一种B样条曲线局部修改算法

针对B样条曲线局部修改的问题,提出一种双正交非均匀B样条小波与外部能量约束相结合的算法。与传统能量约束法相比,该算法使曲线除局部修改外整体形变较小,具有一定的保形效果。     

NURBS曲线曲面的多分辨率几何建模

针对均匀和准均匀B样条小波多分辨率建模表示能力和适应性的不足,基于离散内积和非均匀B样条节点插入算法建立了一种非均匀半正交B样条小波,并进一步论述了其在非均匀B样条曲线曲面中的多分辨率设计.最后通过实例对非均匀B样条曲线曲面中的多分辨率建模进行了说明和验证.     

基于双正交非均匀B样条小波的曲线逼近方法

针对B样条曲线逼近有序数据点在应用最小二乘法时出现的计算量较大问题,提出一种基于双正交非均匀B样条小波的曲线逼近方法。其基本思想是：先用最小二乘法生成初始B样条逼近曲线,再用细节曲线逼近误差向量,接着将细节曲线叠加于原逼近曲线得到新的B样条曲线,这个过程是迭代的。细节曲线的基函数是双正交非均匀B样条小波。与传统最小二乘法相比,该方法仅需计算新增线性系统,避免重复计算原系统,降低了计算量,提高了运算效率;此外,给出了B样条逼近曲线的一种多分辨率表示形式。     

任意NUBS曲线的小波分析和造型技术

为了对任意NUBS曲线进行精确的分解和重构，提出了半正交B样条小波分解和重构的新算法，同时给出了处理非均匀B样条曲线的非整数阶分辨率的小波分解和重构算法，并实现了任意非均匀B样条曲线的多分辨率表示，对于任意非均匀B样条或NUBS曲线，无论它有多少个控制点，均可以对它进行半正交分解和重构，而不受控制点数必须等于2＋3的限制，从这个意义上讲，该方法不仅可以实现连续分辨率水平（continuous-resolutionlevel)的非均匀B样条曲线造型，还可以对非均匀B样条和NURBS曲线进行精确的分解和重构，这对于B样条曲线曲面的多分辨率造型与显示具有重大应用价值。     

根据时-频分辨特性的B样条双正交小波的选择

该文简要地分析了在基于小波变换的图像和视频编码中小波基的选择对编码效率和编码质量的影响，从适于提取图像和视频信号高频成分的角主，提出了根据时－频分辨特性对B样条双正交小波进行选择的标准，给出了B样条小波的构造过程和计算时－频窗面积的方法，并对2≤N≤20的N阶B样条函数，得出了使其分析小波函数具有最优时－频分辨特性的条件，该条件表明：B样条函的阶数较低时，其分析波波函数的时－频分辨特性较好，并且N取偶数时的B样条双正交小波的时－频分辨特性要相对优于N取奇数时的B样条双正交小波的时－频分辨特性，据此条件，可以求出相应的对偶尺度函和小波函，最后，通过选用几个典型的双正交小波进行编码模拟实验，验证了得出的结论。     

正交样条小波在图像压缩中的应用

给出了正交样条小波滤波器系数的计算方法和数据，将正交样条小波应用于图像压缩中，并与其他常用的小波如Daubechies小波和双正交小波进行了比较。结果表明，用正交样条小波进行图像压缩可以取得很好的效果。     

基于小波的非均匀B样条曲线自动光顺算法

为了更好地对曲线进行自动光顺,针对一般的非均匀B样条曲线,提出一种基于非均匀B样条小波的曲线光顺算法.首先将曲线分解为尺度部分和细节部分,并把细节部分再次分解为小波尺度部分和小波细节部分;然后通过自动设定阈值对小波细节部分进行修复,并通过小波重构得到新的控制顶点;最后对新的控制顶点进行迭代计算,直至达到满意的光顺效果.通过设定光顺误差限,采用该算法可以在计算机上对曲线进行自动光顺操作.实例验证表明,文中算法比其他基于小波的曲线光顺方法具有更好的光顺效果.     

