插值问题

The irrational function forms interpolation on a polygonal element with arbitrary nodal distribution was constructed by using mean value coordinates of polygonal elements.

本文采用多边形单元的平均值坐标，构造任意节点分布的多边形单元无理函数形式的插值函数，提出了一种求解微分方程边值问题的多边形有限元方法。

Differential matrices are obtained on the element in accordance with continuous intervals of discontinuous boundary value problem to divide the computing elements and approximating unknown function on the element in term of barycentric Lagrange interpolation.

按照间断边值问题的连续区间划分计算单元，在每一个单元上采用重心Lagrange插值近似未知函数，得到每一个单元上的微分矩阵。

This method dexterously inverts the three-dimension problem into two dimension and properly uses interpolating method. It also can be applied in the other sensor that has same problem.

该方法巧秒地把一个三维的问题转化成二维问题，并加以合理地应用插值数学方法，可以推广应用到存在相似问题的其他类型传感器中。

A high accuracy finite volume element method was given based on cubic spline interpolation for linear and nonlinear twopoint boundary value problems of ordinary differential equations. The computational scheme was derived and the property of positive type was discussed. Further we presented the convergence analysis and the scheme was proved having fourth order error estimate in discrete energy norm.

针对常微分方程线性和非线性两点边值问题，提出了基于三次样条插值的高精度有限体积元方法，给出了具体计算格式，讨论了格式所具有的优良性质--正型性，并应用能量方法给出了收敛性分析，证明了格式按照离散能量模具有四阶精度。

Based on the summarizing of the exiting algorithms of the texture mapping and antialiasing, this paper goes deeply into the basic theory and processing of texture mapping. The texture compress algorithm which can satisfy the need of the memory and time is given for the stochastic sampling in the inverse texture mapping; the geometry transformation in the texture mapping are discussed and the concepts of the unitary parametrization and the patch parametrization is proposed, some kinds of the unitary parametrization methods of parametric surfaces and the geometry transformation in the patch parametrization are also presented; in order to solve the aliasing in the parametrization of intermediate surface-sphere in two-part texture mapping, an area-preserving transformation is presented also; to improve the quality of the graph the aliasing in the texture mapping is analyzed from the aspect of signal process, and the modified summed-area tables algorithms is proposed; the distortion of the scanline conversion algorithms under perspective transformation is analyzed and the proper interpolation algorithm is presented so the aliasing problem of the polyhedral object after the unitary parametrization is efficiently solved.

本文在总结现有的纹理映射和反走样算法的基础上，深入研究了纹理映射的基本原理与过程，根据反向纹理映射对纹理随机采样的特殊要求，提出了一种可满足存储空间和寻址时间的纹理压缩存储算法；通过对纹理映射中几何变换理论的进一步深入探讨，提出了整体参数化和面片参数化的概念，并给出了参数化曲面的各种整体参数化方法和面片参数化的几何变换形式；针对现有的两步映射算法所存在的中间曲面—球面的参数化问题，提出一种等积映射方法，较好地实现了由非参数化面片拼接而成的多面体表面的纹理映射；从信号采样的角度深入分析了纹理映射中走样产生的原因，提出了改进的区域求和表算法，使图形生成的效果有所提高；还分析了一般的扫描线算法在透视变换中所存在的问题，提出了一种正确的插值算法，从而解决了整体参数化后多面体表面纹理映射的几何变形问题。

This book reviews the many areas of numerical analysis, including the configuration polynomial, finite difference, factorial polynomials, summation, Newton formula, operator and configuration polynomial, Cheung section, close polynomials, TaylM more item type, interpolation, numerical differentiation, numerical integration, and with the series, differential equations, differential equations, least squares polynomial approximation, minimax polynomial approximation, rational function approximation, triangular approximation, non-linear algebra, linear equations, linear programming, boundary value problems, MonteCarIo methods and so on.

本书综述了数值分析领域的诸多内容，包括配置多项式、有限差分、阶乘多项式、求和法、Newton公式、算子与配置多项式、祥条、密切多项式、TaylM多项式、插值、数值微分、数值积分、和与级数、差分方程、微分方程、最小二乘多项式逼近、极小化极大多项式逼近、有理函数逼近、三角逼近、非线性代数、线性方程组、线性规划、边值问题、MonteCarIo方法等内容。本书的特色主要表现在利用例题及大量详细的题解来透彻地阐明所述内容的内涵，同时附有大量的补充题以便读者进一步巩固和深化从书中获得的数值分析知识。

The Neumann boundary value prob-lem is firstly reduced into the equivalent natural boundary integral equation withthe kernel possessing 2nd-order singularity,and then the corresponding variationalproblem on the boundary is obtained.By applying Quak trigonometric wavelet basisBjsee(1.2.3as boundary elements and the method of expanding kernel functionto its Galerkin discretization,we obtain simple computational formulae of the en-tries in the stiffness matrix.

首先，我们将Neumann边值问题归化为等价的带有2阶强奇性核的自然边界积分方程，然后化为边界上相应的变分形式，以Hermite插值Quak三角小波基Bj见(1.2.3作为边界元并利用积分核函数展开法将其离散，得到了十分简单的刚度矩阵系数的计算公式，而且刚度矩阵具有十分简单的形式，它是分块循环对角阵。

A kind of delay parabolic partial differential equation is studied. A numerical method is proposed by discrete skill. The numerical stability for this kind of delay parabolic partial differential is analyzed by interpolation method.

研究了一类时滞的抛物型偏微分方程初边值问题，利用离散技巧，提出了一种数值方法，然后在一定插值技术下分析了算法的稳定性。

Trace interpolation plays an important role in seismic data processing. Spatial aliasing is a principal troublesome problem in seismic trace interpolation.

道间插值方法在地震资料处理中具有十分重要的作用，而地震道空间内插所面临的主要问题是空间假频。

The purpose of this dissertation is to study a principle or method to describe and analyze the complex problems with high gradients arising from practical engineering. The main contents cover:1. The Bezier function was introduced to approximate high gradient functions, and a suitable coupled function was derived. Some detail numerical results show that the Bezier-based function is dominant over other combination function such as polynominal and trigonometric series, when to describe a high gradient function.

针对工程中大量存在的高梯度问题进行函数逼近的研究，引入Bezier函数对高梯度问题进行函数逼近，构成以Bezier函数为主的复合逼近函数，数值考证表明：与常规多项式插值函数的逼近及"幂／三角"复合函数的逼近相比，基于Bezier函数的逼近函数对高梯度问题的描述具有明显优势。

It has been put forward that there exists single Ball point and double Ball points on the symmetrical connecting-rod curves of equilateral mechanisms.

从鲍尔点的形成原理出发，分析对称连杆曲线上鲍尔点的产生条件，提出等边机构的对称连杆曲线上有单鲍尔点和双鲍尔点。

The factory affiliated to the Group primarily manufactures multiple-purpose pincers, baking kits, knives, scissors, kitchenware, gardening tools and beauty care kits as well as other hardware tools, the annual production value of which reaches US$ 30 million dollars.

集团所属工厂主要生产多用钳、烤具、刀具、剪刀、厨具、花园工具、美容套等五金产品，年生产总值3000万美元，产品价廉物美、选料上乘、质量保证，深受国内外客户的青睐