共查询到20条相似文献,搜索用时 0 毫秒
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Lizheng Lu 《Journal of Computational and Applied Mathematics》2011,235(6):1557-1563
We present an iteration method for the polynomial approximation of rational Bézier curves. Starting with an initial Bézier curve, we adjust its control points gradually by the scheme of weighted progressive iteration approximations. The Lp-error calculated by the trapezoidal rule using sampled points is used to guide the iteration approximation. We reduce the Lp-error by a predefined factor at every iteration so as to obtain the best approximation with a minimum error. Numerical examples demonstrate the fast convergence of our method and indicate that results obtained using the L1-error criterion are better than those obtained using the L2-error and L∞-error criteria. 相似文献
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Jie ChenGuo-Jin Wang 《Journal of Computational and Applied Mathematics》2011,235(17):4925-4936
In this paper, we extend the results published in JCAM volume 214 pp. 163-174 in 2008. Based on the bound estimates of higher derivatives of both Bernstein basis functions and rational Bézier curves, we prove that for any given rational Bézier curve, if the convergence condition of the corresponding hybrid polynomial approximation is satisfied, then not only the l-th (l=1,2,3) derivatives of its hybrid polynomial approximation curve uniformly converge to the corresponding derivatives of the rational Bézier curve, but also this conclusion is tenable in the case of any order derivative. This result can expand the area of applications of hybrid polynomial approximation to rational curves in geometric design and geometric computation. 相似文献
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J. Monterde 《Advances in Computational Mathematics》2009,30(1):61-78
We give a full characterization of helical polynomial curves of any degree and a simple way to construct them. Existing results about Hermite interpolation are revisited. A simple method to select the best quintic interpolant among all possible solutions is suggested. 相似文献
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讨论了空间有理曲线中心投影后导数上界的估计,基于曲线各阶差分的递推计算,给出了空间有理参数多项式曲线的快速绘制算法.算法只用到整数的加减法,效率高. 相似文献
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In this paper, we derive the bounds on the magnitude of l th (l=2,3) order derivatives of rational Bézier curves, estimate the error, in the L∞ norm sense, for the hybrid polynomial approximation of the l th (l=1,2,3) order derivatives of rational Bézier curves. We then prove that when the hybrid polynomial approximation converges to a given rational Bézier curve, the l th (l=1,2,3) derivatives of the hybrid polynomial approximation curve also uniformly converge to the corresponding derivatives of the rational curve. These results are useful for designing simpler algorithms for computing tangent vector, curvature vector and torsion vector of rational Bézier curves. 相似文献
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An algorithmic approach to degree reduction of rational Bézier curves is presented. The algorithms are based on the degree reduction of polynomial Bézier curves. The method is introduced with the following steps: (a) convert the rational Bézier curve to polynomial Bézier curve by using homogenous coordinates, (b) reduce the degree of polynomial Bézier curve, (c) determine weights of degree reduced curve, (d) convert the Bézier curve obtained through step (b) to rational Bézier curve with weights in step (c). 相似文献
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Gwang-Il Kim 《Journal of Applied Mathematics and Computing》2005,19(1-2):241-251
In this paper, we introduce a new algebraic method to characterize rational PH plane curves. And using this method, we study the algebraic characterization of generic strongly regular rational plane PH curves expressed in the complex formalism which is introduced by R. T. Farouki. We prove that generic strongly semi-regular rational PH plane curves are completely characterized by solving a simple functional equation ${\mathcal{H}}(f,g) = h^2 $ whereh is a complex polynomial and ${\mathcal{H}}$ is a bi-linear operator defined by ${\mathcal{H}}(f,g) = f'g - fg'$ for complex polynomialsf, g. 相似文献
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Roya Beheshti 《Mathematische Annalen》2014,360(3-4):753-768
We study smooth hypersurfaces of degree \(d\ge n+1\) in \(\mathbf{P}^n\) whose spaces of smooth rational curves of low degrees are larger than expected, and show that under certain conditions, the primitive part of the middle cohomology of such hypersurfaces have non-trivial Hodge substructures. As an application, we prove that the space of lines on any smooth Fano hypersurface of degree \(d \le 8\) in \(\mathbf{P}^n\) has the expected dimension \(2n-d-3\) . 相似文献
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Helmut Pottmann 《Advances in Computational Mathematics》1995,3(1-2):147-170
The dual Bézier representation offers a simple and efficient constructive approach to rational curves with rational offsets (rational PH curves). Based on the dual form, we develop geometric algorithms for approximating a given curve with aG 2 piecewise rational PH curve. The basic components of the algorithms are an appropriate geometric segmentation andG 2 Hermite interpolation. The solution involves rational PH curves of algebraic class 4; these curves and important special cases are studied in detail. 相似文献
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Hans-Peter Schröcker 《Journal of Geometry》2002,73(1-2):134-147
We investigate the one-parametric set of projective subspaces that is generated by a set of rational curves in projective relation. The main theorem connects the
algebraic degree of , the number of degenerate subspaces in and the dimension of the variety of all rational curves that can be used to generate . It generalizes classical results and is related to recent investigations on projective motions with trajectories in proper
subspaces of the fixed space.
