Visualizing 2-dimensional Manifolds with Curve Handles in 4D
Visualizing 2-dimensional Manifolds with Curve Handles in 4D
复制标题
使用 4D 曲线手柄可视化 2 维流形
DOI：
10.1109/tvcg.2014.2346425
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发表时间：
2014
影响因子：
5.2
通讯作者：
Guangchen Ruan
中科院分区：
文献类型：
--
作者：
Hui Zhang;Jianguang Weng;Guangchen Ruan
在本文中，我们提出了一种数学可视化范式，用于探索嵌入在3D中的曲线和4D数学世界中的曲面。基本的问题是，4D数学实体的3D图形通常会扭曲、翻转和折叠回来，在表面片后面留下重要的属性。我们提出了一个交互式系统，通过将原始4D曲面的三维图形切片成一系列特征图来可视化原始4D曲面的拓扑特征。设计了一种新颖的4D可视化界面，允许用户使用所建立的曲线操纵机制通过图句柄集合来控制4D拓扑形状。我们的系统可以支持4D数学对象的丰富的数学交互，这在任何现有的方法中都是非常困难的。我们通过各种实验结果和案例研究进一步证明了所提出的可视化工具的有效性。
In this paper, we present a mathematical visualization paradigm for exploring curves embedded in 3D and surfaces in 4D mathematical world. The basic problem is that, 3D figures of 4D mathematical entities often twist, turn, and fold back on themselves, leaving important properties behind the surface sheets. We propose an interactive system to visualize the topological features of the original 4D surface by slicing its 3D figure into a series of feature diagram. A novel 4D visualization interface is designed to allow users to control 4D topological shapes via the collection of diagram handles using the established curve manipulation mechanism. Our system can support rich mathematical interaction of 4D mathematical objects which is very difficult with any existing approach. We further demonstrate the effectiveness of the proposed visualization tool using various experimental results and cases studies.