Question

计算机论文翻译

抽象信息之间的关系最普遍的一种就是层次关系，如磁盘目录结构，文档管理，图书分类等。层次关系几乎无处不在，并且，在某些情况下，任意的图都可以转化为层次关系[6]。传统的描述层次信息的方法就是将其组织成一个类似于树的节点连线图，这也是层次信息可视化结构最直观的方式。许多层次结构往往非常庞大, 不能将它们整个显示在计算机屏幕上。常规的显示方式是将整个层次信息结构显示在一个比显示器更大的区域内, 利用滚动来调整可见区域。该方法的问题在于,用户无法看到可见部分与整个层次结构的关联。
人们对层次信息可视化深入研究，提出了一系列新的可视化技术方法，其中，典型的有普通目录树型；Robertson，Machkinlay和Card等提出的利用三维图形技术对层次结构进行可视化的方法三维圆锥树ConeTree[7]（如图1）；Shneiderman等提出的一种可以充分利用屏幕空间的层次信息表示模型树图Tree-map[8]（如图2）；Lamping和Rao等提出的一种基于双曲空间的可视化和操纵大型层次结构的Focus+Contxt技术，称为双曲树Hyperbolic-tree[9]（如图3）。三维圆锥树在表现组织结构图的时候表现出色，它能把大量的节点显示在单一的屏幕中。不足之处在于很难同时看到某个层次的所有内容，节点查询也比一般的层次信息可视化框架困难。Tree-map的优点在于它可以有效利用计算机屏幕空间，并且能够很容易实现。但是，它丧失了层次结构的直观性。并且对处于同一层次上的不同父亲的子节点的关系(准兄弟关系)也丧失了。而这种关系对于把握节点之间层次关系的结构特征是非常有用的。双曲树很好地解决了怎样在用户屏幕上显示庞大的层次信息结构的问题。双曲空间不同于一般的欧几里得空间，在欧几里得空间中，过直线外一点只有一条线与此直线相平行，而在双曲空间中过直线外一点有很多条直线与原直线平行。因此，欧几里得空间中圆形区域的面积随半径呈线性增长，而在双曲空间中呈指数增长。所以基于双曲空间的层次信息可视化技术可以在有限的空间中有效地显示结构庞大的层次信息。各种方法都有各自的优缺点，人们可以研究出更好的新方法，也可以根据它们的特点进行综合运用。靖培栋[10]在图书馆文献检索的可视化研究中，根据中图法的特点,集成普通树型及双曲树，取得较好的效果。
层次信息可视化的目标之一是根据用户的关注和信息间的关系，把层次结构自动清晰的排列在屏幕上。双曲树技术是将更多的可视化空间分配给当前层次结构中当前关注的部分，而同时又能够把整个层次结构显示出来。该技术通过一种规范的算法将层次关系显示在一个双曲平面上，然后将这个双曲平面映射到显示区域中。所以布局和图形映射是可视化的关键。
(1) 双曲空间布局模型
在双曲空间中节点的布局是通过Klein模型来实现的。图4是某个节点和其子节点的布局示意图。P1、P2、P3是P的三个子节点(如果不是叶节点, 这个子节点是子树的父节点)，QPR是扇形区域。过P1、P2、P3画PQ、PQ'、PQ"的平行线，这样可以保证子树不重叠。由于在双曲空间中过直线外一点有多条直线和已知直线平行, 所以总可以找到一条合适的平行线使所得扇形角度尽可能地和父节点一样大。d1、d2、d3就是子树所分配到的扇形区域，d1=∠QPQ',d2=∠Q'PQ",d3=∠Q"PR，即子节点得到的扇形区域和父节点一样大。以此类推，可得到所有子节点的布局，扇形区域的计算方法如下。
设节点P的扇形区域为(rp,dp) , 那么第k个子节点的扇形区域为：
而在普通的欧几里得空间中，过P1，P2，P3建立PQ，PQ'，PQ"建立的平行线得到的扇形角度比较小（见图5），几次递归后扇形角度就变得非常小，这正是普通排列算法不能显示大型数据结构的原因。
（如果用翻译机，请修改后再回答哦，谢谢！）

