向量图形

We propose a unified method to approximate important geometric attributes, including normal vector, gauss curvature, mean curvature, principal curvatures and principal directions on point sampled surface. Based on MLS projection our method is robust to noise and stable to the sampling density.

曲面的微分性质包括法向量和切平面、高斯曲率、平均曲率、主曲率和主方向，在计算机图形学、机器视觉和计算机辅助设计等领域发挥了重要的作用，比如曲面绘制、内外测试、曲面重建、曲面简化、去除曲面噪声和模型分割等。

The surface representation in discrete form and its differential computation are important issues in computer graphics and geometric design.

0引言一般来说，曲面的一阶微分量是指曲面的切平面方向和法向量，二阶微分量是指曲面的曲率等有关量·它们作为重要的曲面信息度量指标，在计算机图形学，机器人视觉和计算机辅助设计等领域发挥了重要的作用·传统的曲面是连续形式的参数曲面和隐式曲面，其微分量的计算已经有了较完备的方法·随着激光测距扫描等三维数据采样技术和硬件设备的长足进步，以及图形工业对任意拓扑结构光滑曲面造型的需求日益迫切，离散形式的曲面———细分曲面、网格曲面和点云曲面正在逐渐成为计算机图形学和几何设计领域的新宠·于是，对这种离散形式的曲面如何估

Also in the 3-D space, we assign the 20 amino acids to 20 vertices of the dodecahedron. By the symmetry of the dodecahedron we obtain 3-D representation of 20 amino acids, and 3-D graphical representation and the corresponding numerical sequence of protein sequences. And similarity and dissimilarity analysis based on the invariants of graphs and characteristics of numerical sequences are given for nine RNA secondary structures of RNA-3 of virus. We construct sequence phylogenetic tree of a group of cytochromes C protein.

在DNA三联体密码子表示的基础上，在半复平面上给出了蛋白质序列的非退化的2-D图形表示，同时利用复向量的主要特征—模和相位，给出了蛋白质序列的一种数值刻划，进一步在3-D空间里，把20种氨基酸分别分配给正12面体的20个顶点，根据正12面体的对称性得到了20种氨基酸的3-D表示，进而得到了蛋白质序列的3-D图形表示和对应的数字序列，并利用图的不变量和数字序列的特征比较了9种动物的神经元

System is used VB6.0, MATLAB6.5 and MATLAB and Visual Basic OLE interface methods of production, use VB Visual Interface, the real object-oriented, event-driven approach using the structure of high-level programming language, the perfect tool Integrated production and friendly interface and features of MATLAB numerical terms, such as a strong graphic image processing function for the core to achieve the limit, derivative, differential, integral and indefinite integral, vector algebra and analytic geometry of space for the function will be Two aspects of the unique advantages of combining the strong points, to shorten the development cycle and reduce programming difficulty, the current rapidly changing information age is of high practical value.

在线等汉-英翻译，网上在线翻译的别回！！！！！系统是采用VB6.0、MATLAB6.5 和MATLAB与Visual Basic接口OLE方法制作的，利用VB界面的可视化、真正面向对象、采用事件驱动方式的结构化高级程序设计语言、工具的完美集成和友好性特点制作界面和MATLAB的数值计算、图形图像等强大的处理功能为内核来实现函数极限、导数、微分、定积分和不定积分、空间解析几何和向量代数的求解功能；将两方面具有的独特优势结合起来，取长补短，以缩短开发周期，降低编程难度，这对当前日新月异的信息时代是具有很高的实用价值。

Function graphing and analyzing: 2D, 2.5D functiongraphs and animations, extrema, root, tangent, limit,derivative, integral, inverse; sequence of number: arithmetic progression, geometric progression; analytic geometry: vector, line, circle, ellipse,hyperbola and parabola; solid geometry: spatial line, prism, pyramid, cylinder, cone, dado and sphere; Ability to save graph as data file or bmp file; Ability to save animation as AVI file; Ability to move, zoom in, zoom out and rotate the scene.

