Based on the test data , and by using the distillerys grain drying curve and drying - rate curve , this paper analysed the distillerys grain drying process , and demonstrated the characteristics of the drying and the change of drying - rate of the distillerys grain in heat - air penetrating bed 根据试验所测数据，利用三次样条插值函数拟合酒精糟干燥曲线和干燥速度曲线，深入分析酒精糟的干燥过程，得出酒精糟在热风穿床干燥方式下的干燥特点和干燥速度的变化规律。
The theoretic analysis of the characteristic of piping vibration is carried out in this paper , and the mathematic model is established . hermite insert function and finite element method , by means of matlab software , are adopted to solve the high level partial differential equation . the natural frequency and vibration pattern of the pipeline are obtained 对管道的振动特性进行了理论分析，建立了管道系统的数学模型，采用有限元方法，建立hermite插值函数，对高阶偏微分方程进行了求解，得到了管道系统的固有频率和振型。
The numerical example shows that if we use the correct guess integral , this method will give right answer . it has good performance for both p - version and hybrid stress fem . last , a hybrid stress finite element with second stress completion is presented , which keeps the virtue of normal hybrid finite element , especially good for incompressble material , because it can avoid the self lock of displacement and instability of stress results 第一部分还首次提出了一个满足二次应力完备的杂交应力单元，它的应力满足二次应力完备，而且通过巧妙的应力插值函数，避免了一般杂交应力元的矩阵求逆过程，而通常这个求逆过程都是很耗时的，这个二次应力完备杂交元保持了一般杂交元的优点，对于不可压缩问题具有较好的性能。
To improve computing precision , the latter applies interpolating function of curved - quadrilateral element containing six npdes to thicking the influence surface of grillage . compared with lagrangian interpolation for rectangular element and triangle plane interpolation , this way not only improves computing precision but be more suitable for the curved - bar grillage analyzing method introduced this paper 为了提高计算精度，本文应用六结点曲边四边形单元插值函数加密梁格影响面，与矩形单元拉格朗日插值及三角平面插值方法相比，不但提高了计算精度，且更适于曲杆梁格分析。
At first , this paper presents two - demensional quartic convolution interpolation to smooth digital terrain . it is acquired from that it makes use of that the interpolation function of cubic spline interpolation has a continuous third derivative on the base of two - dementional cubic convolution interpolation . two - demensional quartic convolution interpolation is more precise than two - dementional cubic convolution and simpler than cubic spline interpolation in calculation . it can satisfy real - time route planning of ucav 首先，在轨迹规划前需要对数字地图进行平滑处理，本文提出了二维四次卷积插值法。它在二维三次卷积插值法的基础上利用三次样条插值法的插值函数具有三阶连续导数的性质而得来的。
First , cyberware laser scanner scans the face of a specific person to acquire its geometry data and texture image . then , the 3d coordinates of the feature points on the face model can be decided upon the geometry data and texture image of the specific face . a deformation method based on interpolation function is adopted for face model calibration 首先用cyberware激光扫描仪获取一个特定人的人脸的几何数据和纹理图像；然后由特定人的人脸的几何数据和纹理图像，可以获得人脸模型的特征点的三维坐标，采用基于插值函数变形的方法进行一般人脸模型的校准；最后使用纹理映射的方法将纹理图像贴在人脸模型上，经过渲染可以得到特定人的人脸模型。
The water quality respond relation of input - output measurements are established by systematic theory in this paper . according to the peculiarity of hydrology and the necessity of water quality inverse problem the multi - parameter inverse problem model based on ordinary differential equation is developed . the existence and uniqueness of the solution of the ordinary differential equation about two parameters or multi - parameter are to be proved . the unstability depending on errors between monitoring data and interpolation approximate data are analyzed and demonstrated . cubic spline interpolation function , the least two multiply and positive rule method are conjoined for obtained solution of multi - parameter . the results from this algorithm indicats its efficient to the multi - parameter identification in water quality modeling 本文应用系统理论，建立了水质多参数输入输出之间的响应关系；根据河流水文水质变化特点和参数反问题的需求，建立了水质常微分方程多参数反问题模型.根据常微分方程参数反问题的数学理论，作者给出了两参数和多参数水质常微分方程反问题的解的存在性、唯一性的理论证明过程和结论；还针对水质现有监测资料的测验误差和插值近似计算误差造成参数反问题的不稳定性，将三次样条插值函数、超定方程最小二乘法和正则化算法有机地结合使用，成功地给出了水质参数反问题的稳定化算法.最后给出了应用计算结果
And in this part , the algorithm of polygons is emphasized . the second part is focused on image morphing . after expatiating its principal algorithms and mature methods , a method among multiple images is presented and analysed in detail . second , in the second chapter of this thesis , the basic theories and methods are systematically discussed , especially thiele continued fractions , because it is the main interpolation tool in the experiments . and finally , the processes and results of experiments in the application of continued fractions to 2d object metamorphosis are given , and detailed analyzing and discussing are made . the experiments show that the results are good . this demonstrates that it is successful for continued fractions to be applied in the processes of 2d object metamorphosis 其次，在本文的第二章，系统地论述了连分式的基本原理和应用方法，尤其是对thiele型连分式插值函数作了具体的讨论，因为，它是在实验中所用到的主要的插值工具。最后，本文的结尾，给出连分式应用于二维物体渐变的实验过程和结果，并对其进行了仔细的分析和讨论。实验表明，把连分式用在二维物体的渐变过程中，取得了不错的效果，是成功的。
The interpolation is applied widely in medical image processing . since the ideal interpolation function spatially is unlimited , several class of practical interpolation kernels have been introduced : piecewise local polynomials , windowed sinc , lagrange , gaussian et al . . and their properties have been analyzed in spatial and frequency domain and from evaluation and result 插值在医学图像处理中应用非常广泛，因为理想插值函数在空域无限扩展，论文引入了几类实际插值核：分段局部多项式、加窗sinc 、 lagrange和gaussian等，并从空域、频域、实现代价和实际效果上进行了分析和讨论。
With the review of digital image properties and continued fractions theory , this dissertation focuses on the study of the image interpolation and image reconstruction ; the main contributions are as fallows : first of all , the methods of solving the problem of inverse difference being infinite are successfully found while constructing the thiele - type continued fractions . in this case it is proposed to reorder the set of interpolating points and then construct a thiele - newton blending continued fraction 本文的主要工作可归纳如下：首先，在以图像像素为插值节点集，构造连分式插值函数过程中出现逆差商为无穷大的情况，给出了合理的解决办法，提出了重新调整插值节点集的节点顺序、构造thiele - newton型混合有理的插值方法。
