Drawing Graphs on the Sphere

Scott Perry, Mason Sun Yin, Kathryn Gray, S. Kobourov
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引用次数: 5

Abstract

Graphs are most often visualized in the two dimensional Euclidean plane, but spherical space offers several advantages when visualizing graphs. First, some graphs such as skeletons of three dimensional polytopes (tetrahedron, cube, icosahedron) have spherical realizations that capture their 3D structure, which cannot be visualized as well in the Euclidean plane. Second, the sphere makes possible a natural "focus + context visualization with more detail in the center of the view and less details away from the center. Finally, whereas layouts in the Euclidean plane implicitly define notions of "central and "peripheral nodes, this issue is reduced on the sphere, where the layout can be centered at any node of interest. We first consider a projection-reprojection method that relies on transformations often seen in cartography and describe the implementation of this method in the GMap visualization system. This approach allows many different types of 2D graph visualizations, such as node-link diagrams, LineSets, BubbleSets and MapSets, to be converted into spherical web browser visualizations. Next we consider an approach based on spherical multidimensional scaling, which performs graph layout directly on the sphere. This approach supports node-link diagrams and GMap-style visualizations, rendered in the web browser using WebGL.
在球体上绘制图形
图形通常在二维欧几里得平面上可视化,但球面空间在可视化图形时提供了几个优势。首先,一些图形,如三维多面体(四面体、立方体、二十面体)的骨架,具有球形实现,可以捕获它们的三维结构,这在欧几里得平面上也无法可视化。其次,球体使自然的“焦点+上下文可视化”成为可能,在视图的中心有更多的细节,远离中心的细节更少。最后,尽管欧几里得平面上的布局隐式地定义了“中心”和“外围”节点的概念,但这个问题在球面上得到了简化,在球面上,布局可以以任何感兴趣的节点为中心。我们首先考虑了一种投影-重投影方法,这种方法依赖于制图中经常看到的转换,并描述了该方法在GMap可视化系统中的实现。这种方法允许许多不同类型的2D图形可视化,如节点链接图、LineSets、BubbleSets和mapset,转换成球形的web浏览器可视化。接下来,我们考虑了一种基于球面多维缩放的方法,该方法直接在球体上执行图形布局。这种方法支持节点链接图和gmap风格的可视化,使用WebGL在web浏览器中呈现。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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