Answer 1

The relationship between the abstract information of a most general level is the relationship, such as the disk directory structure, document management, books classification 等. Hierarchy almost everywhere, and, in some cases, any map can be transformed into hierarchy [6]. The traditional way to describe the level of information to their organization into a similar tree node link diagram, which is the most hierarchical structure of information visualization, intuitive way. Many hierarchies are often very large, they can not be displayed on the computer screen throughout. Conventional display is the information structure of the entire hierarchy is displayed in a larger area than the display, scroll to adjust the visible area use. The problem is that this method, the user can not see the visible part of the hierarchy associated with the whole.
People on the hierarchical information visualization, in-depth study of a series of new methods of visualization technology, which, typical of ordinary directory tree; Robertson, Machkinlay Card and so on, and the use of 3D graphics technology to visualize the hierarchy The method of three-dimensional cone tree ConeTree [7] (Figure 1); Shneiderman and so on can take advantage of a level of screen space of information representation model tree Tree-map [8] (Figure 2); Lamping and Rao, etc. proposed based on hyperbolic space visualization and manipulation of large hierarchical Focus + Contxt technology, known as the hyperbolic tree Hyperbolic-tree [9] (Figure 3). Three-dimensional cone tree organization chart in the performance of outstanding performance when it can show a large number of nodes in a single screen. Shortcomings is that it is very difficult to see all the contents of a certain level, query nodes than the general level framework for information visualization problems. Tree-map is that it can effectively use the computer screen space, and can be easily achieved. But it lost the intuitive hierarchy. And in the same level of the father of the child nodes different relationship (quasi-fraternal relationship) is also lost. The master node for this relationship between the structural characteristics of the hierarchy is very useful. Hyperbolic Tree solves the user screen how large hierarchical information structure. Hyperbolic space is different from ordinary Euclidean space, in Euclidean space, the straight one except the one outside Xian in parallel with this linear phase, and in the hyperbolic space, the straight line outside the point that many of the original article parallel lines. Therefore, the Euclidean space in the area of a circular area with radius of linear growth in the hyperbolic space increases exponentially. Therefore, the level of hyperbolic space-based information visualization technology effectively in the limited space to display large hierarchical information structure. Various methods have their advantages and disadvantages, people can work out new and better ways are the characteristics according to their comprehensive use. Jing Pei Dong [10] in the library literature search visualization study, according to the characteristics in law, integration of ordinary hyperbolic tree and the tree, get better results.
Level One of the goals of information visualization is based on the user's attention and the relationship between information, to arrange the hierarchy automatically clear the screen. Hyperbolic tree technology is more visual space allocated to the current hierarchy part of the current concern, while allowing the entire hierarchy is displayed. The technical specification of the algorithm through a hierarchy displayed in a hyperbolic plane, then the hyperbolic plane mapped to the display area. The layout and graphics visualization mapping is the key.
(1) model of hyperbolic space layouts
In hyperbolic space the layout of the nodes is achieved through the Klein model. Figure 4 is a node, and the schematic layout of its child nodes. P1, P2, P3 is the P of the three sub-nodes (if not leaf node, this child is a child tree node parent node), QPR is a sector area. Through P1, P2, P3 art PQ, PQ ', PQ "of parallel lines, so you can ensure that sub-tree do not overlap. As the lines in hyperbolic space outside a little more than straight lines and parallel lines are known, it can always be found an appropriate point of parallel lines and makes the fan as much as possible and as large as the parent node. d1, d2, d3 is the sub-tree assigned to the fan-shaped area, d1 = ∠ QPQ ', d2 = ∠ Q'PQ ", d3 = ∠ Q "PR, the child nodes have fan-shaped area, and as large as the parent node. and so on, available to all child nodes of the layout, fan-shaped region is calculated as follows.
Fan-shaped area located node P is (rp, dp), then the first k nodes of fan-shaped sub-regions are:
In ordinary Euclidean space, over P1, P2, P3 establish PQ, PQ ', PQ "parallel lines created by the fan angle is small (see Figure 5), several times after the fan point of view becomes a recursive very small, this is the general arrangement of algorithm can not show the reasons for large data structures.