拟合曲线

A new curvature-based algorithm in free-form curve fitting was proposed to fit a 2D NURBS profile with an arc spline ,where a new form of curvature formula with matrix representation was also proposed,and then the arc spline tool path with G~(1) continuity was generated.

给出了一种平面曲线轮廓的圆弧样条拟合及刀具路径生成算法，该算法面向零件轮廓的光顺性刀具路径生成，通过应用曲线的曲率关系，对以NURBS表示的被拟合自由曲线按参数递增的方向用G1连续的圆弧或直线段逐段拟合，并生成相应的圆弧样条刀具路径，从而实现零件曲线轮廓表面的光顺加工。

Methods Through the triaxial creep test, the triaxial creep curves and isochorounous stress-strain curves have been obtained, then the creep characteristics of mica-quartzose schist have been obtained by analyzing the triaxial creep curves, and the isochrounous stress-strain characteristics of mica-quartzose schist have been obtained by analyzing the isochorounous stress-strain curves. Finally, an empirical formula of creep curve is obtained by data fitting and the analysis of the relation between time and parameter of fitting formula.

通过三轴蠕变试验首先得到了云母石英片岩的蠕变曲线和应力应变等时曲线，然后对试验曲线进行分析得到云母石英片岩的蠕变特性和云母石英片岩的等时应力应变特性，最后拟合应力应变等时曲线，并分析时间和拟合公式中参数的关系，得出了蠕变经验公式。

Leastsquare method and Lagrange's interpolation formula see their applicationsfor fitting fore-and-aft lines-whose aim is to calculate the intersection point ofequivalent inclined waterline-and differences. In order to replace theinconvenient alternate conduct of drawing and calculating, improvement hasbeen introduced into the paper which means all work can be done bycomputer. Capacity calculation cannot be done without boundary layer build-up. Fit every area curve and area moment curve is necessary because ofinterpolation.

在第二章中，给出了B样条函数的数学表达形式，推导了B样条曲线下所围面积、面积矩公式；讨论了最小二乘法和拉格朗日插值法的数学形式，并在拟合船体型线上给出首、尾轮廓线的具体实例，对比不同方法进行拟合的差异，其目的是为了求得与等体积倾斜水线的交点；而水线的确定改变了以往人工作图与计算交替进行的不足，尝试用计算机完全代替人工作图，以求有所改进；在舱容计算中，在至少包括舱室前、后壁的范围内拟合横剖面积、面积矩曲线，插值求得任一纵向位置处的剖面，以解决舱室边界条件。

Results There was a linear trend between logarithmic X and Y, the equation of logarithmic curve was able to be fitted, There was a linear trend between logarithmic Y and X, the equation of exponential curve was able to be fitted, There was a linear trend between logarithmic X and logarithmic Y, the equation of power curve can be fitted. There is a parabola pattern between X and Y, the equation of parabola was able to be fitted.

结果 X取自然对数与Y作散点图有直线趋势，拟合对数曲线方程；Y取自然对数与X作散点图有直线趋势，拟合指数曲线方程；X取自然对数与Y取自然对数作散点图有直线趋势，拟合幂函数曲线方程；原始数据X和Y成抛物线关系，拟合抛物线方程。

First, a smooth curve is obtained from the data by curve fitting with the method of non-linear least squares fit. Then the tangent vector and the radius of curvature of each point on the curve can be calculated for the error evaluation. With the fitted curve, the focusing state of the aspheric lens can be obtained by the method of ray tracing.

主要过程为首先采用非线性最小二乘拟合的方法进行曲线拟合，并计算出曲线上各点的切矢量和曲率半径，分析它们的误差，最后对拟合后的曲线用光线追迹的方法得到非球面镜的聚焦情况。

As the complete characteristic curves of reversible pump turbine are often used to calculate the instantaneous parameters, this paper studies the characteristic curve and the wicket closure and opening law in pumped storage plants.Chapter 1 presents the importance and the necessity of this study and reviews the previous related research on hydraulic transient process and valve regulation in pumped storage plants.Chapter 2 analyzes the six collected characteristic curves of reversible pumped turbine and studies their diversification from the point of view of specific speed. The six collected discharge and moment curves with maximum efficiency have been fitted to piecewise continuous curves. This curve-fitting procedure is listed.Chapter 3 takes Liyang Pumped storage plant as an example and analyzes the effect of different characteristic curves on regulation guarantee parameters and the variety of its trochoid during the same operation status.Chapter 4 takes three pumped storage plants with different heads as examples and studies the characteristic of coordinated closure with wicket gate and ball valve and its effect on dynamic pressure in the spiral case, inlet pressure in the draft tube and the rise of rotating speed.Chapter 5 summarizes this paper and point out what should be done in the future research.

