区间算术和仿射算术的研究与应用

综述了近几年来在计算机图形学及计算机辅助几何设计中得到广泛应用的区间算术、仿射算术及其修正形式——诸如矩阵或张量形式的修正仿射算术、递归Taylor方法的理论研究成果及应用情况,并对未来的研究方向和研究重点进行了探讨。     

Extension of Affine Shape

In this paper, we extend the notion of affine shape, introduced by Sparr, from finite point sets to more general sets. It turns out to be possible to generalize most of the theory. The extension makes it possible to reconstruct, for example, 3D-curves up to projective transformations, from a number of their 2D-projections. An algorithm is presented, which is independent of choice of coordinates, is robust, does not rely on any preselected parameters and works for an arbitrary number of images. In particular this means that a solution is given to the aperture problem of finding point correspondences between curves.     

Adaptive Enumeration of Implicit Surfaces with Affine Arithmetic

We discuss adaptive enumeration and rendering methods for implicit surfaces, using octrees computed with affine arithmetic, a new tool for range analysis. Affine arithmetic is similar to standard interval arithmetic, but takes into account correlations between operands and sub-formulas, generally providing much tighter bounds for the computed quantities. The resulting octrees are accordingly much smaller, and the rendering faster.     

Global Practical Stabilization of Discrete-Time Switched Affine Systems via a General Quadratic Lyapunov Function and a Decentralized Ellipsoid

This paper addresses the problem of global practical stabilization of discrete-time switched affine systems via state-dependent switching rules. Several attempts have been made to solve this problem via different types of a common quadratic Lyapunov function and an ellipsoid. These classical results require either the quadratic Lyapunov function or the employed ellipsoid to be of the centralized type. In some cases, the ellipsoids are defined dependently as the level sets of a decentralized Lyapunov function. In this paper, we extend the existing results by the simultaneous use of a general decentralized Lyapunov function and a decentralized ellipsoid parameterized independently. The proposed conditions provide less conservative results than existing works in the sense of the ultimate invariant set of attraction size. Two different approaches are proposed to extract the ultimate invariant set of attraction with a minimum size, i.e., a purely numerical method and a numerical-analytical one. In the former, both invariant and attractiveness conditions are imposed to extract the final set of matrix inequalities. The latter is established on a principle that the attractiveness of a set implies its invariance. Thus, the stability conditions are derived based on only the attractiveness property as a set of matrix inequalities with a smaller dimension. Illustrative examples are presented to prove the satisfactory operation of the proposed stabilization methods.      

非法计算检测的通用模型

非法计算是导致系统崩溃的一个常见故障.文中总结了Java语言中可能产生非法计算的运算符和数学库函数;建立了一个通用模型,用以检测一般函数(包括系统函数和自定义函数)在使用时是否合法;基于该通用模型提出了非法计算检测算法,并在此算法中引入区间运算.实验结果表明,文中模型及算法可以在检测出更多的非法计算故障的同时降低误报率.     

Mamdani模糊推理算法的直觉化扩展

对Mamdani模糊推理算法进行了直觉化扩展。首先将Mamdani定义的模糊关系R_c进行直觉化扩展;然后推出了其对应的直觉模糊取式推理算法和直觉模糊拒式推理算法;最后以具体算例叙述了推理计算过程中的细节,验证了该方法的正确性和有效性依据直觉准则对其性能进行了评价。     

一种采用二次式作为阻尼项的点匹配算法

为了对基于确定性退火技术的点匹配算法进行改进，提出了一种采用二次式作为阻尼项的算法。现有的此类算法为了控制匹配矩阵P的熵，通常都在目标函数中加入∑Pi,jlogpi,j形式的阻尼项，其缺点是需要用迭代逼近的方法使P满足双向的行列约束，由于这会因引起误差的积累而降低算法的整体匹配精度，为此，提出采用∑Pi,j(Pi,j-1)形式的阻尼项，这样目标函数就成为P的正定二次式，因而就可以在退火的每一步求解出使目标函数最小的Po仿真结果表明，该新算法在精确性和稳定性方面都有显著的改善。     

A New Form of the Quadratic Assignment Problem and Approximate Solutions

A new formulation of the quadratic assignment problem is given. Based on the properties of this formulation, new bounds of an objective function are obtained.     

