共查询到20条相似文献,搜索用时 140 毫秒
1.
Ghulam MUSTAFA 《数学年刊B辑(英文版)》2017,38(5):1077-1092
The objective of this article is to introduce a generalized algorithm to produce the m-point n-ary approximating subdivision schemes(for any integer m, n ≥ 2). The proposed algorithm has been derived from uniform B-spline blending functions. In particular, we study statistical and geometrical/traditional methods for the model selection and assessment for selecting a subdivision curve from the proposed family of schemes to model noisy and noisy free data. Moreover, we also discuss the deviation of subdivision curves generated by proposed family of schemes from convex polygonal curve. Furthermore, visual performances of the schemes have been presented to compare numerically the Gibbs oscillations with the existing family of schemes. 相似文献
2.
In this paper, a new method for geometrically continuous interpolation in spheres is proposed. The method is entirely based on the spherical B′ezier curves defined by the generalized de Casteljau algorithm. Firstly we compute the tangent directions and curvature vectors at the endpoints of a spherical B′ezier curve. Then, based on the above results, we design a piecewise spherical B′ezier curve with G 1 and G 2 continuity. In order to get the optimal piecewise curve according to two different criteria, we also give a constructive method to determine the shape parameters of the curve. According to the method, any given spherical points can be directly interpolated in the sphere. Experimental results also demonstrate that the method performs well both in uniform speed and magnitude of covariant acceleration. 相似文献
3.
Energy minimization has been widely used for constructing curve and surface in the fields such as computer-aided geometric design, computer graphics. However, our testing examples show that energy minimization does not optimize the shape of the curve sometimes. This paper studies the relationship between minimizing strain energy and curve shapes, the study is carried out by constructing a cubic Hermite curve with satisfactory shape. The cubic Hermite curve interpolates the positions and tangent vectors of two given endpoints. Computer simulation technique has become one of the methods of scientific discovery, the study process is carried out by numerical computation and computer simulation technique. Our result shows that: (1) cubic Hermite curves cannot be constructed by solely minimizing the strain energy; (2) by adoption of a local minimum value of the strain energy, the shapes of cubic Hermite curves could be determined for about 60 percent of all cases, some of which have unsatisfactory shapes, however. Based on strain energy model and analysis, a new model is presented for constructing cubic Hermite curves with satisfactory shapes, which is a modification of strain energy model. The new model uses an explicit formula to compute the magnitudes of the two tangent vectors, and has the properties: (1) it is easy to compute; (2) it makes the cubic Hermite curves have satisfactory shapes while holding the good property of minimizing strain energy for some cases in curve construction. The comparison of the new model with the minimum strain energy model is included. 相似文献
4.
A piecewise-smooth second-order singularly perturbed differential equation whose right-hand side is a nonlinear function with a discontinuity on some curve is investigated. This is a new class of problems in the case where the degenerate equation has a multiple root on the left-hand side of the curve which separates the domain and an isolated root on the right-hand side of that curve. The asymptotics of a solution with an internal layer near a point on the discontinuous curve and the transition point is constructed. The method to construct the internal layer function is proposed. The behavior of the solution in the internal layer consisting of four zones essentially differs from the case of isolated roots. For sufficiently small parameter values, the existence of a smooth solution with an internal layer from the multiple root of the degenerate equation to the isolated root in the neighborhood of a point on the discontinuous curve is proved. The method can be shown to be effective in the given example. 相似文献
5.
The space-time monopole equation is the reduction of anti-self-dual Yang-Mills equations in R2,2 to R2,1. This equation is a non-linear wave equation, and can be encoded in a Lax pair. An equivalent Lax pair is used by Dai and Terng to construct monopoles with continuous scattering data, and then the equation can be linearized by the scattering data, allowing one to use the inverse scattering method to solve the Cauchy problem with rapidly decaying small initial data. In this paper, we use the terminology of holomorphic bundle and transversality of certain maps, parametrized by initial data, to give more initial data, with which we can use scattering method to solve the Cauchy problem of the monopole equation up to gauge transformation. 相似文献
6.
