SHALAB 2014

Four-dimensional Space Interaction Using Principal Vanishing Points Operation

Takanobu MIWA†, Yukihito SAKAI‡, Shuji HASHIMOTO†

†Waseda University, ‡Fukuoka Universitytakmiwa@shalab.phys.waseda.ac.jp

A concept of “dimension” forms a basis for human knowledge, science and culture. Although humans physically live in 3-D space, there is no obstacle to imaginarily define 4-D space where four axes are orthogonal to each other. However, to understand 4-D space and objects is more difficult than perception of 3-D space and objects, because most people have only a spatial experience in 3-D space. In order to eliminate this difficulty and acquire 4-D spatial perception, it is necessary to provide an interactive environment where humans can get hands-on experiences of 4-D space and objects.

In this poster, we present a novel interactive 4-D visualization technique which utilizes principal vanishing points as an interface to freely look around and move in 4-D space, and show recent findings from user experiments which assess whether humans can obtain 4-D spatial understandings using the interactive system.

Introduction

Principal Vanishing Points

Figure 1 shows a 4-D visualization model to observe the 4-D object from an arbitrary eye-point, viewing direction and distance in 4-D space. We obtain a 3-D perspective drawing of the 4-D object by converting data defined in the 4-D world-coordinate system xwywzwww to those of the 3-D screen-coordinate system xsyszsws. The visualization algorithm is composed of a view field transformation, a perspective transformation and a clipping transformation using 5-D homogeneous processing.

The principal vanishing points are represented by projecting points at infinity in the xw-, yw-, zw- and ww-directions onto 3-D space. Pictures of Figure 2 show examples of the principal vanishing points and the 3-D perspective drawing of one hypercube obtained from different eye-points. The number of the displayed principal vanishing points and their 3-D positions are determined by a spatial relationship between the 4-D world-coordinate system and the 4-D viewing direction which is defined as the direction from the 4-D eye-point pf to the 4-D observed point pa.

References

Application for Robot Co-workerFor development of robot co-worker, it is necessary to analyze time-series data of 3-D positions and distances between humans and robots. Our interactive system can visualize such data at one time by assuming it as 4-D space-time data. We expect that the proposed system and the findings from our research will improve the outlook of action sequence in designing the robot behavior.

1. Miwa, T., Sakai, Y., Hashimoto, S.: Four-dimensional eye-point control by principal vanishing points operation and its evaluations. The Journal of the Society for Art and Science 12(4), 162-174 (2013). (in Japanese)

2. Miwa, T., Sakai, Y., Hashimoto, S.: Interactive four-dimensional space exploration using viewing direction control based on principal vanishing points operation. In: The cognitive effects of spatial interaction, learning and ability. LNCS. Springer, Heidelberg. (in press)

Construction of 4-D Interactive System

Findings from User Experiments

Through our previous studies, we found that the principal vanishing points are utilized as a landmark to understand a viewing position in 4-D space. Therefore, it is assumed that the principal vanishing points can be used for the interface to control movement of the 4-D eye-point and a change of the 4-D viewing direction. We develop the interactive system for humans to look around and move in 4-D space via operation of the principal vanishing points in 3-D space.

Our Approach

Based on a spatial position relationship of the principal vanishing points in 3-D space, we have constructed algorithm to determine the 4-D eye-point and the 4-D viewing direction, and developed the interactive system whichmakes handling of the principal vanishing points correspond to the movement of the 4-D eye-point (see Figure 3(a)) and the change of the 4-D viewing direction (the observed point) (see Figure 3(b)) [1, 2].

As shown in Figure 4, the system consists of a personal computer, a head-mounted display with a built in a 6-DoF sensor, a motion sensor and a five-button wireless mouse. The 3-D perspective drawing of the 4-D object and the principal vanishing points are displayed in the 3-D virtual space through the head mounted display. As shown in Figure 5, for example, when picking and moving the principal vanishing points using a 3-D cursor associated with the user’s hand motion, the user can observe the hypercube from various 4-D eye-points and viewing directions.

We have conducted the user experiments to evaluate usability of the proposed system and examine whether humans can obtain the 4-D spatial perception through the interaction. From the results, we found that:» The principal vanishing points operation is more suitable to understand

4-D space and objects than conventional interaction techniques.» The principal vanishing points are especially useful to understand

orthogonality and parallelism of the 4-D object.» The users can understand structure of the 4-D object such as a 4-D maze

by moving through its inside.» The users can understand the spatial position relationship of the multiple

4-D objects by looking around 4-D space.

Before

After

3-D cursor

Fig. 1. Visualization model of 4-D space.

Fig. 2. Principal vanishing points and the 3-D perspective drawing of one hypercube.

Fig. 3. Movement of the 4-D eye-point and the change of the 4-D viewing direction.

Fig. 4. Configuration of the system. Fig. 5. Example of the system use.