函数图表和分析：2D， 2.5D 函数图表和动画，极值，根，正切，极限，导数；序列号：等差数列，等比级数；解析几何：向量，矢量，直线，圆，椭圆，双曲线和抛物线；立体几何：空间线，棱柱，三角锥，圆柱，圆锥体，梯形台和球体；保存图形为数据文件或者图像文件的功能；保存动画为 AVI 文件的功能；移动，缩小，放大和旋转场景的功能。

The relational database is used to organize data. The pre-processing with graphical human-computer interaction and 3D visual output is applied as a dramatic analysis method for engineer including data form, sample contour, isobar graph, vector graph, histogram and so on.

该系统以关系型数据库组织各种数据，完全实现了人机图形交互式前处理及三维可视化输出，为工程人员提供了包括数据表格、取样曲线、等位线、等位面图、向量图及二元函数图等一系列生动形象的数据分析手段。

We compute the Wigner function using the Qotoolbox of Matlab computer language, which creates the orthogonal bases on the vector space.

计算Wigner函数时，我们利用了Matlab语言的Qotoolbox工具包在向量空间中绘出其图形，这比解析的方法更快捷、方便。

A positive and negative projection method of object to be tested based on universal pattern display card includes using 3D texture to present rebuilt body data of object to be tested, calculating out directional vector array of ray outgoing point to detectors, storing said vector array into pattern display card to form directional vector texture, rotating directional vector texture and directional vector around rotary shaft to realize once of positive projection course on any projective angle, using 3D texture index technique to let virtual slab set position be not limited any more in negative projection course.

本发明属于投影探测与成像技术领域，其特点在于该方法含有以下步骤：把被测物体的重建体数据用三维纹理存储表示；预先计算射线出射点至平面探测器上个探测器之间的方向向量数组，并存储到通用图形显示卡中形成方向向量纹理；利用方向向量纹理与方向向量绕旋转轴旋转来实现任一投影角度的正投影过程的一次完成，无中间结果转存；在反投影过程中，利用三维纹理索引技术使虚拟切片组的放置位置不再受到限制。

The book review first vector and matrix algebra, the basic concepts and then described in detail geometry involved in a variety of two-dimensional graphics and three-dimensional geometric measurement of the object, the intersection of various algorithms and other issues, and provides information on the theme of a large number of computational geometry materials in order to facilitate quick reference.

全书先复习了向量和矩阵代数的基本概念，而后详细地描述了图形几何学涉及的各种二维和三维对象的几何测量、相交等问题的各种算法，并提供了关于计算几何学主题的大量材料以便于快速参考。

Existing processors used for media processing and scientific computation, such as general purpose processor, DSP, vector microprocessor, special graphics processor and multiprocessor in chip etc, have their own limitations in applications.

现有的用于媒体处理和流式科学计算的处理器，如通用处理器、DSP、向量微处理器、专用图形处理器和片内多处理机等，都存在各自的局限性。

We have no common name for a mime of Sophron or Xenarchus and a Socratic Conversation; and we should still be without one even if the imitation in the two instances were in trimeters or elegiacs or some other kind of verse--though it is the way with people to tack on 'poet' to the name of a metre, and talk of elegiac-poets and epic-poets, thinking that they call them poets not by reason of the imitative nature of their work, but indiscriminately by reason of the metre they write in.

索夫农 、森那库斯和苏格拉底式的对话采用的模仿没有一个公共的名称；三音步诗、挽歌体或其他类型的诗的模仿也没有——人们把&诗人&这一名词和格律名称结合到一起，称之为挽歌体诗人或者史诗诗人，他们被称为诗人，似乎只是因为遵守格律写作，而非他们作品的模仿本质。

The relationship between communicative competence and grammar teaching should be that of the ends and the means.

交际能力和语法的关系应该是目标与途径的关系。