优化端点条件的平面二次均匀B样条插值曲线

在利用反求法构造B样条插值曲线时,往往需要选取端点条件。 因此,可对端点条件进行优化选取,使得构造的B样条插值曲线满足特定要求。提出了一种利用曲线内能极小选取平面二次均匀B样条插值曲线端点条件的算法。首先给出了二次均匀B样条插值曲线分控制顶点与首个控制顶点（即端点条件）的递推关系式;然后给出了利用曲线内能极小优化选取首个控制顶点的算法,证明了利用该算法构造的C¹连续二次均匀B样条插值曲线为保形插值,并通过数值算例证明了算法的有效性;最后,为便于实际应用,基于MATLAB平台设计了算法所对应的图形用户界面,用户通过简单的操作即可获得光顺的C¹连续二次均匀B样条保形插值曲线。     

导数振荡与应变能极小的平面分段三次参数Hermite插值

由于分段三次参数Hermite插值的切矢往往被作为变量,故可对其进行优化以使得构造的插值曲线满足特定的要求.为了构造兼具保形性与光顺性的平面分段三次参数Hermite插值曲线,给出了一种通过同时极小化导数振荡和应变能来确定切矢的方法.首先以导数振荡函数和应变能函数为双目标建立了切矢满足的方程系统;然后证明了方程系统存在唯一解,并给出了解的具体表达式;最后给出了误差分析,并通过数值算例表明方法的有效性.结果表明,相对于导数振荡极小化方法和应变能极小化方法,所提出的导数振荡和应变能极小化方法同时兼顾了平面分段三次参数Hermite插值曲线的保形性和光顺性.     

q-Stancu算子的保形性及收敛定理

给出了基于q-整数的Stancu算子Ln（·,q）,同时研究了该算子的一些基本性质．首先,利用q-Stancu算子作用于某一函数f（x）以后Ln（f,q;x）与f（x）变号数的关系,得到了该算子的保形性定理．其次,通过精细的不等式放缩,该算子作用于一般的连续函数后收敛于一极限算子,而不像一般算子那样收敛于函数本身,并用光滑模刻画了其收敛速度．     

On Non-Uniform Algebraic-Hyperbolic （NUAH） B-Splines

The recurrence algorithm is given for the calculation of NUAH B-splines in the space Sn 1 = span{sinh t, cosh t,tn-3,...,t2.t, 1} (n≥3). The case of NUAH B-spline bases of low order with multiple knot sequences is studied. The limiting cases of UAH B-splines are recovered when shape parameters a's→0 and ∞. Then the corresponding NUAH B-spline curve is defined and its main properties such as shape-preserving properties are investigated.     

Shape-Preserving C 2 Functional Interpolation via Parametric Cubics

The paper proposes a method for the construction of a shape preserving C² function interpolating a given set of data. The constructed interpolant is a parametric cubic curve. The shape of the curve can be easily controlled via tension parameters which have an immediate geometric interpretation. The approximation order is investigated and numerical examples are presented.     

解y"=g(x,y)初值问题含参数线性多步方法的相容阶和收敛阶

1 引 言对于直接积分二阶常微分方程的初值问题 y"=g(x,y) y (x_0)=y_0,y'(x_0)=y"_0,x_0 x T,(1)     

STANCU POLYNOMIALS BASED ON THE Q-INTEGERS

A new generalization of Stancu polynomials based on the q-integers and a nonnegative integer s is firstly introduced in this paper.Moreover,the shape-preserving and convergence properties of these polynomials are also investigated.     

保形闭圆弧样条插值的改进算法

在CNC加工中,直线段和圆弧是加工路径的重要组成部分.而圆弧样条的段数和曲线的保形性,是比较重要而且富有实际意义的.提出了一种改进的G1圆弧样条保形插值算法,该算法在型值点列满足较弱的条件下,具有圆弧段数较少,并且保形的特点.     

基于双二次样条函数的一类保形拟插值

给定一组数据点{(xi,yj,f(xi,yj)}(i=1,2,…,n;j=1,2,…,m)构造一类由双二次样条函数生成的保形拟插值σ(x,y)=(n+k∑i=1-k)(m+l∑j=1-lf)(xi,yj)Bkl ij(x,y),1≤k≤n,1≤l≤m,证明了σ(x,y)具有线性再生性,并且保持原有数据点的单调性和凸性等一系列保形性质.在计算机辅助几何设计和曲线曲面造型技术中利用这一性质设计和构造曲线或者曲面是相当便利的.     

SOME SHAPE-PRESERVING QUASI-INTERPOLANTS TO NON-UNIFORMLY DISTRIBUTED DATABY MQ-B-SPLINES

Based on the definition of MQ-B-Splines, this article constructs five types of univariate quasi-interpolants to non-uniformly distributed data. The error estimates and the shape-preserving properties are shown in details. And examples are shown to demonstrate the capacity of the quasi-interpolants for curve representation.