曲线的曲率

By means of uniting geometry with algebra, the arc length, tangent line, cotangent space and curvature of curve in four dimensional space are investigated, and the corresponding calculation formula in each cases are given.

用形数结合的观点研究了四维空间中曲线的弧长、切线、法空间和曲率问题，并给出了其计算公式。

After analyzing and evaluating the related references, a rapid algorithm working out control points of uniform cubic B-spline is proposed, and is realized in Matlab, the complexity of program is greatly reduced and the operation efficiency is improved.

在Matlab中编程实现，大大降低了程序的复杂性和提高了运算效率，并使重构所得曲线的两个端点处曲率不为零，至少满足了一阶连续。

The quadratic patches is fixed,and its parametric representation method is gained.The cubic patches reduce to three local factors through reducing Bernstein coefficients to control shape of curve,two of them are used to join segments into G2- continuity approximating curves for given sequence data in space,and the other is used to adjust shape of segment.

先固定二次曲面片，并得到其参数形式，然后约简三次曲面片所对应的Bernstein系数，使之为带有三个形状调整的形状因子，其中两个分别代表曲线段端点处的曲率，另外一个作为形状的调整。

A new method for planar curves has been developed. Curvature signal is decomposed with wavelet at first, and then select interpolative dots by altering pace, which is used to construct a G2 continuous rational cubic Bezier spline curve.

给出了一种先对初始曲率进行小波分解，再用变步长的方法选取待插值点，最后利用C^2连续的三次有理Bezier样条插值重建出光顺的平面曲线的方法。

Its principle is that the turning points of the curve are decided by the sign and the magnitude of τ, the relative curvature of y=f, and T=yxn/(1+y'x2)3/2, where x=lg△K, y=lg.

其原理是：根据y=f的相对曲率τ=y_x~n/1+y_x~(′2~(3/2)的正负和大小来判定曲线的转折点，这里x=1g，y=Ig。

The torsion of a curve;.

曲线的第二曲率

Design the Route Fitting Program based on Cubic Spline and, output viewdata, interface with AUTOCAD program, built up vary layers with different color, directly plot the fig of route ichnography, slope and curvature.

运用VB设计开发基于三次样条曲线的路线拟合小程序，可视化输出上述数据结果，并与AUTOCAD程序接口，建立不同的图层及颜色，直接输出路线平面图、斜率图、曲率图。

Scan line is used to detect the boundary of the horizontal rim, least square estimation is applied to compute its orientation, and elastic thread techniques is proposed to approach the curve with very low curvature.

提出了扫描线测量横向边框外沿并利用最小二乘法计算其走向的方法以及用来拟合曲率极小曲线的弹性线技术。

Mokhtarian and Mackworth [6.8] introduced several new shape representation methods for planar curves based on the curvature scale space image.

Mokhtarian和Mackworth[6.8]介绍了几种基于曲率尺度空间并适用于平面曲线的图像形状表示法。

Therefore, the contour description combines the simple global information with lo-cal feature points.

轮廓曲线的描述就由其上每一点的曲率和挠率以及特征点来表征。

Cynanchum Lingtai apricot production in the average weight 65 grams, the brightly-colored fruit, juicy rich, sweet-sour taste, sweet from the nucleolus, when the late Qing Dynasty famous Shaanxi, Gansu provinces, the Qing imperial court Tongzhi tribute for years.

灵台生产的牛心杏平均单果重65克，果实色泽鲜艳，汁多味浓，甜酸适口，离核仁甜，清末时就驰名陕、甘两省，清同治年间曾为朝廷贡品。

Chenopodium album,Solanum nigrum, and Amaranthus retroflexus were very susceptible to the herbicides. Polygonum persicaria and Abutilon theophrasti were relatively less susceptible to the herbicides, and Lycopersicon esculentum was not susceptible to it. The relationship between reduction rates of weed biomass and PPM values of weed leaves 2,4, and 6 days after treatment was established.

供试的6种杂草对该混剂的敏感性存在显著差异：红心藜Chenopodium album、龙葵Solanum nigrum和反枝苋Amaranthus retroflexus对该混剂最敏感，ED90值分别为47.65、71.67和29.17g/hm2；春蓼Polygonum persicaria和苘麻Abutilon theophrasti敏感，ED90值分别为96.91、114.20g/hm2；而番茄不敏感。