Yukihito Sakai

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 first-person fly-through. The results of the user experiments show that the proposed system has a sufficient usability and an efficiency for 4-D interaction.

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.

Learning Four-dimensional Spatial Representations through Perceptual Experience with Hypercubes

Imagine a day when humans can form mental representations of higher-dimensional space and objects. These higher-dimensional spatial representations may enable us to gain unique insights into scientific and cultural advancements. To augment human spatial cognition from three to four dimensions, we have developed an interactive 4-D visualization system for acquiring an understanding of 4-D space and objects. In this paper, we examine whether humans are capable of formulating 4-D spatial representations through perceptual experience in 4-D space with 4-D objects. Participants learn about 4-D space and hypercubes through an interactive system, and are then examined on a series of 4-D spatial ability tests. They demonstrate the ability to perform perspective taking, navigation, and mental spatial transformation tasks in 4-D space. The results provide empirical evidence that humans are capable of learning 4-D spatial representations. Moreover, the results support the interpretation that humans form a cognitive coordinate system, consisting of an origin and four directional axes, to understand 4-D space and objects.

4-D spatial perception established through hypercube recognition tasks using interactive visualization system with 3-D screen

We have developed an interactive 4-D visualization system that employed the principal vanishing points operation as a method to control the movement of the eye-point and the change in the viewing direction in 4-D space. Different from conventional 4-D visualization and interaction techniques, the system can provide intuitive observation of 4-D space and objects by projecting them onto 3D space in real time from various positions and directions in 4-D space. Our next challenge is to examine whether humans are able to develop a spatial perception of 4-D space and objects through 4-D experiences provided by the system. In this paper, as the first step toward our aim, we assessed whether participants were able to get intuitive spatial understanding of 4-D objects. In the evaluation experiment, firstly, the participants learned a structure of a hypercube. Then, we evaluated their spatial perception developed in the learning period by tasks of controlling the 4-D eye-point and reconstructing the hypercube from a set of its 3-D projection drawings. The results indicated evidence for that humans were able to get 4-D spatial perception by operating the system.