样条函数

In Chapter 1,some elementary knowledge was introduced,such as theBernstein-Bezier representation for polynomials,conform triangulation,theconditions of convexity for Bézier spline surfaces,the funtional andgeometric continuity condition for neibour Bézier surface patches etc.,specially,based on the Liu-Ding-Yuan Theorem for geometric continuity,some simple and practical conditions were obtained.

第一章介绍一些基本知识，如多项式的Bernstein-Bézier表示，相容三角剖分的定义，Bézier三角样条曲面保凸的条件，相邻Bézier曲面片函数连续和几何连续的条件等，特别地，在刘鼎元关于几何连续条件的一般定理的基础上，导出了几个较简单的实用的一阶几何连续条件。

This is for my use of cubic spline function interpolation method procedures.

详细说明：这是我编的利用三次样条法进行函数插值的程序。

This is a cubic spline interpolation function of the realization of the C code.

详细说明：这是一个三次样条插值函数实现的C代码。

Programming with VB Numerical Analysis of cubic spline interpolation function.

详细说明：用VB程序编写的数值分析三次样条插值函数。

This procedure using cubic spline to be smooth margin function programming curve.

详细说明：本程序利用三次样条差值函数编程得到顺滑的曲线。

A projection method is used to smooth out start and end points of the ruling line sets. With predefined Euclidean 6 space distances, the problem of ruled surface approximation from line sets in Euclidean 3 space can be converted into a least square B-spline curve fitting issue in Euclidean 6 space.

利用"投影"光顺法对齐直母线段族首末端点，再通过定义欧氏6空间下的距离函数，将欧氏3空间下的直线族逼近直纹面问题转换成欧氏6空间下B样条曲线最小二乘拟合问题。

During the calculation the results got by quintic spline kernel was the best so it was chosen as the proper kernel for the SPH simulation. By comparison of the simulation results got by SPH and finite volume method, it was proved that the buffer cells method proposed in the SPH simulation to implement the Dirichlet boundary conditions was accurate, and this is of great importance for the simulation of flows pass a pipe. At last, the SPH method was improved to simulate the liquid-solid two phase flows and the results show that this method was appropriate for the simulation of flows containing viscous fluid and macroscopic solid components. Now the two methods are both able to predict the continuum flows and rarefied flows severally, but the hybrid program still has some aspects to be improved.

首先用标准算例验证了SPH方法的理论模型和计算程序的准确性；通过比较确定选用五次样条核作为计算低雷诺数下的粘性连续流动时的核函数；采用SPH方法和有限体积法分别对同一管道流动进行了对比计算，证明了本文提出的边界缓冲区方法在实现SPH方法中的流体边界条件时的有效性，解决了SPH方法模拟管道流动时的一个关键问题；巧妙地使用SPH方法对化工分离流动中常见的固液两相流及固液耦合作用进行了模拟尝试，获得了较好的结果；在跨尺度计算方面，目前两个子程序已经能够分别模拟连续的和稀薄的二维管流问题，二者的耦合计算程序还处于调试和优化阶段，各个参数对于计算精度和计算速度的影响规律仍在探索中。

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。

Signal analysis;parabola parameter spline curve;Empirical Mode Decomposition;Intrinsic Mode Function;Hilbert transform

信号分析；抛物参数样条曲线；经验模态分解；固有模态函数；希尔伯特变换

Taking the first boundary condition as an example, it used the second order derivative of the junctions to represent the cubic spline interpolation function, and solved the relative equations with chasing method.

以第1边界条件为例，用节点处二阶导数表示三次样条插值函数，用追赶法求解相关方程组。

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。