插值函数

Application of FLAC and numerical differential to surface deformation observation;2. The formulas solving numerical differential and integral of discrete function arc deduced in this paper.

推导了三次样条插值在求解列表函数的数值微分与积分的公式，给出了余项估计，编写了用于求解数值微分与积分的通用程序，通过数值算例表明，三次样条在插值逼近中具有非常好的性质。

Finding out the maximum point of the equivalent plastic strain on each of the vertical lines, a group of discrete points on the critical slip surface will be obtained. Last, the discrete points are smoothed by means of the thin-plate smoothing spline; and the position of the critical 3D slip surface is determined.

最后，采用被称为薄板光顺样条(thin-plate smoothing spline)函数的插值方法对滑面上的离散点进行了插值光顺处理，在不指定边坡滑动模式和滑面形状的前提下就可以得到三维边坡的临界滑面。

Because we mainly involve visual fields of medical science , have placed more contents on the development in the field of medical image of visual technology and argumentation used. Second part It is the visual technology knowledge, the generalization in such respects as the basic principle , basic functions, function store and three-dimensional animation technology to OpenGL ,etc. The realization of the system using OpenGL functions finish that three-dimension demonstration. The third part It is number value that calculate knowledge, three-dimension rebuild technology is it is it is it punish to fit to go on to need, the research of interpolator technology that cant leave, So this part has quoted the Hermite function principle , define cubic Hermite function to begin, calculate the differential coefficient among them draws cubic spline again.

由于我们主要是涉及医学可视化领域，所以将更多的内容放在了可视化技术在医学影像领域的发展与应用的论述；第二部分是可视化技术方面的知识，主要对 OpenGL 的基本原理、基本功能、函数库及三维动画技术等方面的概括，在系统实现时就是通过调用 OpenGL 函数库实现三维显示的；第三部分是数值计算方面的知识，三维重建技术需要进行拟合处理，离不开插值技术的研究，所以这一部分从埃尔米特函数原理开始讨论，引入三次埃尔米特函数，进一步计算时又引用三次样条函数。

Test and simulation shows that the method can eliminate the unsmooth shortcoming caused by subsection low order interpolation with its inherent feature, and can meet the vision effect in inner capacity reconstruction. Further more the volume measurement error are reduced after interpolated by cubic spline without increasing any calculation, and the measurement relative error could reach 2‰ required by the system.

实验和仿真结果证明：该方法能够克服直接累加和传统的分段低次线性插值方法由于函数本身的特性，在各次间歇测量点处产生的衔接不光滑性，满足了变径内腔内表面容积重建中的视觉需求；同时在不增加计算量的前提下使得插值后容积的测量精度得到了提高，且满足2‰测量误差的要求。

On the basis of error processing interpolation theory of non-circular curve and data processing function of Excel, an accurate model of curved parts can be made in Solid Edge with establishing the point curve in Excel.

研究了复杂曲线零件的精确建模，在研究非圆曲线插值算法理论的基础上，利用Excel的数据处理功能，对函数进行误差处理插值计算，在Solid Edge环境中使用Excel创建点曲线的方法进行曲线零件的精确建模，探索出了一种Excel与Solid Edge的完美结合方法，通过凸轮零件精确建模的实际案例，示出了曲线零件建模的整个过程，给出了这种方法在分段曲线中的具体应用。

The results indicate that the inverse distance weighted and kriging interpolation methods are more suitable than the function method and statistical method. And the validity of calibration is influenced by the type and quality of external data. When the external data is precise and regular, the result will be the best.

实验结果表明，相较于函数方法和统计方法，反距离加权法与Kriging方法是更适用的插值方法，而它们的插值效果会受到辅助数据的类型、精度及分布的影响，当辅助数据质量较高且呈规则分布时效果最好。

This paper has discussed four different gridding methods in space domain, i.e., linear interpolation, multiquadric function, ordinary Kriging and inverse interpolation. The calculation of these gridding methods is illustrated by both theoretical model and real aeromagnetic data examples.

文中介绍了线性插值法、多元二次函数法、普通克里格法、反插值法等4种空间网格化法的原理，并利用这些网格化方法进行了理论模型和实际航磁数据的试验分析。

Three kinds of interpolation methods including Inverse Distance Weight, Ordinary Kriging and Thin Plate Smoothing Spline were used to interpolate monthly average air temperature, precipitation and relative humidity at the spatial resolution by 1.0 km×1.0km in 1971-2000 in 92 meteorological stations, which covered the mountainous areas of the Southwest China. The results were verified by the cross validation and the random validation.

用反距离加权法、普通克里格法、薄盘光滑样条函数法三种空间插值方法，对西南地区复杂山地92个气象站点30 a（1971-2000年）的温度、降水和相对湿度月平均资料进行分辨率为1.0km×1.0km的空间插值，并进行了交叉验证和随机站点验证。

The research of both theories and practices of gridding in the dissertation shows that: Linear interpolation based on triangulation is simple computationally and fast, but its gridding results isn't smooth and its precision is low; Multiquardric method is also simple computationally with high precision and good effect, but its gridding is slow because it is based on global calculation; Minimum curvature method is fast with high precision and good effect, but its gridding quickly degrades over areas with sparse data control when grid spacing smaller than the actual grid spacing is used; Ordinary Kriging method is high-precision, but its gridding is slow because of large calculation; Inverse interpolation is a computationally fast, efficient and robust method with high accuracy and perfect effect, and its gridding results of different gridding orientations are basically identical. Inverse interpolation is suitable for thegridding of geophysical irregular data, especially for large-scale geophysical irregular data.

本文的方法研究和数据试验分析表明：基于三角网的线性插值法计算简单，速度快，但其网格化结果不光滑，精度不够；多元二次函数法计算简单，网格化精度高，效果良好，但它是基于全局计算的，计算速度较慢；最小曲率法计算速度快，网格化精度高，效果良好，但其在稀疏控制点的网格化容易出现振荡现象；普通克里格法网格化精度高，效果良好，但其计算量较大，一般计算速度慢；反插值法网格化计算稳定，速度快，精度高，效果好，而且在网格化方向不同的情况下其网格化精度效果都达到基本一致，适合于地球物理不规则分布数据的网格化，特别是大规模地球物理不规则分布数据的网格化。

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。

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 。