参数Bezier三角曲面的GC^1设计

本文从三次Ｂｅｚｉｅｒ三角曲面片边界曲线构造入手，综合分析了计算几何中有关Ｂｅｚｉｅｒ三角曲面ＧＣ＾１拼接设计的理论和方法。针对３Ｄ离散数据曲面插值问题，全面讨论了Ｂｅｚｉｅｒ三角曲面片内部Ｂｅｚｉｅｒ顶点计算。提出了一种基于三次Ｂｅｚｉｅｒ三角曲面片内部Ｂｅｚｉｅｒ顶点ｄ１１１选取优化的整体ＧＣ＾１Ｂｅｚｉｅｒ三角曲面设计方法。     

边界面法数值结果的云图表征

边界面法继承了传统边界元法的优点,并将几何实体的边界曲面离散为参数空间里的曲面单元,在处理一些特殊问题如移动边界、高梯度、大变形等方面显示出特殊的优越性。但是也使得计算结果的后处理遇到困难。提出了一种基于黎曼度量推进波前法生成三角背景网格的实用边界面法计算结果后处理方法。该法对求解域剖分成三角背景网格然后将计算结果映射到网格节点上,通过区域填充获得计算结果的云图。温度场的数值算例表明该方法可靠实用。     

定义在三维曲面域上的四维曲面插值

本文对定义在三维曲面域上的四维曲面的构造进行了系统的分析。提出了对三维曲面域上的离散点集进行三角剖分的算法,基于Shepard思想构造了定义在三维曲面域上的四维曲面的插值方案,对四维曲面的图形表示进行了分析,建立了曲面上等值线三角形追踪算法,并进行了填充处理。最后,列举了一些实例,展示了该成果的应用前景。文中所有算法均在IBM PC机上实现,算法简单,而且具有通用性,易于在工程中得到应用。     

裁剪曲面的三角化及图形显示

结合自主版权的超人ＣＡＤ／ＣＡＭ系统的开发，本文提出了一种适合于裁剪曲面图形显示的曲面三角化算法，该算法将曲面的三角化转化为曲面参数域的三角化，并将二维图形的集合运算与Ｄｅｌａｕｎａｙ三角剖分应有和于曲面参数域边界的处理，从而使裁剪曲面在边界上的三角形分布均匀。     

一种任意拓扑网上曲面构造方法及应用研究

本文提出了一种任意拓扑网上构造离散曲面的双二次(Bi-quadratic)方法,缩写为BQ.理论分析表明。该方法包括了二次B样条曲面在内的一类广泛的曲面,曲面至少达到一阶几何连续。在引入了内边界及边界控制的新方法之后,实现了在任意拓扑网上构造多连通城的曲面的设想。实际应用表明,读方法具有简单、实用、构造曲面灵活,计算效率高等优点。     

基于遥感图像散乱数据点的三角曲面片插值构造

基于散乱数据点集构造三角插值曲面的方法，在CAD／CAM、科学计算可视化、图像处理等领域有着广泛的应用。本文介绍一种基于遥感图像散乱数据点的三角曲面片插值构造方法。该方法通过在遥感图像上选取局部极值点来构成平面散乱数据点集，并在此基础上进行三角剖分、优化和三角插值曲面构造。此方法在海洋遥感图像多尺度分解处理应用中取得了较为理想的结果。     

复合三角Bezier曲面/平面的过渡和裁剪

由初始交点出发,利用拓扑关系跟踪计算复合三角Bezier曲面与平面的交线,对一系列交点进行点对应修正,曲面片间边界点计算、交线两端交点的跟踪、截面线构造、截面线离散,构造出与基曲面达到G′连续、结构相似的过渡曲面,交点作为型值点值入复合曲面的型值点集中、对三角网格局域三角化,以交线为界分离,重新构造拓扑关系生成两张新的曲面,实现裁剪的目的,测试显示,上述方法简单可靠。     

C1连续曲面重构与光顺的有限元算法

提出了一种基于离散的测量数据重建光顺自由曲面的有限元新方法。根据最佳逼近与能量光顺原理，建立正定的目标泛函，采用18自由度三角形板单元对泛函离散，进行极小化，求得最优解。根据有限元插值计算，重新构造出全场C^1连续的自由曲面。这种方法结合了能量光顺技术，有效地抑制了输入数据上误差噪声的影响，曲面重建的精度高、光顺性好，而且能给出合理的一阶导数。该方法计算简单、便于应用，所需的输入数据点少，并可用于处理曲线边界区域的问题。     

