共查询到20条相似文献,搜索用时 62 毫秒
1.
变参数四点法的理论及其应用 总被引:8,自引:0,他引:8
蔡志杰 《数学年刊A辑(中文版)》1995,(4)
四点插值细分法(简称四点法)是一种离散插值方法,在曲线和曲面造型中有着广泛的应用.本文主要讨论当参数可变时,四点法的收敛性和连续性以及变参数四点法的应用. 相似文献
2.
3.
4.
5.
由分段三次参数多项式曲线拼合成的C1插值曲线的形状与数据点处的切矢有很大关系.基于对保形插值曲线特点的分析,本文提出了估计数据点处切矢的一种方法:采用使构造的插值曲线的长度尽可能短的思想估计数据点处的切矢,并且通过四组有代表性的数据对本方法和已有的三种方法进行了比较. 相似文献
6.
C^3连续的保形插值三角样本曲线 总被引:2,自引:0,他引:2
本给出了构造保形插值曲线的三角样条方法,即在每两个型值点之间构造两段三次参数三角样条曲线。所构造的插值曲线是局部的,保形的和C^3连续的而且曲线的形状可由参数调节。 相似文献
7.
8.
梁军 《数学的实践与认识》2016,(17):229-235
采用重心Lagrange插值配点法计算了二维Poisson方程.采用重心Lagrange插值法构造近似函数,由配点法离散Poisson方程及其边界条件.数值算例表明方法具有理论简单、计算精度高的特点. 相似文献
9.
蔺青冲 《数学的实践与认识》1989,(4)
本文给出在平面上插值点列为凸的时,构造一类 C~2连续且保凸的插值三次参数样条曲线的方法.这里通过选择插值节点 P_i 处插值曲线 p(t)的切矢方向和长度来代替以往常用的参变量,从而得到一类新的方法. 相似文献
10.
结合α-三角样条插值曲线的构造方法,本文具体构造了一类基于四点分段的α-B3样条插值曲线,并结合图例分析了其相关的一些性质及优缺点. 相似文献
11.
Carolina Beccari 《Journal of Computational and Applied Mathematics》2011,235(16):4754-4769
Starting from a well-known construction of polynomial-based interpolatory 4-point schemes, in this paper we present an original affine combination of quadratic polynomial samples that leads to a non-uniform 4-point scheme with edge parameters. This blending-type formulation is then further generalized to provide a powerful subdivision algorithm that combines the fairing curve of a non-uniform refinement with the advantages of a shape-controlled interpolation method and an arbitrary point insertion rule. The result is a non-uniform interpolatory 4-point scheme that is unique in combining a number of distinctive properties. In fact it generates visually-pleasing limit curves where special features ranging from cusps and flat edges to point/edge tension effects may be included without creating undesired undulations. Moreover such a scheme is capable of inserting new points at any positions of existing intervals, so that the most convenient parameter values may be chosen as well as the intervals for insertion.Such a fully flexible curve scheme is a fundamental step towards the construction of high-quality interpolatory subdivision surfaces with features control. 相似文献
12.
A criterion of convergence for stationary nonuniform subdivision schemes is provided. For periodic subdivision schemes, this criterion is optimal and can be applied to Hermite subdivision schemes which are not necessarily interpolatory. For the Merrien family of Hermite subdivision schemes which involve two parameters, we are able to describe explicitly the values of the parameters for which the Hermite subdivision scheme is convergent. 相似文献
13.
Costanza Conti Luca Gemignani Lucia Romani 《Linear algebra and its applications》2009,431(10):1971-1987
In this paper we present a general strategy to deduce a family of interpolatory masks from a symmetric Hurwitz non-interpolatory one. This brings back to a polynomial equation involving the symbol of the non-interpolatory scheme we start with. The solution of the polynomial equation here proposed, tailored for symmetric Hurwitz subdivision symbols, leads to an efficient procedure for the computation of the coefficients of the corresponding family of interpolatory masks. Several examples of interpolatory masks associated with classical approximating masks are given. 相似文献
14.
赵乃良 《高校应用数学学报(A辑)》1996,(1):91-96
Nira Dyn等提出的四点插值法是一种典型的自由曲线离散造型方法,但该方法不能控制插值点的切向。本文利用薄板样很可能 量的极小化原理给出了具有切向控制的四点分插值条件。用户可以方便地交互控制任一插值点的切向,使得四点插值法更为有效和实用。 相似文献
15.
