样条函数

Experimental results show the recognition rate of the method is 95%for a known expresser and 72% for a novel expresser. Aiming at the shortcomings of optical flow technique,two improved optical flow algorithms are presented.One way is to introduce forward and backword constraint eqution and Hessian matrix of optical flow equation is computed.The well- posedness of each point of local neighbourhood is examined and the weight of Lucas-Kanade's method is defined as the reciprocal of the conditioning number of its Hessian Matrix.

3针对传统光流法的缺点，分别提出了两种不同的改进方法：其一为引入前向-后向光流方程，计算其Hessian矩阵，把Hessian矩阵条件数的倒数作为Lucas-Kanade光流法的加权阵，可有效消除局部邻域中不可靠约束点，同时提高基本约束方程解的稳定性；其二为针对传统光流法只适用于刚体运动的特点，在扩展约束光流方程的基础上引入了div-curl样条函数作为扩展光流约束方程的附加约束条件，给出了一阶和二阶div-curl样条约束下光流的数值解。

According to the hypothesis of continuum, a tube with the corner strengthened is gained to make an equal of the frame-tube. B3-spline functions and parabola functions are applied to simulate the displacement functions of the frame-tube. The system of equations about the undetermined coefficients of displacement functions is deduced by using energy-variational principle, by solving which the displacement of the frame-tube is gained. Then the internal forces in the columns and beams of the former frame-tube are obtained according to the principles of elasticity mechanics.

根据连续化假设将框筒等效为角部加强筒体，将三次样条函数与抛物线函数结合假定框筒的位移函数，运用能量变分原理推导出了关于位移函数待定系数的方程组，解得位移函数待定系数进而解得框筒的位移，再根据弹性力学原理确定原框筒中梁柱的内力。

With thw cubic B spline function treated as displacements, the spline element stiffness matrix is established based on the principle of minimum potential energy.

用3次B样条函数来构造结构的位移模式，基于最小势能原理导出了桥梁结构的样条单元刚度矩阵。

Lastly,we present an algorithm to isolate real roots of a univariate spline, i.e., computing asequence of disjoint intervals such that each of them contains exactly one real root of agiven spline function, which is primarily based on the use of Descartes rule of signs withits B-spline coefficients and de Casteljau algorithm of Bzier curve.

最后，基于B-样条系数的Descartes符号准则和Bézier曲线的de Casteljau算法，我们给出了一元样条实根分离算法，也就是计算出一列不相交区间，使得每个区间恰好只包含此样条函数的一个实根。

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。

The benefit of this method is its mathematical simplicity and its consequent ease in programming. Secondly, it brings out a new 3D interpolation method—hypersurface spline method, this method extends the surface spline method of 2D interpolation into 3D space.

其次，提出了一种基于超曲面样条函数进行三维空间插值的新的三维空间插值方法，该方法将二维的曲面样条函数插值法进一步拓展到三维空间。

Introduced is a kind of space uniform rational spline curve, which possesses tension parameters and is based on hyperbolic spline functions.

引入了基于双曲样条函数的、具有张力参数的空间有理等距节点样条参数曲线，给出了这种曲线在每个样条子区间上为挠曲线段的充分必要条件；分析了这种挠曲线段没有尖点、重结点和泛拐点的特性；因而在用于空间曲线几何造型时可避免奇异性。

Reconstructs the surface by one and two dimensional spline functions with 3D data obtained from laser scanning system.

针对获得的三维扫描数据，应用一元、二元的多种样条函数进行了三维表面信号的恢复和重建。文中研究了样条函数的构造和使用方法。

Average annual precipitation data of the last 30 years from 1961 to 1990 at 186 meteorological stations in Gansu and its nearby regions was compared and analyzed by Inverse distance weight tension, Spline, Ordinary Kiging methods. The result showed that the three interpolators could reflect the spatial distribution of precipitation of Gansu province. Ordinary Kriging method was the most effective, followed by Spline methods and Inverse distance weight tension method.

利用甘肃及其周边186个气象台站30年平均降水资料，分别采用了反距离加权法(In-verse distance weight tension)、样条函数法和普通克里格法等3种常见的空间内插方法较为系统的分析比较了这3种内插方法插值结果，结果表明：3种方法的结果都基本上反映了甘肃降水大体空间分布规律，而普通克里格法的插值效果最好，样条函数法次之，反距离加权法较差。

This paper is mainly focused on data segmentation and model reconstruction problems in Reverse Engineering fields,The main contents include Sharp Featurebased quadrilateral domain extraction from a mesh model,connectivity between multiple B-spline surfaces,fast algorithm for fitting multiple B-spline surfaces on model with arbitrary topology,setting up a hierarchically structured constraintbased data model and binary cubic interpolation of splines with C~2 connectivity for type-Ⅱtriangulations on rectangular domain.

主要内容包括：网格数据的数据分割及矩形片的提取、多个B样条曲面间光滑拼接、任意模型的多个B样条曲面拟合的分块快速算法、基于二元三次样条函数在TYPE-Ⅱ分割下的曲面重建方法、基于约束和层次结构的模型表示及一个小型逆向工程软件系统的建立等。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。