三角域上C~1连续的H-Coons曲面片

在三角形域上利用两类H-Hermite多项式构造C1连续的两种形式的H-Coons曲面片。构造的三角曲面片均含有形状参数α,调整α的值,可改变曲面的内部形状,而不影响曲面的边界形状。当α→0时,可退化为通常的边-边与边-点方法插值的曲面片。最后,通过实例显示了该文方法的实际效果。     

多变量问题等值线形成的数学方法及物理意义

本文应用广义逆解法,将多变量散乱数据曲面(超曲面)拟合,把拟合后的曲面(超曲面)作为多变量问题等值线形成的数学模型,从而把超曲面、等值面、等值线这些几何概念,与等值线形成的物理意义结合起来,使人们能够从离散数据中揭示出所蕴含的物理规律。     

Computer plotting of stress contours in excavated slopes

The contouring of stresses in two-dimensional slopes is done quickly and efficiently by using the computer and an incremental plotter. The computer program developed here interpolates in two directions between centroids of finite elements at which the stresses are given, determines contour line co-ordinates, and plots the contours. This program can be easily modified to plot stresses produced by other two-dimensional finite element analysis programs as long as the arrangement of elements in the mesh is similar.     

Designing coupled free-form surfaces

The problem of designing optical systems that contain free-form surfaces is a challenging one, even in the case of designing a single surface. Here we present a method for the coupled design of two free-form reflective surfaces that will have a prescribed distortion. On one hand, the method can be described using traditional vectors and matrices, which we do, but it is motivated by viewing the problem in the language of distributions from differential geometry and makes use of the exterior differential systems, which we relegate to an appendix. Example applications are given to the design of a mirror pair that increases the field of view of an observer, a similar mirror pair that also rotates the observer's view, and a pair of mirrors that give the observer a traditional panoramic strip view of the scene.     

A new approach to free-form surface mesh control in a CAD environment

An adaptive process controlling the position of nodes on a surface mesh is presented. The control can depend on one (or more) criterion(ria) about element quality. The mesh is attached, through the concept of classification, to a geometric model issued by a computer aided design software. Thus, the surface domain is described by entities currently available in such systems, i.e. any free-form patches like Non-Uniform Rational B-Spline or Bézier patches can be used, even if they are restricted. Multi-connected surface domains can be treated using the same geometrical definition. The method described allows nodes to slide on a patch or jump from a patch onto another one. Such movements greatly improve the mesh quality with regard to a chosen criterion. Problems occurring with patch-by-patch meshing techniques when surfaces patches exhibit significant size differences are then overcome. The adaptation technique can be made independent of CAD data structures and meshing techniques, hence it constitutes the basis of a mesh management module.     

Optimization of a Reconstitutable Suspension of Rifampicin Using 24 Factorial Design

In this study 2⁴ factorial design associated with surface response methodology was used to develop and optimize a reconstitutable suspension of rifampicin. The study illustrated the effect of the percentage of each of sucrose, avicel RC-591, hydrophilic aerosil, and aerosol-OT on the flowability and the bulk density of the dry mixture as well as the viscosity, the sedimentation volume, and the redispersibility of the suspension. An empirical equation developed for each of the above responses was used with the aid of computer software to plot a contour map of the most significant effects and interactions. Five replicates at the center of the design were used to independently calculate the experimental error and to detect any curvature in the response surface. Three formulas which are not included in the design were prepared to check the validity of the model equation.     

Survey of methods to visualize alternatives in multiple criteria decision making problems

When solving decision problems where multiple conflicting criteria are to be considered simultaneously, decision makers must compare several different alternatives and select the most preferred one. The task of comparing multidimensional vectors is very demanding for the decision maker without any support. Different graphical visualization tools can be used to support and help the decision maker in understanding similarities and differences between the alternatives and graphical illustration is a very important part of decision support systems that are used in solving multiple criteria decision making problems. The visualization task is by no means trivial because, on the one hand, the graphics must be easy to comprehend and not too much information should be lost but, on the other hand, no extra unintentional information should be included. In this paper, we survey and analyze different ways of visualizing a small set of discrete alternatives graphically in the context of multiple criteria decision making. Some of the ways discussed are widely used and some others deserve to be brought into a wider awareness. This survey provides a starting point for all those who deal with multiple criteria decision making problems and need information of what kind of visualization techniques could be put to use in order to support the decision maker better.     

