Four-dimensional viewing direction control by principal vanishing points operation and its application to four-dimensional fly-through experience

This paper presents a novel interactive method that handles the 4-D viewing direction via the pick and move operation of principal vanishing points displayed in 3-D space. The principal vanishing points are represented by projecting the points at infinity in the directions of the 4-D principal coordinate axes onto 3-D space. Since the principal vanishing points are associated with the 4- D visual axis, they act as a landmark when users move in 4-D space. We utilize them as an interface of the 4-D viewing direction control to achieve intuitive 4-D interaction. Using the proposed method, we construct an interactive system that enables users to observe 3-D perspective drawings of 4-D data from an arbitrary 4-D viewing direction at an arbitrary 4-D position. Moreover, translating the 4-D eye-point along the 4-D viewing direction, the proposed system provides the 4-D firstperson fly-through. The results of the user experiments show that the proposed system has a sufficient usability and an efficiency for 4-D interaction.