The complexity and size of data is rapidly increasing in modern science, business and engineering. This has resulted in increasing demands for more sophisticated data analysis methods. Multidimensional scaling has been used to visualize large high-dimensional datasets in the form of a map. Such maps are very intuitive for us, as we are familiar with reading geographical maps. However, they typically result in a flat space (world), which presents undefined discontinuous edges at the end of the world.
rnIn order to provide a continuous space for visualizing high-dimensional data, a closed three-dimensional (3D) surface, such as surfaces of a sphere and a torus, has been used as a target mapping space for multi-dimensional scaling. This paper proposes an application of a portal-based rendering technique to visualize such closed 3D surfaces. This 3D rendering technique allows users to see and navigate through the surface in a natural manner. This eliminates any discontinuous boundaries usuallyintroduced by a process of projection from 3D to two-dimensional space. Furthermore, as our initial investigations show, it is a general technique that is applicable to any closed 3D surface.
在现代科学,商业和工程中,数据的复杂性和规模正在迅速增加。这导致对更复杂的数据分析方法的需求增加。多维比例缩放已用于以地图形式可视化大型高维数据集。这样的地图对我们来说非常直观,因为我们熟悉阅读地理地图。但是,它们通常会导致一个平坦的空间(世界),在世界末尾呈现出不确定的不连续边缘。 P> rn
为了提供一个连续的空间来可视化高维数据,封闭的三个三维(3D)曲面(例如球体和圆环的曲面)已用作多维缩放的目标映射空间。本文提出了一种基于门户的渲染技术来可视化此类封闭3D曲面的应用。这种3D渲染技术允许用户以自然的方式查看和浏览表面。这消除了通常从3D投影到二维空间的过程所引入的任何不连续边界。此外,正如我们的初步研究表明的那样,这是一种适用于任何封闭3D表面的通用技术。 P>
The University of Sydney;
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