双参数Bézier曲线的升二次扩展

本文以二次Bernstein基函数为例,首次提出了含双参数基函数的新扩展——αβQ—Bern-stein基函数,此类基函数具有新的特点,即基函数的扩展次数一次性升高两次,且包含了二次多项式和带一个参数的三次多项式基函数的所有性质。基于这组基函数定义了αβQ—Bézier曲线,该曲线也含有参数,具有形状可调性,当α与β取某些值时曲线能达到C4连续或在某个端点处C0连续。最后与含两个参数的升一次Bézier曲线进行比较,该曲线具有调节范围广、灵活性更强的优势。     

三次Bézier曲线的α扩展

利用一个对称的调配函数,结合NURBS曲线中权的思想,在曲线控制顶点处引进调配参数,将三次Bézier曲线进行扩展,得到的新曲线比原来的曲线有更强的描述能力,并且包含了原曲线形式。讨论了扩展曲线的基表示及曲线的性质,调配参数可以用来控制曲线的局部形状,特别适用于自由曲线曲面的设计,在CAD/CAM中具有很好的应用前景。     

带有给定切线多边形的G2连续Bézier闭曲线

描述了一种与给定多边形相切的五次Bézier曲线的算法。在算法中,所有的五次Bézier曲线的控制点可以通过对多边形的顶点简单计算产生。所构造的曲线对多边形具有保形性,曲线可以局部修改,最后给出了一个算例。     

具有分布时滞的Liénard型方程周期解的存在性

考察了具有分布时滞的Liénard型方程,利用重合度理论研究其周期解问题,得到了该方程周期解存在的充分条件,结论丰富了现有文献的结果．     

融合多向学习的混沌麻雀搜索算法

对于原始麻雀搜索算法（SSA）在迭代过程中表现出的种群多样性减小,易陷入局部最优等问题,提出一种融合多向学习的混沌麻雀搜索算法（MSSA）。利用Hénon混沌映射初始化种群,增加麻雀种群的多样性,扩大可行解的搜索范围,为全局寻优奠定基础;采用多向学习策略增加麻雀跟随者探索未知领域的机会,平衡算法的局部开发性能和全局搜索能力;当算法陷入局部最优时,引用遗传算法中的变异策略依据动态的变异概率对当前最优个体进行扰动变异;将MSSA算法应用到无线传感器网络节点覆盖优化问题。数值实验结果与Wilcoxon秩和检验结果均表明MSSA算法在收敛精度与收敛速度等方面具有更明显的优势。     

A Novel Contour Tracing Algorithm for Object Shape Reconstruction Using Parametric Curves

Parametric curves such as Bézier and B-splines, originally developed for the design of automobile bodies, are now also used in image processing and computer vision. For example, reconstructing an object shape in an image, including different translations, scales, and orientations, can be performed using these parametric curves. For this, Bézier and B-spline curves can be generated using a point set that belongs to the outer boundary of the object. The resulting object shape can be used in computer vision fields, such as searching and segmentation methods and training machine learning algorithms. The prerequisite for reconstructing the shape with parametric curves is to obtain sequentially the points in the point set. In this study, a novel algorithm has been developed that sequentially obtains the pixel locations constituting the outer boundary of the object. The proposed algorithm, unlike the methods in the literature, is implemented using a filter containing weights and an outer circle surrounding the object. In a binary format image, the starting point of the tracing is determined using the outer circle, and the next tracing movement and the pixel to be labeled as the boundary point is found by the filter weights. Then, control points that define the curve shape are selected by reducing the number of sequential points. Thus, the Bézier and B-spline curve equations describing the shape are obtained using these points. In addition, different translations, scales, and rotations of the object shape are easily provided by changing the positions of the control points. It has also been shown that the missing part of the object can be completed thanks to the parametric curves.     

四次C-Bézier曲线的拼接技术研究

为了解决造型设计中复杂曲线难以用单一曲线来表示的问题,研究了一种带形状参数的四次C-Bézier曲线的光滑拼接技术.在对四次C-Bézier曲线基函数及其端点性质分析的基础上,给出了两相邻四次C-Bézier曲线间G1、G2和C1、C2的光滑拼接的充要条件,同时还给出了两相邻四次C-Bézier曲线间光滑拼接的基本步骤和几何造型实例.实例结果表明,所提方法简单有效、易实现,极大地增强了四次C-Bézier曲线表达复杂曲线的能力,可广泛地应用于各种CG/CAD/CAID/CAM造型系统中.     

Cramér-Rao lower bound analysis for guidance systems with bearings-only measurements

Most currently existing investigations on the observability of passive guidance systems can only protimability analysis of closed-loop guidance systems with bearings-only measurements, is proposed. The new method provides an intuitive result for observability of the guidance system through graphical analysis. As a demonstration, a numerical example is presented, in which the degrees of observability of the guidance systems under two commonly used guidance laws are compared by using the new approach.     

A simulation study of protons heated by left/right-handed Alfvén waves generated by electromagnetic proton-proton instability

Most protons in the solar wind belong to one of two different populations,the less dense beam protons and the denser core protons.The beam protons,with a velocity of(1-2)VA(VA is the local Alfvén speed),always drift relative to the core protons;this kind of distribution is unstable and stimulates several kinds of wave mode.In this study,using a 2D hybrid simulation model,we find that the original right-handed elliptically polarized Alfvén waves become linearly polarized,and eventually become right-handed and circularly polarized.Given that linearly polarized waves are a superposition of left-handed and right-handed waves,cyclotron resonance in the right-handed/left-handed component heats beam/core protons perpendicularly.The resonance between beam protons and right-handed polarized waves is stronger when the beam relative density is lower,resulting in more dramatic perpendicular heating of beam protons,whereas the situation is reversed when the beam relative density is larger.     

基于共轭梯度的布谷鸟搜索算法

布谷鸟搜索算法(Cuckoo Search,CS)是基于群体智能的新型随机全局优化算法,具有控制参数少、搜索路径优和全局寻优能力强等优点,但也存在局部搜索能力较弱、收敛速度偏慢和收敛精度不够高等缺点。为了克服CS算法的缺点,提出一种基于共轭梯度的布谷鸟搜索算法(CGCS),使经过Levy飞行机制和淘汰机制进化后的布谷鸟种群沿着相互共轭的方向迅速下降.从而在保持算法的强大全局寻优能力的基础上大幅提高算法的收敛能力。用4个典型测试函数分别对CGCS算法和CS算法进行性能测试,结果表明,CGCS算法比CS算法具有更快的收敛速度、更高的收敛精度和更稳定的优化结果。CGCS算法同时具有很强的全局寻优能力、收敛能力和鲁棒性,特别适合多峰及高维函数的优化。