On the Mean Absolute Geodesic
Curvature of Closed Curves in 2-Dimensional Space
Forms 总被引:3,自引:0,他引:3
YouNingWANG 《数学学报(英文版)》2003,19(4):757-764
In this paper,we establish some formulas on closed curves in 2-dimensional space forms.Mean absolute geodesic curvature is introduced to describe the average curving of a closed curve.Inthis sense,a closed curve could be compared with a geodesic circle that is the boundary of a convex geodesic circular disk containing the closed curve.The comparison can be used to show some properties of space forms only on themselves. 相似文献
7.
In this paper, the authors consider a class of generalized curve flow for convex curves in the plane. They show that either the maximal existence time of the flow is finite and the evolving curve collapses to a round point with the enclosed area of the evolving curve tending to zero, i.e., limt→T A(t) = 0, or the maximal time is infinite, that is, the flow is a global one. In the case that the maximal existence time of the flow is finite, they also obtain a convergence theorem for rescaled curves at the maximal time. 相似文献
8.
This paper is devoted to counting the number of isomorphism classes of pointed hyperelliptic curves over finite fields. We deal with the genus 4 case and the finite fields are of even characteristics. The number of isomorphism classes is computed and the explicit formulae are given. This number can be represented as a polynomial in q of degree 7, where q is the order of the finite field. The result can be used in the classification problems and it is useful for further studies of hyperelliptic curve cryptosystems, e.g. it is of interest for research on implementing the arithmetics of curves of low genus for cryptographic purposes. It could also be of interest for point counting problems; both on moduli spaces of curves, and on finding the maximal number of points that a pointed hyperelliptic curve over a given finite field may have. 相似文献
9.
Receiver operating characteristic (ROC) curves are often used to study the two sample problem in medical studies. However, most data in medical studies are censored. Usually a natural estimator is based on the Kaplan-Meier estimator. In this paper we propose a smoothed estimator based on kernel techniques for the ROC curve with censored data. The large sample properties of the smoothed estimator are established. Moreover, deficiency is considered in order to compare the proposed smoothed estimator of the ROC curve with the empirical one based on Kaplan-Meier estimator. It is shown that the smoothed estimator outperforms the direct empirical estimator based on the Kaplan-Meier estimator under the criterion of deficiency. A simulation study is also conducted and a real data is analyzed. 相似文献
10.
This paper proposes a method to construct an G3cubic spline curve from any given open control polygon.For any two inner Bezier points on each edge of a control polygon,we can de ne each Bezier junction point such that the spline curve is G2-continuous.Then by suitably choosing the inner Bezier points,we can construct a global G3spline curve.The curvature combs and curvature plots show the advantage of the G3cubic spline curve in contrast with the traditional C2 cubic spline curve. 相似文献
11.
本文讨论六次PH(pythagorean hodograph)曲线的Hermite插值问题.六次PH曲线可以分为两种类型,本文使用参数曲线的复数表示形式,分别给出这两类曲线的构造方法.在给定C1连续的Hermite条件下,需要指定一个自由参数以确定插值曲线,本文进一步阐述这个自由参数的几何意义.由于六次PH曲线是非正则曲线,对于第一类曲线,不易控制奇异点在曲线中的位置;而对于第二类曲线,奇异点可以在构造过程中显式地被指定,因此可以有效地避免其在特定曲线段上的出现. 相似文献
12.
This paper presents the dual bases for Wang-Bézier curves with a position parameter L, which include Bézier curve, Wang-Ball curve and some intermediate curves. The Marsden identity and the transformation formulas from Bézier curve to Wang-Bézier curve are also given. These results are useful for the application of Wang-Bézier curve and their popularization in Computer Aided Geometric Design. 相似文献
13.