无网格方法数值结果的可视化方法与实现

科学计算可视化是科学计算中不可缺少的一个组成部分,其主要任务是将数值模拟产生的大量复杂的数据信息通过计算机技术转换成图形、图像信息。无网格方法是一种基于点的数值计算方法,各离散点之间没有联结信息,其数值结果的可视化后处理是一件很困难的事情,尤其当离散点随机分布时,更是如此。Delaunay 三角化是十分理想的散乱数据的可视化工具,它可以根据一组随机分布的离散点数据生成唯一的近似等边三角形。首先介绍了 Voronoi 图与 Delaunay 三角化的基本原理,然后介绍了实现 Delaunay 三角剖分的算法及无网格方法数值结果可视化的实现方法,最后给出了无网格方法可视化的若干应用实例。     

泵站流道出口断面轴向流速的可视化

泵站流道出口断面轴向流速可视化,可检测流道设计性能,是泵站流道流场可视化的组成部分。其主要内容为轴向等速线图的处理。本文在分析标量场中等值线几种抽取算法的基础上,根据等速线图的特点选择合适的算法,并在AucoCAD环境下用ARX编程加以实现。文中对网络序列法中的交点连线二义性判别方法加以深入探讨,提出解决这一问题的新方法。     

标准大数据实践（4）--可视化展现

大数据的分析过程离不开机器和人的相互协作与优势互补,一方面从机器角度出发,需要研究数据挖掘,一方面从人的分析出发,需要研究人的认知规律,其中大数据的可视化分析为重要的分析方法。本文首先探讨了大数据可视化的基本概念,在此基础上,结合标准文本分析的特点,选择了文本可视化、网络图可视化以及时空可视化作为标准大数据可视化分析的研究重点,并选择热词分析、起草人和起草单位网络关系以及起草单位分布图作为试点,实践了标准大数据的可视化。     

Burr Control for Removal of Metal Coating from Plastics Substrate by Micro-Milling

Manufacturing of miniaturized circuits on the surface of plastic substrate plays an important role for the industrial application. Many of these kinds of parts cannot be fabricated by conventional processing methods due to the manufacturing requirements are improved continuously and the plastic substrate presents 3D structure. Since the superior advantages of the micro-milling, graphically removal of metal coating from plastic substrate by micro-milling has led the way in manufacturing of high-accuracy circuits. In order to improve the edge quality of the circuits, the effect of processing parameters on burr sizes is quantitatively analyzed and a control model of burr formation is established based on the experiments. Furthermore, aiming at the problem that surface of the polyimide (PI) substrate often shows free-form state due to the machining error, the technology that removal of constant material from free-form substrate surface is proposed. With the optimized parameters and compensation technology of milling depth, a typical antenna circuit is machined via micro-milling at last. The experimental results indicate that the edge of the pattern is smooth, and there are almost no burrs. The achievements in this study could be applicable to industrial production.     

Surface waves and atomic force microscope probe-particle near-field coupling: discrete dipole approximation with surface interaction

Evanescent waves on a surface form due to the collective motion of charges within the medium. They do not carry any energy away from the surface and decay exponentially as a function of the distance. However, if there is any object within the evanescent field, electromagnetic energy within the medium is tunneled away and either absorbed or scattered. In this case, the absorption is localized, and potentially it can be used for selective diagnosis or nanopatterning applications. On the other hand, scattering of evanescent waves can be employed for characterization of nanoscale structures and particles on the surface. In this paper we present a numerical methodology to study the physics of such absorption and scattering mechanisms. We developed a MATLAB implementation of discrete dipole approximation with surface interaction (DDA-SI) in combination with evanescent wave illumination to investigate the near-field coupling between particles on the surface and a probe. This method can be used to explore the effects of a number of physical, geometrical, and material properties for problems involving nanostructures on or in the proximity of a substrate under arbitrary illumination.