Interactive four-dimensional space visualization using five-dimensional homogeneous processing for intuitive understanding

We have developed an interactive visualization system that enables people to both experience and intuitively understand 4-D space. We proposed a framework in which people can visualize 4-D space using 5-D homogeneous processing. This way of processing uses 5 × 5 matrices to express various types of transformations and simplifies geometric operations without using any division operations. Therefore, the proposed method improved the system's reliability. We also constructed an interactive environment that associates the user's 3-D position with a 4-D eye point that lies on a 4-D spherical surface surrounding a 4-D solid. The system is composed of a glasses-free 3-D display, a controller pad, and a personal computer. In this environment, we were able to smoothly observe a 4-D solid from an arbitrary 4-D eye point and direction.