B样条工线的小波光顺法

本文研究了Ｂ样条曲线的小波光顺法，首先介绍了利用准均匀Ｂ样条曲线逼近具有任意节点矢量的Ｂ样线的方法，从而将任意Ｂ样条曲线转化为多分辨率表示，进而提出了基于小波的曲线光顺误差控制算法。小波光顺法在光顺曲线的同时具有减少控制顶点的作用，兼具简单性和通用性的优点。     

参数三次B样条曲线的一种整体光顺方法

本文在能量法的基础上，提出了一种新的目标函数，给出了参数三次Ｂ样条曲线的一种新的整体光顺方法。利用这种方法得到的曲线不仅具有较小的应变能，而且曲率变化比较均匀，具有很好的光顺效果。该方法能推广到对曲面的光顺。     

基于半正交B样条小波的任意控制顶点数曲线光顺

目前,小波分析应用于逆向工程时,对控制顶点有特殊要求,只能处理2j r个控制顶点的图形,为此提出了一种可以光顺任意控制顶点B样条曲线的小波分析新方法。在介绍B样条定义的基础上,从小波分析的定义出发,用严格的数学证明推导了任意控制顶点曲线的小波分解与重构具体算法。最后,该算法成功应用于B样条曲线的小波光顺,实例表明,该算法准确、结果稳定,效率理想。     

均匀B样条曲线曲面的小波表示

小波基为曲线曲面带来了更为灵活的表达方式,均匀B样条曲线曲面在经过小波分解以后所得到的小波在定义域边界与内部可以采用统一的表达式,在进行小波重构时仅需作乘法运算,计算效率高。本文试图从几何概念出发由浅入深地论述基于小波的均匀三次B样条曲线曲面多分辨表示的原理及其实现。     

Box－样条级数的单调性

研究了Ｂｏｘ－样条级数的控制点与Ｂｏｘ－样条级数单调性之间的关系，给出其必要条件、充分条件。同时，建立了三方向和四方向Ｂｏｘ－样条级数在任意方向上的单调性条件，这些结论推广了Ｗ．Ｄａｈｍｅｎ和Ｃ．Ａ．Ｍｉｃｃｈｅｌｉ给出的单调性结果［１］。     

基于B样条函数的模糊神经网络

通过研究Ｂ样条函数在模糊系统和神经网络系统中的应用，探讨了通过Ｂ样条函数，结合模糊系统和神经网络的各自特点，构造模糊神经网络的方法，并提出了具体的网络模型以及相应的学习方法。     

带有给定切线多边形的保形有理三次B样条曲线

本文给出了带有给定切线多边形的保形有理三次Ｂ样条曲线，其部分权因子可通过选取切点的位置来确定，由此方法还导出了保形有理三次Ｂ样条插值曲线，最后，给出了两个例子。     

小波基特征提取的复合材料损伤检测

借助小波函数良好的时频带通性，利用Ｂ样条小波级数展开提取信号特征，并使之输入到自适应Ｂ样条小波神经网络进行学习和识别。最后从损伤检测领域中特征信号模式识别的应用角度，给出了利用上述理论进行复合材料无损检测的实例     

B-样条曲面的局部形状改进算法

提出了一种双三次B-样条曲面局部形状改进算法。首先根据节点处三阶不连续性的近似局部光顺准则，选择曲面待光顺的节点；然后利用约束的最小二乘逼近法修改相应的局部控制顶点网，从而降低曲面局部的三阶不连续性，使局部形状得到改进。在详细描述算法原理后，给出了算法的实现步骤。     

一种密集采样数据用特征点表示的处理方法及应用研究

提出了一种密集采样数据的特征点表示法。该方法首先对密集采样数据进行滤波处理，去掉测试过程中的干扰信号和随机误差；然后，采用预定的特征点表示的Ｂ样条曲线与密集采样数据比较，若超过允差，则增加特征点修改Ｂ样条曲线与密集样点值相符为止。     

NURBS曲面光顺方法综述

NURBS曲线、曲面的光顺处理是CAD/CAM中非常重要的问题。在研究了NURBS曲面光顺中的几种常用方法的基础上,针对现有光顺算法在多尺度特征并存曲面光顺中的不足,提出利用各向异性小波在表达高维信息的优势,将各向异性小波融入曲面的多分辨率分析中的思想,应用于NURBS曲面光顺,以达到对曲面特征的保存。     

B样条曲线的小波光顺法

本文研究了B样条曲线的小波光顺法。首先介绍了利用准均匀B样条曲线逼近具有任意节点矢量的B样条曲线的方法，从而将任意B样条曲线转化为多分辨率表示，进而提出了基于小波的曲线光顺误差控制算法。小波光顺法在光顺曲线的同时具有减少控制顶点的作用，兼具简单性和通用性的优点。     

曲面光顺的分片能量法

能量法是一种目前被广泛采用的光顺方法,但当数据点较多时,能量法的存储量和计算量都很大。本文研究Ｂ样条曲面光顺的分片能量法。应用该法可以在保持光顺效果的能量法基本一致的前提下,大大地减少了存储量和计算量。实例表明,这是一种行之有效的曲面光顺方法。     

Multiresolution topology optimization using isogeometric analysis

The paper introduces a novel multiresolution scheme to topology optimization in the framework of the isogeometric analysis. A new variable parameter space is added to implement multiresolution topology optimization based on the Solid Isotropic Material with Penalization approach. Design density variables defined in the variable space are used to approximate the element analysis density by the bivariate B‐spline basis functions, which are easily obtained using k‐refinement strategy in the isogeometric analysis. While the nonuniform rational B‐spline basis functions are used to exactly describe geometric domains and approximate unknown solutions in finite element analysis. By applying a refined sensitivity filter, optimized designs include highly discrete solutions in terms of solid and void materials without using any black and white projection filters. The Method of Moving Asymptotes is used to solve the optimization problem. Various benchmark test problems including plane stress, compliant mechanism inverter, and 2‐dimensional heat conduction are examined to demonstrate the effectiveness and robustness of the present method.     

