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一类非端点插值B样条曲线降阶的方法 总被引:1,自引:0,他引:1
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. 相似文献
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B样条基的转换矩阵及其应用 总被引:2,自引:2,他引:0
本文研究任意两个B样条基可转换的条件及转换矩阵,给出了关于转换矩阵元素的表示及性质等理论结果,并推导出了两个递推公式,为实际计算转换矩阵的元素提供了易于实现的数学方法。本文还讨论了B样条基转换矩阵在CAGD中的应用,特别讨论了B样条曲线的节点插入、升阶和分解问题。本文的结果为B样条曲线的节点插入、升阶、分解等运算提供了一个统一的数学模型和实现方法。 相似文献
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Bezier曲线的升阶公式在[1]中给出了简单的递推表达式,而B样条曲线的升阶公式则相对地复杂,本文利用[4]提出的n次多项式的blossom即一个与此多项式一一对应的对称的n—仿射映射,给出了Bezier曲线和B样条曲线直接升r阶的升阶公式。 相似文献
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1.问题的提出 近年来,多元样条的研究进程表明,从多变量的观点重新认识一元样条的理论是很有必要的.本文运用重心坐标,以近代的B网方法为工具,重新探讨一元分片多项式的结构,进而为研究多元样条提供工具. 假设Q_n(t)是给定的分割: 相似文献
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带有面积约束的B样条曲线拟合方法 总被引:1,自引:0,他引:1
1984年刘鼎元等给出了B样条曲线的光顺拟合方法,本文在其基础上处理了带有面积约束的B样条曲线拟合问题。它来源于船舶线型设计:设计者往往先确定横剖面面积曲线,再设计线型。因而,在横剖面的光顺拟合中,就要求各站的横剖面面积保持不变。本文用B样条参数曲线表达拟合曲线,导出了曲线与坐标轴所围面积的表达式,目标函数由偏离的平方和、二阶导数平方和以及Lagrange乘子与面积公式的乘积所组成。 相似文献
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B样条曲线的升阶是CAGD中的一个重要课题。本文根据传统的样条函数理论,提出了一个用高次B样条函数表示低次B样条函数的方法。该方法用于B样条曲线的升阶是快捷、有效的。 相似文献
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本文从广义差商-Green函数-B样条的观点出发,绘出了以正则系统{Φi-1(x)}i-1m为基解组的一类微分算子的正规B样条的递推公式. 相似文献
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In this paper, matrix representations of the best spline quasi-interpolating operator over triangular sub-domains in $S^1_2 (∆^{(2)}_{mn})$, and coefficients of splines in terms of B-net are reviewed firstly. Moreover, by means of coefficients in terms of B-net, computation of bivariate numerical cubature over triangular sub-domains with respect to variables $x$ and $y$ is transferred into summation of coefficients of splines in terms of B-net. Thus concise bivariate cubature formulas are constructed over rectangular sub-domain. Furthermore, by means of module of continuity and max-norms, error estimates for cubature formulas are derived over both sub-domains and the domain. 相似文献
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Ren-Hong WangJiang Qian 《Applied mathematics and computation》2011,217(19):7620-7635
By means of the barycentric coordinates expression of the interpolating polynomial over each ortho-triple, some properties are obtained. Moreover, the explicit coefficients in terms of B-net for one ortho-triple, and two ortho-triples are worked out, respectively. Thus the computation of multiple integrals can be converted into the sum of the coefficients in terms of the B-net over triangular domain much effectively and conveniently. Based on a new symmetrical algorithm of partial inverse differences, a novel continued fractions interpolation scheme is presented over arbitrary ortho-triples in R2, which is a bivariate osculatory interpolation formula with one-order partial derivatives at all corner points in the ortho-triples. Furthermore, its characterization theorem is presented by three-term recurrence relations. The new scheme is advantageous over the polynomial one with some numerical examples. 相似文献
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Edward Neuman 《Journal of Computational and Applied Mathematics》1981,7(1):51-62
The problem of determining the moments and the Fourier transforms of B-splines with arbitrary knots is considered. There exists a simple connection between the moments of such splines and the so-called extended Stirling numbers of the second kind which are defined in section 2. Some recurrence relations for the moments of B-splines with arbitrary knots are given in section 3. In the case of equidistant knots we have also further recurrences. For the forward, central and perfect B-splines the explicit formulas for the moments are given in section 3. The Fourier transforms of B-splines is treated in section 4. The final section is devoted to so-called Stieltjes series connected with the nonnegative weight function w(x) and such that in some closed interval [a, b]. It is proved that such series for the particular values of the independent variable may be expressed by the finite sums which contain the nodes and coefficients of the optimal (in the Davies sense) quadrature formulas. 相似文献
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Four-term recurrence relations with constant coefficients are derived for a wide class of T chebycheffian B-splines, LB-splines
and complex B-splines. Such a relation exists whenever the differential operator defining the underlying “polynomial” space
can be factored in two essentially different ways. The four lower order B-splines in the recurrence relation appear in two
pairs, each pair corresponding to one of these factorization. It is shown that the two-term recurrence relations for polynomial,
trigonometric and hyperbolic B-splines as well as other known two-term recurrence relations are obtained directly from the
four-term recurrence relations in a unified and systematic way. The above derivation also yields two different two-term recurrence
relations for Green’s functions of these “polynomial” spaces In this context the special examples of exponential functions
and rational functions are analyzed in detail. 相似文献
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设P_n是具有n个顶点的路,令δ=rn+1,我们S_δ~*表示把rP_(n+1)的每个分支的一个1度点重迭在一起得到的图.用Y_(λ_1δ)~(S*)表示把r_1S_δ~*中每个分支的r度顶点与S_δ~*的r度顶点依次邻接后得到的图,Y_(λ_2δ)~(S*)表示把用r_2Y_(λ_1δ)~(S*)中每个分支的r+r1度顶点与S_δ~*的r度顶点依次邻接后得到的图,一般地,Y_(λ_kδ)~(S*)表示把用r_kY_(λ_(k-1)δ)~(S*)中每个分支的r+r_k-1度顶点与S_δ~*的r度顶点依次邻接后得到的图,运用图的伴随多项式的性质,证明了图Y_(λ_kδ)~(S*)∪β_kS_δ~*的伴随多项式的因式分解定理,进而得到了这类图的补图的色等价性. 相似文献
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<正> 在其中我們設被積分的大數函數係在D域的某種型式的邊界上取絕對極大值。在早先的一篇文章中,作者曾證明了一個關於此類積分的漸近公式,在該處係假定D域的邊界為歐氏空間R_n中的一個(n—1)維曲面。被積分的大數函 相似文献
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朱玉扬 《数学的实践与认识》2008,38(4):142-148
记平面边长为1的正m边形为S_m,将S_m剖分成n块:S_(m1),S_(m2),…,S_(mn),这样的剖分称S_m的n剖分,并以T(m,n)表示.以d_(mi)表示区域S_(mi)(i=1,2,…,n)的直径(即区域S_(mi)任意两点之间距离的最大者).记D(m,n)=max{d_(m1),d_(m2),…,d_(mn)}及Ψ(m,n)=■{D(m,n)}.本文将估计Ψ(m,n)的上下界.证明Ψ(6,3)=3/2,Ψ(6,4)=3-3~(1/2),Ψ(6.6)=1,Ψ(6,7)=3/2,估计Ψ(6,n)的渐进性.提出几个猜想. 相似文献