Hermite subdivision schemes have been studied by Merrien, Dyn, and Levin
and they appear to be very different from subdivision schemes analyzed before since the rules depend on the subdivision level.
As suggested by Dyn and Levin, it is possible to transform the initial scheme into a uniform stationary vector subdivision
scheme which can be handled more easily.With this transformation, the study of convergence of Hermite subdivision schemes
is reduced to that of vector stationary subdivision schemes. We propose a first criterion for C0-convergence for a large class of vector subdivision schemes. This gives a criterion for C1-convergence of Hermite subdivision schemes. It can be noticed that these schemes do not have to be interpolatory. We conclude
by investigating spectral properties of Hermite schemes and other necessary/sufficient conditions of convergence. 相似文献
16.
A.Mehaute和F.Utreras(1994)给出了一种平面函数型保凸插值构造光滑曲线的方法(以下简称为M-U方法).本文在利用其方法本质的基础上,给出了一种平面上参数型保凸插值构造光滑曲线的方法,同Mehaute和Utreras的方法一样,这里的方法也有局部性.另外这种方法还可以构造平面上的封闭曲线. 相似文献
17.
Thomas P.-Y. Yu 《Journal of Mathematical Analysis and Applications》2005,302(1):201-216
It is well known that the critical Hölder regularity of a subdivision schemes can typically be expressed in terms of the joint-spectral radius (JSR) of two operators restricted to a common finite-dimensional invariant subspace. In this article, we investigate interpolatory Hermite subdivision schemes in dimension one and specifically those with optimal accuracy orders. The latter include as special cases the well-known Lagrange interpolatory subdivision schemes by Deslauriers and Dubuc. We first show how to express the critical Hölder regularity of such a scheme in terms of the joint-spectral radius of a matrix pair {F0,F1} given in a very explicit form. While the so-called finiteness conjecture for JSR is known to be not true in general, we conjecture that for such matrix pairs arising from Hermite interpolatory schemes of optimal accuracy orders a “strong finiteness conjecture” holds: ρ(F0,F1)=ρ(F0)=ρ(F1). We prove that this conjecture is a consequence of another conjectured property of Hermite interpolatory schemes which, in turn, is connected to a kind of positivity property of matrix polynomials. We also prove these conjectures in certain new cases using both time and frequency domain arguments; our study here strongly suggests the existence of a notion of “positive definiteness” for non-Hermitian matrices. 相似文献
18.
Manabu Sakai 《Numerische Mathematik》1997,76(3):403-417
Summary. This paper considers the distribution of inflection points and singularity on the parametric rational cubic curve, using
much algebraic manipulation. Its use allows one to find a shape preserving interpolatory rational cubic curve of a planar
data. Some numerical examples are given to illustrate usefulness of the method.
Received April 30, 1995 / Revised version received January 15, 1996 相似文献
19.
This paper is concerned with a family of nonstationary, interpolatory subdivision schemes that have the capability of reproducing
functions in a finite-dimensional subspace of exponential polynomials. We give conditions for the existence and uniqueness
of such schemes, and analyze their convergence and smoothness. It is shown that the refinement rules of an even-order exponentials
reproducing scheme converge to the Dubuc—Deslauriers interpolatory scheme of the same order, and that both schemes have the
same smoothness. Unlike the stationary case, the application of a nonstationary scheme requires the computation of a different
rule for each refinement level. We show that the rules of an exponentials reproducing scheme can be efficiently derived by
means of an auxiliary orthogonal scheme , using only linear operations. The orthogonal schemes are also very useful tools in fitting an appropriate space of exponential
polynomials to a given data sequence. 相似文献
20.
We propose a general study of the convergence of a Hermite subdivision scheme ℋ of degree d>0 in dimension 1. This is done by linking Hermite subdivision schemes and Taylor polynomials and by associating a so-called
Taylor subdivision (vector) scheme
. The main point of investigation is a spectral condition. If the subdivision scheme of the finite differences of
is contractive, then
is C
0 and ℋ is C
d
. We apply this result to two families of Hermite subdivision schemes. The first one is interpolatory; the second one is a
kind of corner cutting. Both of them use the Tchakalov-Obreshkov interpolation polynomial.
相似文献