By using the geometric constraints on the control polygon of a Pythagorean hodograph (PH) quartic curve, we propose a sufficient condition for this curve to have monotone curvature and provide the detailed proof. Based on the results, we discuss the construction of spiral PH quartic curves between two given points and formulate the transition curve of a G2 contact between two circles with one circle inside another circle. In particular, we deduce an attainable range of the distance between the centers of the two circles and summarize the algorithm for implementation. Compared with the construction of a PH quintic curve, the complexity of the solution of the equation for obtaining the transition curves is reduced. 相似文献
14.
Binary 3-point scheme, developed by Hormann and Sabin [Hormann, K. and Sabin, Malcolm A., 2008, A family of subdivision schemes with cubic precision, Computer Aided Geometric Design, 25, 41-52], has been modified by introducing a tension parameter which generates a family of C1 limiting curves for certain range of tension parameter. Ternary 3-point scheme, introduced by Siddiqi and Rehan [Siddiqi, Shahid S. and Rehan, K., 2009, A ternary three point scheme for curve designing, International Journal of Computer Mathematics, In Press, DOI: 10.1080/00207160802428220], has also been modified by introducing a tension parameter which generates family of C1 and C2 limiting curves for certain range of tension parameter. Laurent polynomial method is used to investigate the continuity of the subdivision schemes. The performance of modified schemes has been demonstrated by considering different examples along with its comparison with the established subdivision schemes. 相似文献
15.
本文基于Pythagorean-hodograph (PH)曲线和代数双曲线的良好几何特性,构造了Pythagorean-Hodograph Hyperbolic (PH-H)曲线,并给出了PH-H曲线的定义以及相应性质.同时,分别利用Hyperbolic基函数和Algebraic Hyperbolic (AH) B\''ezier基函数,得到了平面三次AH B\''ezier曲线为PH曲线的两个不同的充要条件.此外,三次PH-H曲线也被用于求解具有确定解的$G^1$ Hermite插值问题.文中给出了具体实例来说明我们的方法. 相似文献
16.
Lin Xueru 《Annals of Differential Equations》2005,21(3):331-336
In [2-5], cubic, quartic or quintic homoclinic cycles are found. In this paper, we present a quadratic system with homoclinic cycle which is described by a sextic curve. quadratic system, homoclinic cycle, algebratic invariant curve 相似文献
17.
18.
The problems of determining the B–spline form of a C 2 Pythagorean–hodograph (PH) quintic spline curve interpolating given points, and of using this form to make local modifications, are addressed. To achieve the correct order of continuity, a quintic B–spline basis constructed on a knot sequence in which each (interior) knot is of multiplicity 3 is required. C 2 quintic bases on uniform triple knots are constructed for both open and closed C 2 curves, and are used to derive simple explicit formulae for the B–spline control points of C 2 PH quintic spline curves. These B-spline control points are verified, and generalized to the case of non–uniform knots, by applying a knot removal scheme to the Bézier control points of the individual PH quintic spline segments, associated with a set of six–fold knots. Based on the B–spline form, a scheme for the local modification of planar PH quintic splines, in response to a control point displacement, is proposed. Only two contiguous spline segments are modified, but to preserve the PH nature of the modified segments, the continuity between modified and unmodified segments must be relaxed from C 2 to C 1. A number of computed examples are presented, to compare the shape quality of PH quintic and “ordinary” cubic splines subject to control point modifications. 相似文献
19.
C. Thas 《Geometriae Dedicata》1994,51(2):163-180
In this paper we consider a Desargues configuration in the projective plane, i.e. ten points and ten lines, on each line we have three of the points and through each point we have three of the lines. We construct a rational curve of order 6 which has a node at each of the ten points. We have never seen this kind of curve in the literature, but it is well known that for anyn there exists a rational curve of ordern which has [(n–1)(n–2)]/2 nodes and ifn=6 we find a sextic with ten nodes. The purpose of this paper is to obtain a sextic of this kind as a locus of points in connection with special projectivities of the plane associated with the Desargues configuration and to find a rational parametric representation of it. A large part of this paper is done with MACSYMA: it is an application of computer algebra in algebraic geometry. Special cases, where we find a quintic, a quartic or a cubic, are given in the last section. 相似文献