Ten commandments for good default expression simplification

This article provides goals for the design and improvement of default computer algebra expression simplification. These goals can also help users recognize and partially circumvent some limitations of their current computer algebra systems. Although motivated by computer algebra, many of the goals are also applicable to manual simplification, indicating what transformations are necessary and sufficient for good simplification when no particular canonical result form is required.After motivating the ten goals, the article then explains how the Altran partially factored form for rational expressions was extended for Derive and for the computer algebra in Texas Instruments products to help fulfill these goals. In contrast to the distributed Altran representation, this recursive partially factored semi-fraction form:

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does not unnecessarily force common denominators,

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discovers and preserves significantly more factors,

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can represent general expressions, and

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can produce an entire spectrum from fully factored over a common denominator through complete multivariate partial fractions, including a dense subset of all intermediate forms.

     

一种视相关的网格简化方法*

针对网格模型的实时显示问题提出了一种视相关的网格简化方法。在网格简化中,将影响图形对象重要性的视觉敏感度与图形对象在屏幕上投影面积两者有效结合,实现网格模型的实时大幅度简化, 实验结果表明,简化速度快,但显示并无明显失真。     

逻辑函数的计算机化简

本文针对中型逻辑函数，提出了易于计算机实现的化简方法，即在化简过程中引入代数拓扑运算，在用星积运算求素项的基础上，用选择极值法求最小覆盖，大量的实验证明了该算法的正确性和易于计算机实现的有效性。     

图的布尔矩阵化简

复杂图常常包含有成百个顶点、上千条边，结构庞杂，在分析处理中需进行简化。通常的作法是按顶点的空间分布对原始图进行分块，但分块的准则并非单一。这一特性虽然有助于化简时增加系统的先验条件，但却不利于编制规范的计算机软件来进行复杂图组合结构的变换。该文讨论复杂图组合结构的化简问题，提出通过布尔矩阵把复杂图变换为能够用维数较低的邻接矩阵进行分析与描述的化简算法，这种变换可大大减少图中顶点和边的数量。     

下推自动机的状态转换图与下推自动机的化简

参照有限状态自动机图形表示方式的思想方法,研究了标准下推自动机的图形表示——PAD 状态转换图,证明了下推自动机与标准下推自动机的等价性。给出了对标准下推自动机进行化简的原则,并给出了化简算法,实现了下推自动机的化简。     

Enhancing the experience of 3D virtual worlds with a cartographic generalization approach

In this work we propose a new approach for fast visualization and exploration of virtual worlds based on the use of cartographic concepts and techniques. Versions of cartographic maps with different levels of details can be created by using a set of operations named cartographic generalization. Cartographic generalization employs twelve operators and domain-specific knowledge, being the contribution of this work their transposition to 3D virtual worlds. The architecture of a system for 3D generalization is proposed and the system is implemented. Differently from traditional cartographic processes, we use artificial intelligence for both selecting the key objects and applying the operators. As a case study, we present the simplification of the historical quarter of Recife (Brazil).     

Viewpoint-based simplification using f-divergences

We propose a new viewpoint-based simplification method for polygonal meshes, driven by several f-divergences such as Kullback-Leibler, Hellinger and Chi-Square. These distances are a measure of discrimination between probability distributions. The Kullback-Leibler distance between the projected and the actual area distributions of the polygons in the scene already has been used as a measure of viewpoint quality. In this paper, we use the variation in those viewpoint distances to determine the error introduced by an edge collapse. We apply the best half-edge collapse as a decimation criterion. The approximations produced by our method are close to the original model in terms of both visual and geometric criteria. Unlike many pure visibility-driven methods, our new approach does not completely remove hidden interiors in order to increase the visual quality of the simplified models. This makes our approach more suitable for applications which require exact geometry tolerance but also require high visual quality.     

大型复杂起重机械结构三维有限元子结构模型分析

针对大型复杂的起重机械整体结构力学分析的难题,在子结构技术的基础上,建立了大型起重机械整体结构的有限元模型技术,以大型冶金铸造起重机为例详细阐述了大型复杂结构有限元模型简化原则和子结构划分方法,确保了整机的传力路线完整性,将大型冶金铸造起重机划分为三级子结构,重点突出了六大结构件,即主小车、副小车、主梁、副梁、端梁、行走结构,实现了整机三维有限元模型完整性和准确性。分析结果通过和试验、规范计算对比,应力和位移最大的误差分别为4.2%和4.9%,具有和试验一致性的结果,因此对于子结构的三维有限元模型技术方法在大型起重机械整体结构是可行的。     

TRIZ工具的简化研究及应用

介绍了TRIZ理论的发展及其基本概念,分析了其各个工具在实际使用过程中的难易程度,提出了一条便于企业技术人员及初学者简便应用TRIZ的途径,并将此途径应用于解决某汽车副仪表盘表面缩痕的问题。     

利用运行点和边界值条件简化模型的方法

一个高阶模型G(S)=K_0/(TS 1)~n可以在运行状态及边界条件下通过拟合,简化成确定性模型C_τ(S)=(?)或不确定性模型(?)文中研究这种模型简化原理和方法.仿真试 验表明:这种方法可以广泛应用于仪表及其系统分析与设计.