基于NPS的常微分方程OBVP的研究

根据样条函数中基函数的特殊选取,构造出了一类新的非多项式样条函数,用来求解常微分方程OBVP的边值问题.给出求解的递推公式,并进行了相应的误差分析,结果显示该方法的局部截断误差为O（h6）.     

Smooth cutting pattern generation technique for membrane structures using geodesic line on subplane and spline interpolation

Practical techniques for smooth geodesic patterning of membrane structures were investigated, For the geodesic search, adjustment of the subplane of the extracted elements series was proposed, and various spline approximation methods were used to flatten the strip for the generation of a smooth pattern. This search approach is very simple, and the geodesic line could be easily attained by the proposed method without the need for a difficult computation method. Smooth cutting patterning can also be generated by spline approximation without the noise in discrete nodal information. Additionally, the geodesic cutting pattern saved about 21% of the required area for the catenary model due to the reduction of the curvature of the planar pattern seam line.     

Study of Quintic Spline Interpolation and Generated Velocity Profile for High Speed Machining

Modern high speed machining (HSM) machine tools often operates at high speed and high feedrate with high ac- celerations,in order to deliver the rapid feed motion.This paper presents an interpolation algorithm to generate continuous quintic spline toolpaths,with a constant travel increment at each step,while the smoother accelerations and jerks of two-order curve are obtained.Then an approach for reducing the feedrate fluctuation in high speed spline interpolation is presented.The presented ap- proach has been validated to quickly,reliably and effective with the simulation.     

An investigation into design of fair surfaces over irregular domains using data-dependent triangulation

Design of fair surfaces over irregular domains is a fundamental problem in computer-aided geometric design (CAGD), and has applications in engineering sciences (in aircraft, automobile, ship science etc.). In the design of fair surfaces over irregular domains defined over scattered data, it was widely accepted till recently that the classical Delaunay triangulation be used because of its global optimum property. However, in recent times it has been shown that for continuous piecewise linear surfaces, improvements in the quality of fit can be achieved if the triangulation pattern is made dependent upon some topological or geometric property of the data set or is simply data dependent. The fair surface is desired because it ensures smooth and continuous surface planar cuts, and these in turn ensure smooth and easy production of the surface in CAD/CAM, and favourable resistance properties. In this paper, we discuss a method for construction of C¹ piecewise polynomial parametric fair surfaces which interpolate prescribed ℜ³ scattered data using spaces of parametric splines defined on H³ triangulation. We show that our method is more specific to the cases when the projection on a 2-D plane may consist of triangles of zero area, numerically stable and robust, and computationally inexpensive and fast. Numerical examples dealing with surfaces approximated on plates, and on ships have been presented.     

基于小波变换的桩基缺陷识别方法

在反射波法的桩基信号检测中主要归纳为检测幅值突变,当反射信号较弱时,用一般的时域分析法或频域分析法,就无法检测桩身质量问题.用小波分析就可以解决这一问题,小波分析具有时频局部化特点.从理论上说,桩基信号混有反映桩基缺陷的脉冲信号,通过对称小波变换后,在一定的尺度范围内其极值点对应原信号的突变位置或时刻.工程中信号分析如用连续小波变换产生的数据量多,且计算量大,分析复杂.而用离散小波变换可以有效地减少数据量,并能识别工程信号的奇异性(缺陷).论文通过一个在确定位置有微弱幅值变化,进行小波变换后(其中小波为二次B样条小波),可以清楚地识别幅值发生突变的时刻.同时也对工程实际中的一具体桩基用低应变动态检测的数据进行了分析,根据桩的破坏特征及离散小波变换后计算桩身发生缺陷的位置,可以确定本例中的桩有4处发生了离析.并且可以有效地对桩基缺陷进行识别.     

稠密散乱数据点多分辨率曲面重构

将曲面重构看作是一种信号重构过程，针对大量散乱数据点，借助成熟的三角网格划分和网格化简算法，利用提升小波变换实现曲面重构，可以快速地构造出复杂拓扑结构的Calmull-Clark曲面；给出了小波系数估算方法以及基于网格拓扑结构的局部最优路径搜索算法．通过运行实例证明了文中算法的有效性．     

带切向控制的多结点曲线造型方法

在普通的多结点样条中加入相当于导数条件的可控参数，通过调节这些参数控制插值曲线在各型值点的切向量，从而达到满意的曲线造型效果．该方法保持了多结点样条的优越性（基数型，局部性），因此可以只对插值曲线作局部调整而不影响整体，有助于计算机辅助几何设计领域的工程人员设计、调整曲线的形状．     

一种基于区域分割的几何模型简化方法

根据几何模型简化中保持细节特征的要求,引入了图像的区域分割原理,提出了一种利用曲度进行区域生长的网格模型区域分割方法,用A型种子或B型种子进行生长,将模型分割为一些区域;在此基础之上,提出了一种基于区域分割的几何模型简化方法,各个区域按照三角形数目的比例进行简化.该方法在保持模型细节特征的基础之上,大大地加快了模型简化的速度;另外还提出了一种累进网格模型的实现方法,实现了具有细节特征的多分辨模型间的层次过渡.实验证明本文所提出的几何模型简化方法加快了网格模型的简化速度,并具有保持模型的三角形网格密度分布的特点,是一种实用、方便和有效的简化方法.     

基于坐标法的复杂曲面轮廓度的误差评定

复杂曲面的面轮廓度是一个应用广泛而又难于测量和评定的问题.在面轮廓度误差评定过程中,首先将复杂曲面的理论模型离散化后用双三次样条函数进行精确描述,并用该拟合曲面作为误差评定的依据;其次对测量后所得的测头球心位置曲面进行等距平移以得到实测轮廓曲面;最后再采用坐标轮换法求取实测点在以双三次样条函数所表示的理论轮廓上的对应点,从而实现对复杂曲面轮廓度的评定.由于本文用双三次样条函数所表示的曲面作为复杂曲面的一般表示,因此该评定算法可实现测量及评定软件的通用性,并通过计算机仿真,证明该算法的正确性与可行性.     

基于测量数据优化修匀的特性曲线样条插值方法

针对传感器特性曲线拟合存在的一些问题,提出了测量数据优化修匀思想以有效消除测量数据的随机误差.应用数值处理软件Matlab结合实验数据研究了基于不同修匀方案的特性曲线的三次样条插值表示并提供了可视化的结果.经过对比不难发现,依据优化修匀数据的三次样条插值误差明显减小,可应用于任意类型传感器或其它仪器仪表的特性曲线的描述与分析.