共查询到20条相似文献,搜索用时 46 毫秒
1.
Unbiased Estimates of Circle Parameters 总被引:1,自引:0,他引:1
Chan Y. T. Lee B. H. Thomas S. M. 《Journal of Optimization Theory and Applications》2000,106(1):49-60
It is of practical value to estimate the center and radius of a circle from a given set of noisy coordinate measurements. Since the coordinates of the points on a circle relate to its parameters through the nonlinear circle equation, the estimation problem is inherently nonlinear. Additionally, if the measurements are available only along a small arc, the estimation exhibits generally a bias, together with large variances, even at low-noise magnitudes. This paper presents two algorithms, one iterative and another which has a closed-form solution, aiming at the elimination of biases that occur at small arcs. Simulation results show that the two algorithms do provide unbiased and reliable estimates of the circle parameters for noisy measurements on arcs as small as 45°. 相似文献
2.
Olivier Devillers Alexandra Fronville Bernard Mourrain Monique Teillaud 《Computational Geometry》2002,22(1-3):119-142
The purpose of this paper is to present a new method to design exact geometric predicates in algorithms dealing with curved objects such as circular arcs. We focus on the comparison of the abscissae of two intersection points of circle arcs, which is known to be a difficult predicate involved in the computation of arrangements of circle arcs. We present an algorithm for deciding the x-order of intersections from the signs of the coefficients of a polynomial, obtained by a general approach based on resultants. This method allows the use of efficient arithmetic and filtering techniques leading to fast implementation as shown by the experimental results. 相似文献
3.
A numerical solution method for two-dimensional electromagnetic field problems is presented using the B-spline finite-element expression based on polar coordinates. The technique has two main advantages: (1) to avoid the truncation errors at some curved boundaries and (2) to improve the accuracy of singular boundary-value problems with a sharp corner. The B-spline finite-element formulation in polar coordinates is derived and its numerical applications are illustrated by an eddy current problem and several waveguide eigenvalue problems. 相似文献
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This note aims to present the history of the main researches carried out to represent an ellipse by means of an eight-centered oval and to complete them by giving a geometrical demonstration of the formulas expressing the coordinates of the centers, the radii and the central angles of these arcs of circles making up this oval. These formulas will make it possible to determine its perimeter and thus to approximate the value of that of the ellipse. This result could be useful for archaeologists, who will test the hypothesis according to which some Roman amphitheatres, such as the Coliseum, were built from eight-centered ovals. 相似文献
6.
B. SCARDUA 《数学学报(英文版)》2007,23(12):2247-2252
The author proves that a non-singular polynomial vector field without invariant lines and having an entire finitely curved transcendent orbit on C^2 must be equivalent to a trivial vector field by a holomorphic change of coordinates. Other classification results are obtained for polynomial vector fields having a finitely curved orbit on C^2. 相似文献
7.
《Journal of Computational and Applied Mathematics》1996,75(1):47-56
A planar cubic Bézier curve that is a spiral, i.e., its curvature varies monotonically, does not have internal cusps, loops, and inflection points. It is suitable as a design tool for applications in which fair curves are important. Since it is polynomial, it can be conveniently incorporated in CAD systems that are based on B-splines, Bézier curves, or NURBS. When machining objects, it is desirable that as much as possible of a curved toolpath be approximated by a sequence of circular arcs rather than straight-line segments. Such an arc-spline approximation of a planar cubic Bézier spiral is presented. 相似文献
8.
Mamdouh A. Fahmy M. Zaki 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1983,34(2):154-163
A time-independent dynamical model of storm surge along island coasts using orthogonal curvilinear coordinates is presented. The curved annulus between an island coast and an arbitrary deep-water boundary is mapped conformally onto a rectangular image. Two configurations of island coasts are investigated; circular and elliptic coasts. The corresponding coordinates are circular polar and elliptic respectively. The linearized vertically-integrated equations of motion are used to model storm surges with two assumptions: (i) bottom stress is proportional to horizontal transport, and (ii) storm forces are shear stresses on water surface. Analytical solutions are presented for three dynamical cases: (i) a constant-depth basin acted upon by a uniform storm stress, (ii) variable-depth basin acted upon by a uniform-direction variable-magnitude stress, and. (iii) a basin with closed depth contours acted upon by vortex-shaped storm stress. The obtained solutions clarify the relative importance of the various parameters and variables that affect surge height distribution along island coasts. These solutions may be used to test a time-dependent, numerical dynamical storm model. 相似文献
9.
基于曲梁弹性理论的弯曲覆岩变形及应力分析 总被引:1,自引:1,他引:0
引入适用于极坐标下曲梁的位移函数,通过理论分析得出用位移函数表示的曲梁控制方程和位移分量、应力分量.在此基础上,采用差分原理给出曲梁控制方程、位移分量和应力分量的差分代数方程.最后,采用数值计算方法,分析了煤层开采后弯曲覆岩的位移和应力分布特征,结果表明:1)煤层开采后弯曲覆岩产生下沉变形;弯曲岩层环向位移既有拉伸也有压缩.2)离开切眼不远处径向应力将达到峰值,径向应力由内边界向外逐渐增大;工作面后方不远处环向应力将达到峰值,环向应力较容易引起压缩破断;离开切眼不远处剪应力将达到峰值,对于小角度截面上的剪应力由内边界向外逐渐增大.研究结果为煤矿工程提供了科学依据与参考. 相似文献
10.
