平面离散点集的边界搜索算法

进行有限元仿真首先要建立有限元网格模型。使用不含有任何拓扑信息的离散点集直接进行网格划分可以快速、精确地建立网格模型。使用铺路法进行网格剖分是从边界开始向内生成网格单元。该文提出一种使用搜索盒的搜索平面离散点集边界的算法。该方法将离散点分配到搜索盒中，遍历位于边界的搜索盒，将其中的点连接成边界点链表。该算法能正确地搜索包含有凹点、孔洞特征的离散点集的边界，具有较强的通用性。文中介绍了算法的基本思想，并给出算例。     

平面弹性方程外问题的非重叠型区域分解算法

１．引言 区域分解算法是八十年代兴起的偏微分方程求解新技术．基于有限元法的区域分解算法对求解有界区域问题行之有效［２,４,９］．边界元方法则是处理无界区域问题的强有力的工具［１,１０,１７］,有限元与边界元耦合法得到广泛应用 ［３,５,７］．近年又发展了基于自然边界归化的区域分解算法,特别适用于无界区域问题［８,１１,１２］．迄今这方面的文章主要是针对二维Ｐｏｉｓｓｏｎ方程及双调和方程的［１３－１６］． 本文讨论平面弹性方程的Ｄｉｒｉｃｈｌｅｔ外边值问题其中Ω是充分光滑闭曲线Г０之外的无界区域,ｕ…     

基于组件的电网监测图形系统的设计

本文以某电网监测系统为背景,利用VectorControl.Net组件和SVG语言进行系统的图形建模,结合VectorControl.Net组件对象模型,分析了VectorControl.Net组件开发SVG的步骤和方法,并给出了电网监测网络的拓扑关联矩阵的实现算法.     

类双曲壳的概念及算法

论文提出类双曲壳的概念,类双曲壳是一类通过射影平面无穷远直线的凸壳。运用拓扑同胚来帮助提出射影凸集和类双曲壳的概念。并借助于有向射影几何的正平面上可定向的优势,分析了从经典凸壳到类双曲壳的射影变换。构造出一个在欧氏平面上的实时凸壳算法,用于两个区域中间寻找直线簇。     

始于凸包络线的闭主曲线学习算法研究

本文提出了将凸包技术与自组织拓扑映射技术相结合的一种针对封闭曲线特征提取的主曲线学习算法，解决了一般主曲线算法无法有效模拟封闭和较为复杂分布数据集的难题。算法以数据集的凸包络线为起始步，通过分析数据集的全局和局部特征，逐步逼近数据集分布并获得封闭主曲线。算法的关键在于凹点挖掘算法的研究。实验结果表明，对于一般封闭曲线点集，该方法均能在较短的时间步内较好地逼近源数据集。该算法结构简单，复杂性在最坏情况下也不超过Ｏ（n^2），同时对图像的有界连通区域外部边界特征的提取与图形识别亦将具有较高的应用价值。     

一种平面区域几何划分的自适应算法

给定一个任意形状的平面区域,使用若干条折线段将该平面区域划分为子区域。当折线段存在不完全贯穿平面区域或包含于区域之中时,提出一种自适应算法,将其延长至最近边界以切割区域,并识别子区域输出。通过记录线段与交点的拓扑关系,并对部分线段进行延长处理,以形成记录全部端点问拓扑关系的网状结构,最终通过最小转角法搜索最佳路径输出全部子区域。实验结果表明,该方法能快速、无重复输出所有子区域,效果良好。     

平面构件修形问题的研究

根据常见平面机构的特点，对任意形状平面机构尺寸综合涉及的修形问题进行研究，综合离散法和扫掠法，提出生成扫掠区域边界的算法，即将机构运行分解为一系列绕相对转动极点的旋转运动，从而用圆弧曲线及任意形状的构件外形轮廓曲线形成扫掠区域边界。依据逆扫掠的思想，提出解决生成逆扫掠区域边界的新策略并给出相应的算法。     

二维自适应前沿推进网格生成

针对二维平面问题,通过曲率计算和基于中轴理论的邻近特征计算控制区域边界曲线的离散;修改经典的前沿推进算法,利用边界驱动的单元尺寸控制方式在区域内部布置疏密过渡合理的三角网格;结合几何和拓扑策略提升网格质量。实验表明,上述算法可生成单元质量高、尺寸过渡合理的计算网格。     

