From the view of parameter transformation, this paper develops a comparative thorough discussion about the irrele-vance among the choice of coordinate parameters and the length of a curve, the curvature, the torsion, and the angles of two directions on the surface of the curve, the area of a surface and the curvature of surface, which reflects the geometrical properties of curve and surface do not rely on parameters. |
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| Keywords: | Parameter transform Curve Surface Curvature Torsion |
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