基于一元对称幂基的等距曲面有理逼近算法

给出了基于一元对称幂基的等距曲面蒙面逼近新算法。利用一元对称幂基逼近张量积Bézier曲面u向曲线的等距曲线,得到一组等距逼近曲线,取固定的v值,得到一组数据点,用反算控制顶点的方法得到过这组数据点的v向曲线。对这两组曲线用蒙面算法得到逼近的有理等距曲面。该算法计算简单,将二元等距曲面有理逼近转化为一元曲线有理逼近,同时方便地解决了整体误差问题,随着对称幂基阶数的升高,可以得到较理想的逼近效果。     

A spline wavelets element method for frame structures vibration

A spline wavelets element method that combines the versatility of the finite element method with the accuracy of spline functions approximation and the multiresolution strategy of wavelets is proposed for frame structures vibration analysis. Instead of exploring orthogonal wavelets for specific differential operators, the spline wavelets are applied directly in finite element implementation for general differential operators. Although lacking orthogonality, the two-scale relations of spline functions and its corresponding wavelets from multiresolution analysis are employed to facilitate the elemental matrices manipulation by constructing two transform matrices under the constraint of finite domain of elements. In the actual formulation, the segmental approach for spline functions is provided to simplify the computation, much as conventional finite element procedure does. The assembled system matrices at any resolution level are reusable for the furthur finer resolution improvement. The local approximation and hiararchy merits make the approach competitive especially for higher mode vibration analysis. Some examples are studied as verification and demonstration of the approach.     

自由型曲面的测量与重建

本方法无需要求采样点有序化和被测面边界的切矢和扭矢为已知,其曲面生成精度高,适用于三坐标测量机上自由曲面的快速,精密测量和重建。     

Implicit boundary method for analysis using uniform B‐spline basis and structured grid

Several analysis techniques such as extended finite element method (X‐FEM) have been developed recently, which use structured grid for the analysis. Implicit boundary method uses implicit equations of the boundary to apply boundary conditions in X‐FEM framework using structured grids. Solution structures for test and trial functions are constructed using implicit equations such that the boundary conditions are satisfied even if there are no nodes on the boundary. In this paper, this method is applied for analysis using uniform B‐spline basis defined over a structured grid. Solution structures that are C¹ or C² continuous throughout the analysis domain can be constructed using B‐spline basis functions. As a structured grid does not conform to the geometry of the analysis domain, the boundaries of the analysis domain are defined independently using equations of the boundary curves/surfaces. Compared with conforming mesh, it is easier to generate structured grids that overlap the geometry and the elements in the grid are regular shaped and undistorted. Numerical examples are presented to demonstrate the performance of these B‐spline elements. The results are compared with analytical solutions as well as with traditional finite element solutions. Convergence studies for several examples show that B‐spline elements provide accurate solutions with fewer elements and nodes compared with traditional FEM. They also provide continuous stress and strain in the analysis domain, thus eliminating the need for smoothing stress/strain results. Copyright © 2008 John Wiley & Sons, Ltd.     

Surface wavelets: a multiresolution signal processing tool for 3D computational modelling

In this paper, we provide an introduction to wavelet representations for complex surfaces (surface wavelets), with the goal of demonstrating their potential for 3D scientific and engineering computing applications. Surface wavelets were originally developed for representing geometric objects in a multiresolution format in computer graphics. These wavelets share all of the major advantages of conventional wavelets, in that they provide an analysis tool for studying data, functions and operators at different scales. However, unlike conventional wavelets, which are restricted to uniform grids, surface wavelets have the power to perform signal processing operations on complex meshes, such as those encountered in finite element modelling. This motivates the study of surface wavelets as an efficient representation for the modelling and simulation of physical processes. We show how surface wavelets can be applied to partial differential equations, stated either in integral form or in differential form. We analyse and implement the wavelet approach for a model 3D potential problem using a surface wavelet basis with linear interpolating properties. We show both theoretically and experimentally that an O(h) convergence rate, h_n being the mesh size, can be obtained by retaining only O((logN) ^7/2N) entries in the discrete operator matrix, where N is the number of unknowns. The principles described here may also be extended to volumetric discretizations. Copyright © 2001 John Wiley & Sons, Ltd.     

On the modelling of smooth contact surfaces using cubic splines

In this paper, a new strategy for the smooth representation of 2D contact surfaces is developed and implemented. The contact surfaces are modelled using cubic splines which interpolate the finite element nodes. These splines provide a unique surface normal vector and do not require prior knowledge of surface tangents and normals. C²‐continuous cubic splines are suitable for representing rigid contact surfaces, while C¹‐continuous Overhauser splines are shown to be most suitable for representing flexible contact surfaces. A consistent linearization of the kinematic contact constraints, based on the spline interpolation, is derived. The new spline‐based contact surface interpolation scheme does not influence the element calculations. Consequently, it can be easily implemented in standard FE codes. Several numerical examples are used to illustrate the advantages of the proposed smooth representation of contact surfaces. The results show a significantimprovement in accuracy compared to traditional piecewise element‐based surface interpolation. The predicted contact stresses are also less sensitive to the mismatch in the meshes of the different contacting bodies. This property is useful for problems where the contact area is unknown a priori and when there is significant tangential slip. Copyright © 2001 John Wiley & Sons, Ltd.