Received 9 May 2001. 相似文献
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We take up the study of transnormal graphs again. We recall that some results on this topic appeared in [2], [3], [4] and [8]. The purpose of this paper is two-fold. We start by considering curves in Euclidean n-space and extend the results in [3]. The main result shows that no polynomial curve of positive even degree (see below for the definitions) has transnormal graph. In section 3 we deal with polynomial functions f: of odd degree. Some conditions are proved to be necessary and sufficient for the transnormality of the graph. The results obtained enable us to characterize the polynomial functions of degree less than or equal to 5 which have transnormal graph.To Professor N. K. Stephanidis on his 65th birthday 相似文献
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Nicolae Manolache 《manuscripta mathematica》2001,104(4):503-517
In this note we are looking after nilpotent projective curves without embedded points, which have rational normal curves
of degree d as support, are defined (scheme-theoretically) by quadratic equations, have degree 2d and have only linear syzygies. We show that, as expected, no such curve does exist in ℙ
d
, and then consider doublings in a bigger ambient space. The simplest and trivial example is that of a double line in the
plane. We show that the only possibility is to take rational normal curves in ℙ
d
embedded further in ℙ2
d
and to take a certain doubling in the sense of Ferrand (cf. [5]) in ℙ2
d
. These double curves have the Hilbert polynomial H(t)=2dt+1, i.e. they are in the Hilbert scheme of the rational normal curves of degree 2d. Thus, it turns out that they are natural generalizations of
the double line in the plane considered as a degenerated conic.The simplest nontrivial example is the curve of degree 4 in
ℙ4, defined by the ideal (xz−y
2, xu−yv, yu−zv, u
2, uv, v
2). The double rational curve allow the formulation of a Strong Castelnuovo Lemma in the sense of [7], for sets of points and double points. In the last section we mention some plethysm formulae for symmetric
powers.
Received: 1 September 2000 / Revised version: 15 January 2001 相似文献
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Let Rj : |j| m, be a given set of n×n matrices. Necessary and sufficient conditions for the existence and uniqueness of an invertible function F() = Fjj in the Wiener algebra of n×n matrix valued functions on the unit circle || = 1 such that Fj=Rj for |j| m, and F admits either a right or a left canonical factorization and the matrix Fourier coefficients of F–1 vanish for |j| > m are presented and discussed. In the special case that the block Toeplitz matrix based on the given Rj is positive definite there is exactly one such extension: the so-called maximum entropy or autoregressive extension of statistical estimation theory. Some special properties of this extension are discussed. 相似文献
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圆锥曲线重新参数化可以提高曲线参数的均匀性,且增强在拼接点处的光滑性.常用的参数化方法是采用一次有理多项式或二次有理多项式.采用三次有理多项式对圆锥曲线重新参数化,使曲线的次数由二次升到六次.以圆弧为例所得的实验结果袁明,在两段圆弧的公共点处的连续性为C~3,而且三次有理多项式参数化与弧长参数化的弦长偏差相比二次有理多项式参数化减小两个数量级. 相似文献