Stationary solitons are found to occur in two-dimensional media with a variable saturation magnetization whose square is a
harmonic function of the coordinates. It is shown in this case that the Landau-Lifshits equation can be reduced to the integrable
O(3) sigma-model in curved space. Some properties of the solutions obtained are discussed. Bibliography: 15 titles.
Translated by V. D. Lipovskii. 相似文献
11.
A third-order analytical solution for the gravity–capillary standing wave is derived in Lagrangian coordinates through the Lindstedt–Poincare perturbation method. By numerical computation, the dynamical properties of nonlinear standing waves with surface tension in finite water depth, including particle trajectory and surface profile are investigated. We find that the presence of surface tension leads to a change of the crest form. Moreover, we also find that the particle trajectories near the surface oscillate back and forth along the arcs which will change from concave to convex as the inverse Bond number increases. There is no mass transport of the particles in a wave period. 相似文献
12.
C. Marchal 《Journal of Optimization Theory and Applications》1973,11(5):441-468
There are two different meanings of the wordchattering in control theory and optimization theory. Chattering arcs of the first kind are related to the notion of relaxation of the control (i.e., convexization of the maneuverability domain). Some sufficient conditions of equivalence of these notions are defined. Chattering arcs of the second kind appear before and after some optimal singular arcs, for instance, the intermediate thrust arcs of the optimal transfer problem of astrodynamics. The simplest examples of chattering arcs of the second kind appear in Fuller's problem, two cases of which are examined in detail. The conditions of chattering of the second kind are analyzed; they are related to the Kelley-Contensou optimality test of singular extremals, also known asGeneralized Legendre-Clebsch conditions; they lead to general solutions and not only to solutions restricted to particular terminal conditions; thus, the phenomenon of chattering is very important (fortunately, these solutions can generally be approximated very closely by simple piecewise continuous controls). Finally, some special and complex cases appear, some examples of which are analyzed. 相似文献
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Pursuit evasion in a plane is formulated with both players allowed to vary their speeds between fixed limits. A suitable choice of real-space coordinates confers open-loop optimality on the game. The solution in the small is described in terms of the individual players' extremal trajectory maps (ETM). Each map is independent of role, adversary, and capture radius. An ETM depicts the actual real-space trajectories. A template method of generating constant control arcs is described. Examples of ETM for an aircraft flying at a constant altitude with fixed and varying speeds are presented. 相似文献
15.
Robert J. MacG. Dawson 《Journal of Geometry》2010,98(1-2):1-19
A set in a metric space is called a ?eby?ev set if it contains a unique “nearest neighbour” to each point of the space. In this paper we introduce the concept of a monotone arc of convex sets and show that compact monotone arcs have the ?eby?ev property in the hyperspace of compact strictly convex sets. In the hyperspace of compact convex sets only certain monotone arcs are ?eby?ev ; these are characterized. Results are also obtained for affine segments and for noncompact monotone arcs. 相似文献
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In this paper, the complete geometric characterizations, including decomposition and compression theorems, are obtained for
a connected and compact set to be a critical set in Whitney’s sense, i.e., a set such that there exists a differentiable function
critical but not constant on it. The problem to characterize these sets geometrically was posed by H. Whitney [21] in 1935.
We also provide a complete geometrical characterization for monotone Whitney arc, i.e., there exists a differentiable function
critical but also increasing along the arc. All examples appearing in the literature are monotone Whitney arcs, for example,
the examples by Whitney [21] and Besicovitch [2], Norton’s t-quasi-arcs with Hausdorff dimension > t [14], and self-similar arcs [19]. Furthermore, after introducing the notion of homogeneous Moran arc, we can completely characterize
all the monotone Whitney arcs of criticality > 1, which include t-quasi arcs and self-conformal arcs. Some applications to arcs which are attractors of Iterated Function Systems are discussed,
including self-conformal arcs, self-similar arcs and self-affine arcs. Finally, we give an example of critical arc such that
any of its subarcs fails to be a t-quasi-arc for any t, providing an affirmative answer to an open question by Norton. 相似文献
18.
We present several algorithms for computing normally hyperbolic invariant tori carrying quasi-periodic motion of a fixed frequency in families of dynamical systems. The algorithms are based on a KAM scheme presented in Canadell and Haro (J Nonlinear Sci, 2016. doi: 10.1007/s00332-017-9389-y), to find the parameterization of the torus with prescribed dynamics by detuning parameters of the model. The algorithms use different hyperbolicity and reducibility properties and, in particular, compute also the invariant bundles and Floquet transformations. We implement these methods in several 2-parameter families of dynamical systems, to compute quasi-periodic arcs, that is, the parameters for which 1D normally hyperbolic invariant tori with a given fixed frequency do exist. The implementation lets us to perform the continuations up to the tip of the quasi-periodic arcs, for which the invariant curves break down. Three different mechanisms of breakdown are analyzed, using several observables, leading to several conjectures. 相似文献
19.
Homotopy Algorithm for Optimal Control Problems with a Second-order State Constraint 总被引:1,自引:0,他引:1
Audrey Hermant 《Applied Mathematics and Optimization》2010,61(1):85-127
This paper deals with optimal control problems with a regular second-order state constraint and a scalar control, satisfying
the strengthened Legendre-Clebsch condition. We study the stability of structure of stationary points. It is shown that under
a uniform strict complementarity assumption, boundary arcs are stable under sufficiently smooth perturbations of the data.
On the contrary, nonreducible touch points are not stable under perturbations. We show that under some reasonable conditions,
either a boundary arc or a second touch point may appear. Those results allow us to design an homotopy algorithm which automatically
detects the structure of the trajectory and initializes the shooting parameters associated with boundary arcs and touch points. 相似文献