一种基于行列法离散点边界搜索算法*

平面上构建离散点的边界在地理信息系统(GIS)中应用广泛,提出了基于行列法的平面离散点边界搜索的新算法,目的是解决平面离散点边界问题,通过确定步长大小,按步长对离散点分别进行行搜索和列搜索,得到离散点的边界曲线,介绍了行列边界算法的基本思想和实现过程。该算法能够正确地搜索包含凹凸特征的离散点边界,与传统边界生成算法相比,它具有通用、实现简单等特点。该算法在油田GIS领域边界划分中得到了很好的应用,能够准确地构建油田边界。     

带断层线的等值线生成方法*

结合三角网的拓扑结构提出了一种新的分区算法。该算法首先把与断层线重合的三角形的边标志为边界边;然后根据组成区域边界的边类型,搜索出所有合理区域并插值端点和特殊点高程值;最后得到带断层线的等值线。用大量的数据进行了测试,实践证明,该算法能高效处理各种情况,实现简单。     

A boundary-element method for elastostatics in a plane region bounded by a smooth curve

The traditional boundary-element method for elastostatics in a plane region bounded by a smooth curve is modified. A circular element is used for which an analytical scheme for the traction problem is derived. It is shown that the construction of the elements of the coefficient matrix reduces to computing a simple integral which has a closed form solution. This leads to higher accuracy of the final results and considerable saving of computational efforts. The procedure is illustrated by some examples and the accuracy of the method as well as its efficiency are compared with those obtained from commonly used numerical techniques.     

Boolean representation of bounded BCK-algebras

We define the Boolean center and the Boolean skeleton of a bounded BCK-algebra, and we use the Boolean skeleton to obtain a representation of bounded BCK-algebras, called (weak) Pierce -representation, as (weak) Boolean products of bounded BCK-algebras. We analyze the cases in which the stalks in these representations are directly indecomposable, finitely subdirectly irreducible or simple algebras. We give some examples of algebras and relative subvarieties of bounded BCK-algebras to illustrate the results.     

Radical parametrizations of algebraic curves by adjoint curves

We present algorithms for parametrizing by radicals an irreducible curve, not necessarily plane, when the genus is less than or equal to 4 and the curve is defined over an algebraically closed field of characteristic zero. In addition, we also present an algorithm for parametrizing by radicals any irreducible plane curve of degree d having at least a point of multiplicity d−r, with 1≤r≤4 and, as a consequence, every irreducible plane curve of degree d≤5 and every irreducible singular plane curve of degree 6.     

Distance functions and skeletal representations of rigid and non-rigid planar shapes

Shape skeletons are fundamental concepts for describing the shape of geometric objects, and have found a variety of applications in a number of areas where geometry plays an important role. Two types of skeletons commonly used in geometric computations are the straight skeleton of a (linear) polygon, and the medial axis of a bounded set of points in the k-dimensional Euclidean space. However, exact computation of these skeletons of even fairly simple planar shapes remains an open problem.In this paper we propose a novel approach to construct exact or approximate (continuous) distance functions and the associated skeletal representations (a skeleton and the corresponding radius function) for solid 2D semi-analytic sets that can be either rigid or undergoing topological deformations. Our approach relies on computing constructive representations of shapes with R-functions that operate on real-valued halfspaces as logic operations. We use our approximate distance functions to define a new type of skeleton, i.e, the C-skeleton, which is piecewise linear for polygonal domains, generalizes naturally to planar and spatial domains with curved boundaries, and has attractive properties. We also show that the exact distance functions allow us to compute the medial axis of any closed, bounded and regular planar domain. Importantly, our approach can generate the medial axis, the straight skeleton, and the C-skeleton of possibly deformable shapes within the same formulation, extends naturally to 3D, and can be used in a variety of applications such as skeleton-based shape editing and adaptive motion planning.     

