共查询到16条相似文献,搜索用时 78 毫秒
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加权有理三次插值的逼近性质及其应用 总被引:7,自引:0,他引:7
利用带导数和不带导数的分母为线性的有理三次插值样条构造了一类加权有理三次插值函数,利用这种插值方法,将样条曲线严格约束于给定的折线之上、之下或之间的问题都可以得到解决同时还研究了这种加权有理三次插值的逼近性质。 相似文献
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利用三次非均匀有理B样条,给出了一种构造局部插值曲线的方法,生成的插值曲线是C2连续的.曲线表示式中带有一个局部形状参数,随着一个局部形状参数值的增大,所给曲线将局部地接近插值点构成的控制多边形.基于三次非均匀有理B样条函数的局部单调性和一种保单调性的准则,给出了所给插值曲线的保单调性的条件. 相似文献
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本文研究矩形区域在Ⅱ-型三角剖分下二元三次样条的C2-连续的插值问题.首先给出了一类具有C2-连续的二元三次样条插值格式,然后证明了分片样条的存在性与唯-性,并给出了它的表达式和逼近度. 相似文献
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研究了矩形区域在Ⅱ型三角剖分下具有C2-拼接的二元三次样条插值与逼近问题.给出了一类具有C2-拼接的二元三次样条的插值条件,存在性,唯一性,逼近度估计及其凸性分析. 相似文献
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一种保凸的Spline插值方法 总被引:2,自引:0,他引:2
本文构造笛氏坐标系中一条光滑曲线,使它通过两个有特定切向的给定点,给出了此种插值函数保凸的一个充要条件.文中考虑逐段三次多项式的保凸插值函数,其收敛性的阶与三次样条多项式一样.最后叙述插值函数形状控制的方法. 相似文献
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几种有理插值函数的逼近性质 总被引:6,自引:1,他引:5
1 引 言在曲线和曲面设计中,样条插值是有用的和强有力的工具.不少作者已经研究了很多种类型的样条插值[1,2,3,4].近些年来,有理插值样条,特别是三次有理插值样条,以及它们在外型控制中的应用,已有了不少工作[5,6,7].有理插值样条的表达式中有某些参数,正是由于这些参数,有理插值样条在外型控制中充分显示了它的灵活性;但也正是由于这些参数,使它的逼近性质的研究增加了困难.因此,关于有理插值样条的逼近性质的研究很少见诸文献.本文在第二节首先叙述几种典型的有理插值样条,其中包括分母为一次、二次的三次有理插值样条和仅基于函数值… 相似文献
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Qi Duan Botang Li K. Djidjeli W. G. Price E. H. Twizell 《Journal of Applied Mathematics and Computing》1999,6(3):537-547
Controlling the convexity and the strain energy of the interpolating curve can be carried out by controlling the second-order derivative of the interpolating function. In [1], the rational cubic spline with linear denominator has been used to constrain the convexity and the strain energy of the interpolating curves, but it does not work in some case. This paper deals with the weighted rational cubic spline with linear denominator for this kind of constraint, the sufficient and necessary condition for controlling the convexity and strain energy of the interpolating curves are derived, and a numerical example is given. 相似文献
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The parametric cubic splines interpolating to such closed curves as the circle and ellipse are derived in a form where their parameters are given by simple algebraic expressions. The structure of these expressions enables the error in approximation of the given curves to be precisely determined and some additional features of the spline deduced. 相似文献
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In this paper, an interpolating method for bivariate cubic splines with C
2-join on type-II triangular at a rectangular domain is given, and the approximation degree, interpolating existence and uniqueness
of the cubic splines are studied.
Supported by NSFC General Projects(60473130). 相似文献
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CONSTRAINED RATIONAL CUBIC SPLINE AND ITS APPLICATION 总被引:6,自引:0,他引:6
1. IntroductionDesign of high quality, manufacturable surfaces, such as the outer shape of a ship, car oraeroplane, is an important yet challenging task in today's manufacturing industries. Althoughsignificam progress has been made in the last decade in developing and commercializing pro--duction quality CAD tools, demand for more effective tools is still high due to the ever increajsein model complexity and the needs to address and incorporate manufacturing requirements inthe early stage of … 相似文献
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In this paper, an interpolating method for bivariate cubic splines with C2-join on type-II triangular at a rectangular domain is given, and the approximation degree, inter-polating existence and uniqueness of the cubic splines are studied. 相似文献