共查询到20条相似文献,搜索用时 31 毫秒
1.
Modifying the shape of FB-spline curves 总被引:1,自引:0,他引:1
FB-spline curves are the unification of recently developed trigonometric CB-spline and hyperbolic HB-spline curves, including the classical B-spline curves. These generalized curves overcome some restrictions of B-spline curves and allow to design some important curves like helix, cycloids or catenary. Their properties, however, have been studied only theoretically. In this paper practical shape modification algorithms of FB-spline curves are discussed, including the geometrical effects of the alteration of shape parameters, which are essential from the users’ point of view. 相似文献
2.
The metric sample space of Fréechet curves (Fréechet , 1934,1951,1961) is based on a generalization of regular curves that covers continuous curves in full generality. This makes it possible to deal with both smooth and non-smooth, even non-rectifiable geometric curves in statistical analysis. In the present paper this sample space is further extended in two directions that are relevant in practice: to incorporate information on landmark points in the curves and to impose invariance with respect to an arbitrary group of isometric spatial transformations. Properties of the introduced sample spaces of curves are studied, specially those concerning to the generation and representation of random curves by random functions.In order to provide measures of central tendency and dispersion of random curves, centroids and restricted centroids ofrandom curves are defined in a general metric framework, and methods for their consistent estimation are derived. 相似文献
3.
Chen Caoyu 《代数通讯》2013,41(8):2885-2903
Abstract We study the automorphism and collineation groups of plane curves, i.e., in ?2, that are not necessarily smooth, and obtain bounds for these curves in terms of, their degree and the number of singularities. We also introduce the notion of bad curves and good curves, and show that all bad curves are rational. 相似文献
4.
5.
Riemann Existence Theorems for Galois covers of Mumford curves by Mumford curves are stated and proven. As an application, all finite groups are realised as full automorphism groups of Mumford curves in characteristic zero. 相似文献
6.
In this paper we introduce broccoli curves, certain plane tropical curves of genus zero related to real algebraic curves. The numbers of these broccoli curves through given points are independent of the chosen points — for arbitrary choices of the directions of the ends of the curves, possibly with higher weights, and also if some of the ends are fixed. In the toric Del Pezzo case we show that these broccoli invariants are equal to the Welschinger invariants (with real and complex conjugate point conditions), thus providing a proof of the independence of Welschinger invariants of the point conditions within tropical geometry. The general case gives rise to a tropical Caporaso–Harris formula for broccoli curves which suffices to compute all Welschinger invariants of the plane. 相似文献
7.
For the cubic trigonometric polynomial curves with a shape parameter (TB curves, for short), the effects of the shape parameter on the TB curve are made clear, the shape features of the TB curve are analyzed. The necessary and sufficient conditions are derived for these curves having single or double inflection points, a loop or a cusp, or be locally or globally convex. The results are summarized in a shape diagram of TB curves, which is useful when using TB curves for curve and surface modeling. Furthermore the influences of shape parameter on the shape diagram and the ability for adjusting the shape of the curve are shown by graph examples, respectively. 相似文献
8.
9.
K. E. Bauman 《Proceedings of the Steklov Institute of Mathematics》2011,275(1):47-59
This paper completes the analysis (begun by E.V. Shchepin and the author in 2008) of regular Peano curves of genus 9 in search
of a curve with the minimum square-to-linear ratio. One-side regular Peano curves of genus 9 are considered, and, among these
curves, a class of minimal curves with a square-to-linear ratio of 5 2/3 is singled out. A new language to describe curves
is introduced which significantly simplifies the coding of these curves. 相似文献
10.
Jian Kong 《Transactions of the American Mathematical Society》2003,355(8):3175-3180
We compute the Seshadri constants on the Jacobian of hyperelliptic curves, as well as of curves with genus three and four. For higher genus curves we conclude that if the Seshadri constants of their Jacobian are less than 2, then the curves must be hyperelliptic.
11.
与给定的多边形相切的闭(C~2-连续)Bézier曲线 总被引:1,自引:0,他引:1
Bezier曲线已广泛应用到汽车、航空、造船等许多工业领域中.[1]描述了以给定凸多边形的所有边为切线的.平面三次分段C~2-连续的闭Bezier曲线的构造,并且给出了实际应用. [1]描述的算法有如下缺点:(a)需要解一个大型线性方程组,计算量很大;(b)对 相似文献
12.