由于在过渡过程分析计算中，需要频繁利用可逆式机组的全特性曲线推求机组的瞬时参数，所以本文就特性曲线及关闭规律问题进行了研究，其主要内容如下：第1章，指出本文研究的意义和目的，回顾前人对水力过渡过程、抽水蓄能电站及阀调节的研究成果，在此基础上提出本文的研究内容；第2章，针对收集到的六套特性曲线，从比转速的角度出发来研究可逆式机组特性曲线的变化规律；并对六套曲线的最高效率流量和力矩曲线进行分段拟合，得到各分段函数的具体形式，再通过举例说明最高效率曲线的拟合步骤；第3章，以溧阳抽水蓄能电站为实例，分析讨论不同比转速特性曲线对调保参数造成的影响及对于相同工况其轨迹线的变化；第4章，结合高、中、低三水头段抽水蓄能电站，在导叶直线关闭的基础上，研究导叶与球阀协联关闭规律的特点及对蜗壳动水压力、尾水管进口压力及转速上升造成的影响；第5章，总结全文，提出今后研究的重点和方向。

(1) In the sorption kinetics experiment, Cu2+ sorptions by Ceratophyllum demersum, Myriophyllum triphyllum and Hydrilla verticillata respectively, all reached balance within 35mins, all of the test results of sorption kinetics recommended the pseudo second-order equation and indicated that this kind of sorption was a complicated process of simultaneous actions of many reactions. The test results of thermodynamic sorption fitted with Langmuir model better than Freundlich model, and the maximum sorption quantites were 13.12, 20.12, 7.79mg/g, respectively,In the desorption test, the desorption rates of each plants were all below 1%, indicating strong sorption-holding action of these submersed mcrophytes on Cu2+.

通过上述研究，得到以下结论： 1、狐尾藻、金鱼藻、黑藻在对铜离子的吸附动力学实验中，均在35min内达到吸附平衡，分别用一级动力学方程和伪二级动力学方程拟合，结果均为用伪二级动力学方程拟合效果较好，表明该吸附为多种反应同时作用的复杂过程；在热力学实验中，三种植物的吸附曲线都能较好的用Langmuir曲线拟合，其拟合最大吸附量分别为13.12、20.12、7.79 mg/g；在解吸实验中，三种植物的解吸率都较低，说明对铜离子都有较好的吸持能力。

In general, the main contents and achievements of this paper consist of the following aspects:(1) Based on the characteristics of the transportation and the classic flow-occupancy inverse "V" model, implement polynomial fitting using least-squares algorithm and statistics method on flow curves to detect outliers which are proved to be not accord with practice through the actual implement, then use the moving average model to recorrect the outliers and absent.

本文根据交通领域的流量—时间占有率的倒&V&字型曲线模型，提出了一种基于曲线拟合的交通流异常检测方法，利用三次多项式的最小二乘法拟合流量/时间占有率曲线，并且利用分箱的思想对拟合好曲线上下部分分别采用基于统计的方法划分上下界，有效的识别异常交通流数据。

In order to contribute to analyse and compute easily setback moving devices on the projectile fuzes,and to make the fuze devisers be able to get the approximate acceleration curves with a few parameters such as tube length and muzzle velocity of the guns,the displacement-time curve and velocity-time curve of gun interior ballistic are fitted with the Logistic models,then the formula of projectile acceleration curves in bore are gotten by the derivation of the formula of fitting velocity-time curve.

为了便于炮弹引信后坐运动机构的分析和计算，能使引信工作者只根据身管长度和炮口速度等少量参数就能获得弹丸膛内加速度近似曲线，运用Logistic函数拟合火炮内弹道的位移－时间曲线和速度－时间曲线，再对拟合得到的速度－时间曲线求导便得到了弹丸膛内加速度近似曲线。

The fitting function is established based on the characteristics of the retarders,and the retardations of all wavelengths and all voltages in the working condition of the retarders are obtained by the least-square curve fitting.

根据延迟器件的特性，建立了相位延迟的拟合函数公式，采用最小二乘曲线拟合的方法得到了延迟器件工作范围内全部波长、全部电压值下的相位延迟，曲线拟合的标准差＜0.02λ。

Lugalbanda was a god and shepherd king of Uruk where he was worshipped for over a thousand years.

Lugalbanda 是神和被崇拜了一千年多 Uruk古埃及喜克索王朝国王。

I am coming just now,' and went on perfuming himself with Hunut, then he came and sat.

我来只是现在，'歼灭战perfuming自己与胡努特，那麼，他来到和SAT 。