周期B样条基转换矩阵的表示和计算

周期B样条基以一种简洁的形式表示闭B样条曲线.周期B样条基转换矩阵为闭B样条曲线及相关曲面的不同表示间的转换提供了一个数学模型.本文给出了周期B样条基转换矩阵的存在性条件,给出并证明了周期B样条基转换矩阵的一个简单的递归表示式.在此基础上,本文进一步给出了周期B样条基转换矩阵的计算公式和高效算法.周期B样条基转换矩阵为闭B样条曲线的节点插入、升阶、节点删除和降阶等基本运算提供了一个统一而简单的解决方法,本文给出了一些应用例子.     

带形状参数控制的三次B样条曲线曲面的光顺

三次B样条曲线是一种广泛应用于计算机辅助几何设计中的非常重要的曲线.本文在以曲线的最小应变能作为衡量曲线光顺性的基础上,采用带调节控制参数的方法分别对三次B样条曲线和双三次B样条曲面进行了光顺处理.由所提供的方法以及实例可以看出,本方法可在曲线曲面光顺的基础上通过修改参数大小以达到控制曲线曲面形状的目的,且修改后的点的位置与原坏点的距离是由参数的大小控制决定的,这样就使得我们的光顺处理可以控制在数据测量的误差范围内.     

一类非端点插值B样条曲线降阶的方法

降阶算法是B样条曲线和曲面设计的一个基本算法,它广泛应用于组合曲线,蒙皮或扫描曲面等设计中.Piegl与Tiller曾给出B样条曲线的降阶方法.本文给出了解决更一般的非端点插值B样条曲线降阶的方法.新的方法主要是通过对现有的节点插入方法进行分析,给出了一种端点插值递推公式,并利用此公式对Piegl与Tiller降阶方法加以改进,使之能够解决非端点插值均匀及非均匀B样条曲线的降阶问题.     

B样条曲面的方向导数与高效求值

1 引言 B样条曲面是几何造型中一种用途广泛的方法,在实际应用中,大量问题需要我们研究曲面的凸性与连续性,它们都归结为求曲面在任意点处关于任意方向的各阶导数的求值问题. 给定(m+M)×(n十N)个空间点f_(ij)及两个非减节点向量{u_i;0≤i≤2m+M}和{v_j;0≤j≤2n+N},则定义在[u_m,u_(m+M)]×[v_n,v_(n+N)]上的m×n次B条曲面为 f(u,v)=(sum from i=0 to m+M-1)(sum from j=0 to n+N-1)(f_(ij)N_i~m(u)N_j~n(v), (1)其中N_i~m(u)和N_j~n(v)为定义在前两节点向量上的规范B样条基函数,它们可以按严格形式递推地定义为下式     

逆向工程中基于NURBS的曲面重构

曲面重构是逆向工程中的关键技术.根据非均匀有理B样条曲面矩阵表达式,对于造型曲面上的(2m+1)×(2n+1)个型值数据点,推导了一个仅利用型值点数据反算二次非均匀有理B样条曲面控制顶点的算法.数值算例表明了该算法的有效性.     

T-B样条曲线及其应用

给出一种基于三角函数的类B样条设计方法,称其为 T B样条,它具有 B样条曲线曲面的主要优点,它还能够无需有理形式即可精确表示圆弧、椭圆弧等二次曲线弧以及球面、椭球面等二次曲面片.     

空间圆柱螺旋线的NURBS表示

O．引言用B样条方法或B6zier方法来表示自由曲线、曲面，是在CAD／CAM技术中广泛使用的数学手段．但是由于它们都不能精确地表示除抛物线或抛物面以外的圆锥曲线与初等二次曲面，因此近年来，另一种形式的参数样条-一参数有理多项式方法占据了主导地位．非均匀有理B样条（简称NURBS）已被国际标准组织（ISO）于1991年正式颁布为关于工业产品几何定义的STEP国际标准，将其作为定义产品形状的唯一数学方法．越来越多的CAD系统采用NURBS曲线与曲面来建立图形库，研究各种曲线与曲面的NURBS表示无疑是很有意义的．在描述圆锥曲线…     

两邻接B样条曲面的G1连续条件

本文得到了非均匀重内节点邻接B样条曲面间G1连续的充要条件 ,给出了一类G1连续的充分条件 ;基于对B样条曲线参数连续性的分析 ,本文着重给出了这类充分条件成立的内在约束 ,即对公共边界控制顶点的约束条件 .     