Enrique Artal Bartolo Jorge Carmona Ruber José Ignacio Cogolludo Agustí n 《Transactions of the American Mathematical Society》2007,359(1):165-183
In this paper we construct new invariants of algebraic curves based on (not necessarily generic) braid monodromies. Such invariants are effective in the sense that their computation allows for the study of Zariski pairs of plane curves. Moreover, the Zariski pairs found in this work correspond to curves having conjugate equations in a number field, and hence are not distinguishable by means of computing algebraic coverings. We prove that the embeddings of the curves in the plane are not homeomorphic. We also apply these results to the classification problem of elliptic surfaces.
13.
An algorithmic approach to degree reduction of B-spline curves is presented. The new algorithms are based on the blossoming process and its matrix representation. The degree reduction of B-spline curves are obtained by the generalized least square method. The computations are carried out by minimizing theL 2 distance between the two curves. 相似文献
14.
《Mathematical Methods in the Applied Sciences》2018,41(13):5096-5111
A pedal curve (a contrapedal curve) of a regular plane curve is the locus of the feet of the perpendiculars from a point to the tangents (normals) to the curve. These curves can be parametrized by using the Frenet frame of the curve. Yet provided that the curve has some singular points, the Frenet frame at these singular points is not well‐defined. Thus, we cannot use the Frenet frame to examine pedal or contrapedal curves. In this paper, pedal and contrapedal curves of plane curves, which have singular points, are investigated. By using the Legendrian Frenet frame along a front, the pedal and contrapedal curves of a front are introduced and properties of these curves are given. Then, the condition for a pedal (and a contrapedal) curve of a front to be a frontal is obtained. Furthermore, by considering the definitions of the evolute, the involute, and the offset of a front, some relationships are given. Finally, some illustrated examples are presented. 相似文献
15.
《Mathematical Methods in the Applied Sciences》2018,41(5):1988-1997
In this paper, we will give the definition of the pedal curves of frontals and investigate the geometric properties of these curves in the Euclidean plane. We obtain that pedal curves of frontals in the Euclidean plane are also frontals. We further discuss the connections between singular points of the pedal curves and inflexion points of frontals in the Euclidean plane. 相似文献
16.
文中把二次曲线的几何性质的研究转化成条件极值问题,但又不关心问题的解,而是利用Lagrange乘数来研究二次曲线的几何性质,找到了用Lagrange 乘数判别二次曲线形状的方法,给出了用Lagrange乘数计算二次曲线的对称轴和轴长的公式. 相似文献
17.
Xu-Zheng Liu Xia Cui Guo-Qin Zheng Jun-Hai Yong Jia-Guang Sun 《Journal of Computational and Applied Mathematics》2008,220(1-2):322-334
Dynamic partial differential equation (PDE) parametric curves which can be expressed as a coupled system of two hyperbolic equations are developed. In curve design, dynamic PDE parametric curves can be modified intuitively and are more flexible than ordinary differential equation (ODE) curves. The calculation of dynamic PDE parametric curves must recur to numerical methods and a three-level finite difference scheme is proposed. Approximation and stability properties for the scheme are proved and convergence property is derived. An example of interpolating PDE curves is presented as an application of dynamic PDE parametric curves. 相似文献
18.
The Dual Functionals for the Generalized Ball Basis of Wang-Said Type and Basis Transformation Formulas 总被引:2,自引:0,他引:2
Ping Jiang Hongyi Wu Jieqing Tan 《高等学校计算数学学报(英文版)》2006,15(3):248-256
The generalized Ball curves of Wang-Said type with a position parameter L not only unify the Wang-Ball curves and the Said-Ball curves, but also include several useful intermediate curves. This paper presents the dual functionals for the generalized Ball basis of Wang-Said type. The relevant basis transformation formulae are also worked out. 相似文献
19.
In order to relieve the deficiency of the usual cubic Hermite spline curves, the quartic Hermite spline curves with shape parameters is further studied in this work. The interpolation error and estimator of the quartic Hermite spline curves are given. And the characteristics of the quartic Hermite spline curves are discussed. The quartic Hermite spline curves not only have the same interpolation and conti-nuity properties of the usual cubic Hermite spline curves, but also can achieve local or global shape adjustment and C2 continuity by the shape parameters when the interpolation conditions are fixed. 相似文献
20.
含悬浮固粒射流界面稳定性研究 总被引:1,自引:0,他引:1
利用气固两相耦合模型,理论推导出含悬浮固粒射流的稳定性方程,通过数值计算得到了两相射流稳定性特征曲线、固气扰动速度比值幅值曲线及固气相位差曲线,进而得到了关于固粒对流场中扰动增长和传播的影响及失稳过程中固粒扰动特性的结论。这些结论对于两相射流发展的认识和工程实际中实施对两相射流场的人工控制有重要意义。 相似文献