Fast Ray Tracing of Arbitrary Implicit Surfaces with Interval and Affine Arithmetic

Existing techniques for rendering arbitrary-form implicit surfaces are limited, either in performance, correctness or flexibility. Ray tracing algorithms employing interval arithmetic (IA) or affine arithmetic (AA) for root-funding are robust and general in the class of surfaces they support, but traditionally slow. Nonetheless, implemented efficiently using a stack-driven iterative algorithm and SIMD vector instructions, these methods can achieve interactive performance for common algebraic surfaces on the CPU. A similar algorithm can also be implemented stacklessly, allowing for efficient ray tracing on the GPU. This paper presents these algorithms, as well as an inclusion-preserving reduced affine arithmetic (RAA) for faster ray-surface intersection. Shader metaprogramming allows for immediate and automatic generation of symbolic expressions and their interval or affine extensions. Moreover, we are able to render even complex forms robustly, in real-time at high resolution .     

Semidefinite Relaxation and New Conditions for Sign-Definiteness of the Quadratic Form under Quadratic Constraints

Use of the semidefinite relaxation in the problem of sign-definiteness of the quadratic form under quadratic constraints enables one to establish from the duality conditions an S-procedure. However, the S-procedure giving the necessary and sufficient conditions for signdefiniteness of the relaxed problem provides only the sufficient conditions for sign-definiteness for the original problem for the case of two and more quadratic constraints. This property is called the deficiency of S-procedure. A method was proposed enabling one in some cases to establish the conditional sign-definiteness in the case where the S-procedure provides a negative result. This method give the necessary and sufficient conditions for sign-definiteness in the two-dimensional case. An example was given.     

用于参数曲线自由变形的一种新的缩放因子

提出一种用于参数曲线自由变形的新的缩放因子，用该因子此去作用（缩放）待变形曲线，从而使曲线发生形变。通过交互改变控制参数，可达到预期的变形效果。实验表明，这种方法数学背景简单，易于控制，重复使用可获得丰富的变形效果，适用于几何造型、计算机动画等领域。     

具有块三角结构非线性切换系统的二次稳定性

The problem of globally quadratic stability of switched nonlinear systems in block-triangular form under arbitrary switching is addressed. Under the assumption that all block-subsystems are zero input-to-state stable, a sufficient condition for the problem to be solvable is presented. A common Lyapunov function is constructed iteratively by using the Lyapunov functions of block-subsystems.     

参数域上的任意次B-样条有限元法

该文给出了在参数域上应用任意次B－样条有限元法的方法，文中首先介绍了任意次B－样条基的建立方法，并给出了一般的实施步骤；然后又以三次B－样条有限元法为例，求解了2臂圆锥对数螺旋天线的电流分布，其结果说明了该方法的有效性，此外，该文还在更一般的意义上提出了在参数域及交换域上进行剖分的思想。     

通用快递单打印程序编程方法

介绍了开发通用快递单打印程序的编程构架,实现了自由存取收件人名址、自由设置表单格式、部分或全部选取收件人成批打印的功能。文中的代码具有通用性,可以方便地应用于类似的软件编程实践中。     

招贴设计形态的空间延伸性探析

本文以招贴设计的空间形态作为突破点进行理论与实践探讨,分析如何从平面空间向立体空间、静止空间向运动空间的延伸来完成招贴设计形态的多维性创新,并提出了具体可行的创作方法,通过创意与表现形式的结合来完成招贴设计形态在空间上的延伸设计。     

TPython：一种扩充的Python语言

Python是一种流行的动态语言,但是由于完全的动态性影响了其执行效率和使用。因此,在Python基础上进行了静态化扩充,研制了TPython语言。该语言在注释中引入了可选的类型声明,并提供了包括类型检查在内的静态检查。相对于动态语言而言,TPython能够提高程序的可读性和可靠性,降低调试成本,相对于静态语言而言,TPython又具有语法简单,易于开发的优势。     

支持防火墙规则扩展的匹配算法HERAM

防火墙是一种重要的网络安全技术,但随着网络规模的发展,遇到了许多急需解决的问题,其中就有防火墙网络瓶颈的问题。提出一种新的规则匹配算法来解决这个问题,把多维的问题进行降维处理,根据规则之间有无关联性把规则进行分类处理,另外把新添加的规则运用散列表进行组织,从而做到在增加扩展性的同时,使时间效率不受大的影响。     

关于色彩量化的一种算法

描述了一种色彩量化算法。作为对Herkbert的中点切割法的一种改进，本算法考虑到图像色彩的出现频率，以及图象色彩分量在颜色空间的分布情况。