A closed analytic form for the disturbance switch curve of somesecond-order linear systems

It is shown that the time-maximum disturbance switch curve for some second-order linear systems with the most stressful bounded disturbance has a closed analytic form. This enables a simple state-feedback synthesis for the bounded disturbance stress     

Topological derivative for steady-state orthotropic heat diffusion problem

The aim of this work is to present the calculation of the topological derivative for the total potential energy associated to the steady-state orthotropic heat diffusion problem, when a circular inclusion is introduced at an arbitrary point of the domain. By a simple change of variables and using the first order Pólya-Szegö polarization tensor, we obtain a closed formula for the topological sensitivity. For the sake of completeness, the analytical expression for the topological derivative is checked numerically using the standard Finite Element Method. Finally, we present two numerical experiments showing the influency of the orthotropy in the topological derivative field and also one example concerning the optimal design of a heat conductor.     

Efficient Implementation Techniques for Topological Predicates on Complex Spatial Objects

Topological relationships like overlap, inside, meet, and disjoint uniquely characterize the relative position between objects in space. For a long time, they have been a focus of interdisciplinary research as in artificial intelligence, cognitive science, linguistics, robotics, and spatial reasoning. Especially as predicates, they support the design of suitable query languages for spatial data retrieval and analysis in spatial database systems and geographical information systems. While, to a large extent, conceptual aspects of topological predicates (like their definition and reasoning with them) as well as strategies for avoiding unnecessary or repetitive predicate executions (like predicate migration and spatial index structures) have been emphasized, the development of robust and efficient implementation techniques for them has been largely neglected. Especially the recent design of topological predicates for all combinations of complex spatial data types has resulted in a large increase of their numbers and stressed the importance of their efficient implementation. The goal of this article is to develop correct and efficient implementation techniques of topological predicates for all combinations of complex spatial data types including two-dimensional point, line, and region objects, as they have been specified by different authors and in different commercial and public domain software packages. Our solution consists of two phases. In the exploration phase, for a given scene of two spatial objects, all topological events like intersection and meeting situations are summarized in two precisely defined topological feature vectors (one for each argument object of a topological predicate) whose specifications are characteristic and unique for each combination of spatial data types. These vectors serve as input for the evaluation phase which analyzes the topological events and determines the Boolean result of a topological predicate (predicate verification) or the kind of topological predicate (predicate determination) by a formally defined method called nine-intersection matrix characterization. Besides this general evaluation method, the article presents an optimized method for predicate verification, called matrix thinning, and an optimized method for predicate determination, called minimum cost decision tree. The methods presented in this article are applicable to all known complete collections of mutually exclusive topological predicates that are formally based on the well known nine-intersection model.

Algorithms for Graphs Embeddable with Few Crossings per Edge

We consider graphs that can be embedded on a surface of bounded genus such that each edge has a bounded number of crossings. We prove that many optimization problems, including maximum independent set, minimum vertex cover, minimum dominating set and many others, admit polynomial time approximation schemes when restricted to such graphs. This extends previous results by Baker and Eppstein to a much broader class of graphs. We also prove that for the considered class of graphs, there are balanced separators of size where n is a number of vertices in the graph. On the negative side, we prove that it is intractable to recognize the graphs embeddable in the plane with at most one crossing per edge.     

Globally asymptotically stable saturated PID controllers for a double integrator with constant disturbance

This paper provides a deep insight into the saturated PID control of a double integrator with bounded disturbance. On the basis of the nested saturation functions, a simple PID‐like controller is proposed. The main difficulty in saturation control with bounded disturbances is to prove that the unsaturated regions are invariant. By phase plane and singular perturbation analysis, we prove that the saturation restrictions on the controller can be removed one by one in finite time, and the closed‐loop system can be finally reduced to a nonsaturated PID controlled double integrator. The sufficient conditions for the stability of the closed loop with disturbance are also derived. Finally, numerical simulations are conducted to validate the effectiveness of the proposed control scheme. Copyright © 2012 John Wiley & Sons, Ltd.     

Notes on Sum-Tests and Independence Tests

We study statistical sum-tests and independence tests, in particular for computably enumerable semimeasures on a discrete domain. Among other things, we prove that for universal semimeasures every S⁰₁\Sigma ^{0}_{1} -sum-test is bounded, but unbounded P⁰₁\Pi ^{0}_{1} -sum-tests exist, and we study to what extent the latter can be universal. For universal semimeasures, in the unary case of sum-test we leave open whether universal P⁰₁\Pi ^{0}_{1} -sum-tests exist, whereas in the binary case of independence tests we prove that they do not exist.