Interactive four-dimensional space exploration using viewing direction control based on principal vanishing points operation

This chapter presents an interactive 4-D visualization technique that controls a 4-D viewing direction via handling of principal vanishing points. Principal vanishing points are represented by projecting points at infinity of 4-D principal coordinate axes onto 3-D space. Our previous studies have confirmed that, because the principal vanishing points relate to a 4-D eye-point and the 4-D viewing direction, they can be landmarks to intuitively move in 4-D space. In this chapter, we propose an algorithm that utilizes principal vanishing points as an interface for the intuitive 4-D viewing direction control, and apply an algorithm to a framework of a system which enables one to fly through 4-D space. The developed system can achieve to visualize and explore an intricate 4-D scene such as a maze in 4-D space. We evaluate effectiveness of the proposed 4-D interaction technique by user experiments.