基于离散插值样条的提升小波变换

文中引入了一种对信号递归滤波的提升方法,该方法与通常的提升方法不同之处是使用IIR滤波器.探讨了空间域中基于离散插值样条的预测算子和更新算子的设计.提出的方法以插值为基础,只涉及信号的采样,不要求使用正交公式,更适合信号的处理.最后由数值仿真验证了该算法的性能,对于软阈值法小波系数去噪,提升小波变换T12同B9/7相比,前者略优于后者,提升方法的优点在于其设计上的灵活性和计算花费少.     

基于样条修匀公式的图像边缘检测

本文给出了一类基于Ｂ样条修匀公式的图像边缘检测算子,其过程是先利用等距Ｂ样条函数对图像｛ｆ（ｉ,ｊ）｝Ｎ－１ｉ,ｊ＝０做一个全息光滑曲面公式,进一步利用Ｂ样条函数的局部支撑性质导出,该曲面公式可以严格地局限于每点的某变邻域内计算,即Ｓ（ｘ,ｙ）＝∑（ｉ,ｊ）∈Ｎｋ,ｌ（ｘ,ｙ）ｆ（ｉ,ｊ）Ωｋ（ｘ－ｉ）Ωｌ（ｙ－ｊ）该曲面既有足够的光滑性,又有良好的保凸性;然后,基于这个光滑曲面Ｓ（ｘ,ｙ）,再通过求｜Ｓ｜的局部极大值点或求２Ｓ的零交叉来检测边缘．数值实验表明,这是一类十分成功的边缘检测算法,它简捷、可靠,便于实时处理,如可用于计算机视觉系统中的特征提取、图像分割、纹理分析等．     

Imposing Dirichlet boundary conditions with Nitsche's method and spline‐based finite elements

A key challenge while employing non‐interpolatory basis functions in finite‐element methods is the robust imposition of Dirichlet boundary conditions. The current work studies the weak enforcement of such conditions for B‐spline basis functions, with application to both second‐ and fourth‐order problems. This is achieved using concepts borrowed from Nitsche's method, which is a stabilized method for imposing constraints on surfaces. Conditions for the stability of the system of equations are derived for each class of problem. Stability parameters in the Nitsche weak form are then evaluated by solving a local generalized eigenvalue problem at the Dirichlet boundary. The approach is designed to work equally well when the grid used to build the splines conforms to the physical boundary of interest as well as to the more general case when it does not. Through several numerical examples, the approach is shown to yield optimal rates of convergence. Copyright © 2010 John Wiley & Sons, Ltd.     

Weakening the tight coupling between geometry and simulation in isogeometric analysis: From sub‐ and super‐geometric analysis to Geometry‐Independent Field approximaTion (GIFT)

This paper presents an approach to generalize the concept of isogeometric analysis by allowing different spaces for the parameterization of the computational domain and for the approximation of the solution field. The method inherits the main advantage of isogeometric analysis, ie, preserves the original exact computer‐aided design geometry (for example, given by nonuniform rational B‐splines), but allows pairing it with an approximation space, which is more suitable/flexible for analysis, for example, T‐splines, LR‐splines, (truncated) hierarchical B‐splines, and PHT‐splines. This generalization offers the advantage of adaptive local refinement without the need to reparameterize the domain, and therefore without weakening the link with the computer‐aided design model. We demonstrate the use of the method with different choices of geometry and field spaces and show that, despite the failure of the standard patch test, the optimum convergence rate is achieved for nonnested spaces.     

一种改进的群体智能寻路算法

以游戏中群体智能角色的路径搜索为研究背景,提出一种改进的群体智能寻路算法。该方法把游戏寻路过程划分成三个阶段:第一阶段为预处理阶段,针对特定的目标点,采取逆向路径搜索策略,建立最优解路径表。第二阶段,针对动态障碍物的避让,运用实时A*算法生成局部动态路径,并与初始路径进行拼接。第三阶段,对找到的路径进行关键点优化和Catmull-Rom样条平滑处理。实验结果表明该方法在游戏开发中的实用价值。     

单圆弧样条保形插值算法

该文以插值具有偶数个点的闭多边形为例提出了一种新的圆弧样条插值算法。这种算法具有以下3个特点：（1）生成的圆弧样条曲线具有保形的特点；（2）圆弧样条中圆弧的段数与型值点个数相同。（3）圆弧段之间的连接点不一定在插值的型值点上，这样就能用更多的自由度来控制拟合曲线的形状。同此文中还提出了一个优化的算法来得到光顺的插值曲线，同时还给出了几个例子加以说明。     

基于Black-Karasinski模型的我国债券市场利率期限结构研究

随着利率市场化的推进,与利率挂钩的金融资产的利率风险愈发凸显.为了控制利率风险,对利率衍生品的定价所依赖的利率期限结构的研究显得越来越重要.本文在使用多项式线条法得到即时利率期限结构的基础之上,利用三叉树模拟技术构建并校准了我国银行间债券市场Black-Karasinski利率模型,目前国内还没有利用此模型校准我国利率期限结构的研究.结果显示:利率的均值回复性好,但波动性较小,模型的动态性能较差,这可能与我国债券市场的利率结构受央行存贷款基准利率变化影响有关.     

The double periodic spline space with degreek≥4 on type-1 triangulation

Let S _k ^l (Δ _mn ^(l) ) and denote the space of bivariate splines and the space of double periodic splines of degree k on type-1 triangulation, respectively. We give, in this paper, an integral representation of splines in Let S _k ^l (Δ _mn ^(l) ) and a direct sum decomposition of Let S _k ^l (Δ _mn ^(l) ). By which together with the Bezier net of bivariate splines, we are able to determine the dimension of the space of double periodic splines for degree k≥4.     

复杂型面及其法向等距面的数学模型

对由离散点给出的复杂型面的每一截面的型值点用大挠度三次样条连接,而各截面采用基样条函数连接,组成基样条函数和大挠度样条曲线的混合曲面,从而推导出复杂型面及其法向等距面的数学模型。