共查询到16条相似文献,搜索用时 187 毫秒
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利用带导数的和仅基于函数值的分母为二次的有理三次插值样条构造了一类加权有理三次插值函数.在给定的插值数据条件下,通过调整插值函数中的参数和权系数,给出了插值曲线的保凸方法和该方法得以实现的充分必要条件,推广和改进了一些相关结论.这种条件是对参数和权系数的简单的线性的不等式约束,容易在计算机辅助几何设计中得到实际应用. 相似文献
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本文研究二元二次插值样条函数,揭示了二元二次样条与一元二次样条的紧密联系,可将二元二次样条函数的构造简化为在剖分线上一元二次样条函数的构造。并具体构造了二类双周期样条函数和一类单周期样条函数。当f(x,y)∈C~4时,它们的逼近阶都是3,与一元样条同。 本文方法适用非均匀剖分。 相似文献
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文章给出了基于C-B样条的由网格数据产生三角形和四边形曲面片的方法,C-B样条是由基底函数{sin t,cos t,t,1}导出的一种新型样条曲线,它可以克服现在正在使用的B样条和有理B样条为了满足数据网格的拓扑结构而增加多余的控制点,求导求积分复杂繁琐,阶数过高,从而讨论其连续拼接时增加了困难等缺点,如何将它推广成曲面就成为一个重要问题。作者利用边-顶点方法构造插值算子,再将这些算子进行凸性组合,将C-B样条曲线推广成三角形曲面片和四边形曲面片,它可以用于CAD的逆向工程中散乱数据的曲面重构。 相似文献
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C~3连续的保凸T-B插值曲线及保形插值算法 总被引:1,自引:0,他引:1
基于三角函数的T-B样条曲线虽然具有保凸性,但曲线不通过任何控制点.现在在两个相邻控制点之间插入两个新的控制点,使改造后新的T-B样条曲线插值能够通过原来的控制点,不仅保凸、C~3连续,而且曲线的形状还可作局部修改.给出了T-B样条曲线保形插值算法的保形性条件,并给出了数值计算例子. 相似文献
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Amit Shaw Shravan Bendapudi D. Roy 《International journal for numerical methods in engineering》2008,73(10):1434-1467
An error‐reproducing and interpolating kernel method (ERIKM), which is a novel and improved form of the error‐reproducing kernel method (ERKM) with the nodal interpolation property, is proposed. The ERKM is a non‐uniform rational B‐splines (NURBS)‐based mesh‐free approximation scheme recently proposed by Shaw and Roy (Comput. Mech. 2007; 40 (1):127–148). The ERKM is based on an initial approximation of the target function and its derivatives by NURBS basis functions. The errors in the NURBS approximation and its derivatives are then reproduced via a family of non‐NURBS basis functions. The non‐NURBS basis functions are constructed using a polynomial reproduction condition and added to the NURBS approximation obtained in the first step. In the ERKM, the interpolating property at the boundary is achieved by repeating the knot (open knot vector). However, for most problems of practical interest, employing NURBS with open knots is not possible because of the complex geometry of the domain, and consequently ERKM shape functions turn out to be non‐interpolating. In ERIKM, the error functions are obtained through localized Kriging based on a minimization of the squared variance of the estimate with the reproduction property as a constraint. Interpolating error functions so obtained are then added to the NURBS approximant. While enriching the ERKM with the interpolation property, the ERIKM naturally possesses all the desirable features of the ERKM, such as insensitivity to the support size and ability to reproduce sharp layers. The proposed ERIKM is finally applied to obtain strong and weak solutions for a class of linear and non‐linear boundary value problems of engineering interest. These illustrations help to bring out the relative numerical advantages and accuracy of the new method to some extent. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
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Xiaolin Li Jialin Zhu Shougui Zhang 《Engineering Analysis with Boundary Elements》2009,33(11):1273-1283
The hybrid boundary node method (HBNM) retains the meshless attribute of the moving least squares (MLS) approximation and the reduced dimensionality advantages of the boundary element method. However, the HBNM inherits the deficiency of the MLS approximation, in which shape functions lack the delta function property. Thus in the HBNM, boundary conditions are implemented after they are transformed into their approximations on the boundary nodes with the MLS scheme.This paper combines the hybrid displacement variational formulation and the radial basis point interpolation to develop a direct boundary-type meshless method, the hybrid radial boundary node method (HRBNM) for two-dimensional potential problems. The HRBNM is truly meshless, i.e. absolutely no elements are required either for interpolation or for integration. The radial basis point interpolation is used to construct shape functions with delta function property. So unlike the HBNM, the HRBNM is a direct numerical method in which the basic unknown quantity is the real solution of nodal variables, and boundary conditions can be applied directly and easily, which leads to greater computational precision. Some selected numerical tests illustrate the efficiency of the method proposed. 相似文献
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复杂地质曲面三维插值—逼近拟合构造方法 总被引:1,自引:0,他引:1
针对水利水电工程多源地质数据的特点,充分考虑了地质精度要求、曲面连续性和数据存储量等多方面的均衡,提出并实现了基于NURBS(non-uniform rational B-splines,非均匀有理样条曲线)技术的复杂地质曲面插值—逼近拟合构造方法。该方法对于工程关键区域集中且均匀分布的原始数据,采用NURBS蒙皮插值方法,使曲面严格通过这些数据点;对于周边区域分布离散的数据,采用NURBS逼近拟合方法,使曲面在给定精度下充分逼近原始数据;最后对整体曲面的地质结构合理性、几何性和精度进行检查分析和调整。实例表明,该方法所构造的地质曲面能满足地质工程师的实际需要,并能为进一步的三维地质建模提供基础。 相似文献
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A genetic algorithm with memory for optimal design of laminated sandwich composite panels 总被引:1,自引:0,他引:1
This paper is concerned with augmenting genetic algorithms (GAs) to include memory for continuous variables, and applying this to stacking sequence design of laminated sandwich composite panels that involves both discrete variables and a continuous design variable. The term “memory” implies preserving data from previously analyzed designs. A balanced binary tree with nodes corresponding to discrete designs renders efficient access to the memory. For those discrete designs that occur frequently, an evolving database of continuous variable values is used to construct a spline approximation to the fitness as a function of the single continuous variable. The approximation is then used to decide when to retrieve the fitness function value from the spline and when to do an exact analysis to add a new data point for the spline. With the spline approximation in place, it is also possible to use the best solution of the approximation as a local improvement during the optimization process. The demonstration problem chosen is the stacking sequence optimization of a sandwich plate with composite face sheets for weight minimization subject to strength and buckling constraints. Comparisons are made between the cases with and without the binary tree and spline interpolation added to a standard GA. Reduced computational cost and increased performance index of a GA with these changes are demonstrated. 相似文献