准均匀B样条曲面的多分辨率表示及应用

在多分辨率曲线和曲面造型中，B样条小波已经得到了广泛应用。曲线和曲面的多分辨率造型成为一个研究热点。通过阐述准均匀B样条曲线曲面的基于小波分解的多分辨率表示的数学原理，给出了具体的曲线和曲面小波分解算法和实验结果，说明了准均匀B样条曲面多分辨表示的优点及其在工业上的应用。     

用封闭周期域对称B样条基实现均匀样条逼近

针对现有求解均匀样条曲线控制顶点方法巾使用较为复杂的迭代算法的不足,提出均匀样条曲线控制顶点的快速并行算法.首先将基本B样条基平移建立对称B样条基(参数定义域为单位区间);然后利用复函数组{εk(v)=e1kv}的正交性构造封闭周期区域的正交B样条基,得出正交B样条基系数的显式并行计算公式;进一步,利用正交基系数与对称B样条基系数(样条曲线控制顶点)的关系,得出控制顶点的显式并行计算公式.最后以四阶与三阶样条逼近为例分析并行公式的快速算法,用从封闭及任意给定点列构造B样条曲线的2个例子证明了该算法的有效性.实验结果表明,文中算法为简单的B样条基增加了对称性,能够容易地实现快速并行计算,可提高构造大规模样条曲面的效率.     

关于数字图像压缩中小波基选择问题的探讨

针对数字图像压缩编码中最优小波基的选择问题,论证了双正交样条小波基的优点,并对其进行了推导.样条小波的导数连续性保证了小波基的光滑性,双正交对偶小波的对称性使得滤波器具有线性相位,可减小失真,保证重构图像的质量.     

Multiresolution for Algebraic Curves and Surfaces using Wavelets

This paper describes a multiresolution method for implicit curves and surfaces. The method is based on wavelets, and is able to simplify the topology. The implicit curves and surfaces are defined as the zero-valued piece-wise algebraic isosurface of a tensor-product uniform cubic B-spline. A wavelet multiresolution method that deals with uniform cubic B-splines on bounded domains is proposed. In order to handle arbitrary domains the proposed algorithm dynamically adds appropriate control points and deletes them in the synthesis phase.     

Construction of the matched multiple knot B-spline wavelets on a bounded interval

In order to solve a boundary value problem using Galerkin's method, the selection of basis functions plays a crucial rule. When the solution of a boundary value problem is not enough smooth or the domain is irregular, multiple knot B-spline wavelets (MKBSWs) with locally compact support are appropriate basis functions. However, to have globally continuous basis functions, a matching across the subdomain interfaces is required. In other words, MKBSWs that are non-zero in the interelement boundaries should be matched. In this paper, we present the primal and dual matched multiple knot B-spline scaling and wavelet functions whose main properties of smoothness and biorthogonality are kept.     

The method of moments for solution of second kind Fredholm integral equations based on B-spline wavelets

In this paper, we propose the linear semiorthogonal compactly supported B-spline wavelets as a basis functions for the efficient solution of linear Fredholm integral equations of the second kind. The method of moments (MOM) is utilized via the Galerkin procedure and wavelets are employed as test functions.     

The solution of a second-order nonlinear differential equation with Neumann boundary conditions using semi-orthogonal B-spline wavelets

A numerical technique for solving a second-order nonlinear Neumann problem is presented. The authors’ approach is based on semi-orthogonal B-spline wavelets. Two test problems are presented and numerical results are tabulated to show the efficiency of the proposed technique for the studied problem.     

B样条曲线的多分辨编辑新算法

概述小波分析与重构的基本理论,将小波分解的理论应用于B样条曲线的多分辨编辑中,提出一种小波分析和重构的新算法。该算法利用方程组的增广矩阵为类带状矩阵或者稀疏矩阵这一特点,运用简单的矩阵的行初等变换,将类带状矩阵或者稀疏矩阵化成容易接受的行简化矩阵,解方程组,使小波分解与重构的过程快速准确,使从事相关工作的技术人员更容易理解和接受。     

Wavelet-Based Data Reduction of B-Spline Curves

1 Introduction The problem of reducing the amount of data in the representation of a function or a curve is not new. Many papers have already been published. In these strategies, two trends can be emphasized[1]. The first one deals with polygonal curves for approximating data[2],[3]. Another approach is based on spline curves[4]~[8]. In the first approach, the problem is formulated so that the perpendicular distance of each point on the curve to the fitted line segments is within a predefined…     

The Multi-scale Method for Solving Nonlinear Time Space Fractional Partial Differential Equations

In this paper, we present a new algorithm to solve a kind of nonlinear time space-fractional partial differential equations on a finite domain. The method is based on B-spline wavelets approximations, some of these functions are reshaped to satisfy on boundary conditions exactly. The Adams fractional method is used to reduce the problem to a system of equations. By multiscale method this system is divided into some smaller systems which have less computations. We get an approximated solution which is more accurate on some subdomains by combining the solutions of these systems. Illustrative examples are included to demonstrate the validity and applicability of our proposed technique, also the stability of the method is discussed.