双三次B样条插值曲面

本文研究三次B样条插值曲面。对于给定的拓扑网格点阵Pi,j。导出了其插值三次B样条曲面的控制顶点,每四个顶点Pi,j,Pi l,j,Pi,j 1,Pi 1,j 1由九个三次B样条曲面片构成,整个曲面是C^2连续的,最后,给出了一个数值实例。     

有理B-样条曲线、曲面的包络性质

研究有理Bezier曲线和B-样条曲线、曲面的包络性质,愈来愈广泛,因为它从包络磨光的角度解释了曲线、曲面的一种几何构造特征,形象地说明了模型是由多边形或多面体逐步磨光的结果.     

RECENT PROGRESS ON SPHERICAL HARMONIC APPROXIMATION MADE BY BNU RESEARCH GROUP ——In memory of Professor Sun Yongsheng

As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years （2001-2005）. The main topics are： convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.     

A unified approach to certain problems of best local approximation

In this paper we study best local quasi-rational approximation and best local approximation from finite dimensional subspaces of vectorial functions of several variables. Our approach extends and unifies several problems concerning best local multi-point approximation in different norms.     

Boundedness for commutators of multipliers on Hardy type spaces

In this paper, we study the commutators generalized by multipliers and a BMO function. Under some assumptions, we establish its boundedness properties from certain atomic Hardy space Hb^p（R^n） into the Lebesgue space L^p with p 〈 1.     

THE 8~(th) INTERNATIONAL CONGRESS ON INDUSTRIAL AND APPLIED MATHEMATICS

<正>August 10-14,2015Beijing,ChinaThe International Congress on Industrial and Applied Mathematics(ICIAM)is the premier international congress in the field of applied mathematics held every four years under the auspices of the International Council for Industrial and Applied Mathematics.From August 10 to 14,2015,mathematicians,scientists     

Towards Excellence in Science Chinese Academy of Sciences

<正>May 26,2014,Beijing Science is a human enterprise in the pursuit of knowledge.The scientific revolution that occurred in the 17th Century initiated the advances of modern science.The scientific knowledge system created by     

Bounds for the zeros of polynomials

Let P(z)=∑↓j=0↑n ajx^j be a polynomial of degree n. In this paper we prove a more general result which interalia improves upon the bounds of a class of polynomials. We also prove a result which includes some extensions and generalizations of Enestrǒm-Kakeya theorem.     

Boundedness of commutators related to Marcinkiewicz integrals on hardy type spaces

In this paper, the authors study the boundedness of the operator [μΩ, b], the commutator generated by a function b ∈ Lipβ(Rn)(0 ＜β≤ 1) and the Marcinkiewicz integrals μΩ, on the classical Hardy spaces and the Herz-type Hardy spaces in the case Ω∈ Lipα(Sn-1)(0 ＜α≤ 1).     

Jacobi polynomials used to invert the laplace transform

Given the Laplace transform F(s) of a function f(t), we develop a new algorithm to find an approximation to f(t) by the use of the classical Jacobi polynomials. The main contribution of our work is the development of a new and very effective method to determine the coefficients in the finite series expansion that approximation f(t) in terms of Jacobi polynomials. Some numerical examples are illustrated.     

Generalization of the interaction between Haar approximation and polynomial operators to higher order methods

In applications it is useful to compute the local average empirical statistics on u. A very simple relation exists when of a function f（u） of an input u from the local averages are given by a Haar approximation. The question is to know if it holds for higher order approximation methods. To do so, it is necessary to use approximate product operators defined over linear approximation spaces. These products are characterized by a Strang and Fix like condition. An explicit construction of these product operators is exhibited for piecewise polynomial functions, using Hermite interpolation. The averaging relation which holds for the Haar approximation is then recovered when the product is defined by a two point Hermite interpolation.