Abstract

Three-dimensional (3D) displays having regular-polyhedron structures are proposed and their imaging characteristics are analyzed. Four types of conceptual regular-polyhedron 3D displays, i.e., hexahedron, octahedron, dodecahedron, and icosahedrons, are considered. In principle, regular-polyhedron 3D display can present omnidirectional full parallax 3D images. Design conditions of structural factors such as viewing angle of facet panel and observation distance for 3D display with omnidirectional full parallax are studied. As a main issue, image volumes containing virtual 3D objects represented by the four types of regular-polyhedron displays are comparatively analyzed.

© 2009 Optical Society of America

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References

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2008 (4)

2007 (1)

2005 (2)

2004 (1)

2002 (1)

Baasantseren, G.

Choi, H.

Hahn, J.

Javidi, B.

Jeong, M.-O.

Jung, S.

Kim, E.-S.

Kim, H.

Kim, M.-S.

Kim, N.

Kim, Y.

Lee, B.

Lim, Y.

Martinez-Corral, M.

Martinez-Cuenca, R.

Min, S.-W.

Navarro, H.

Park, G.

Park, J.-H.

Saavedra, G.

Shin, D.-H.

Shin, S.-H.

Takaki, Y.

Y. Takaki, "Thin-type natural three-dimensional display with 72 directional images," Proc. SPIE 5664, 56-63 (2005).
[CrossRef]

Appl. Opt. (2)

J. Opt. Soc. Korea (2)

Opt. Express (4)

Proc. SPIE (1)

Y. Takaki, "Thin-type natural three-dimensional display with 72 directional images," Proc. SPIE 5664, 56-63 (2005).
[CrossRef]

Other (5)

R. Lopez-Gulliver, S. Yoshida, S. Yano, and N. Inoue, "gCubik: a cubic autostereoscopic display for multiuser interaction - grasp and group-share virtual images," ACM SIGGRAPH 2008, Poster Proceedings, 133, (2008).

B. Lee, J.-H. Park, and S.-W. Min, "Three-dimensional display and information processing based on integral imaging," in Digital Holography and Three-Dimensional Display, T.-C. Poon, ed., (Springer, 2006), pp. 333-378.

R. Lopez-Gulliver, S. Yoshida, S. Yano, and N. Inoue, "Toward an interactive box-shaped 3d display: study of the requirements for wide field of view," IEEE Symposium on 3D User Interfaces, 157-158 (2008).
[CrossRef]

I. Stavness, F. Vogt, and S Fels, "Cubee: A Cubic 3D display for physics-based interaction," ACM SIGGRAPH 2006, Sketches, 165 (2006).

A. Jones, I. McDowall, H. Yamada, M. Bolas, and P. Debevec, "An interactive 360° light field display," ACM SIGGRAPH 2007, Emerging Technologies 13, (2007).

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Figures (5)

Fig. 1.
Fig. 1.

Four regular-polyhedron displays: (a) hexahedron, (b) octahedron, (c) dodecahedron, and (d) icosahedron.

Fig. 2.
Fig. 2.

Observation windows of (a) hexahedron, (b) octahedron, (c) dodecahedron, and (d) icosahedron displays, and observable images through them. Facet viewing angles for (a), (b), (c) and (d) are set to 60(deg.), 60(deg.), 45(deg.), and 45(deg.), respectively.

Fig. 3.
Fig. 3.

(a) Observation geometry of spherical display, (b) R' v and (c) R v as a function of observation distance R and facet viewing angle θ.

Fig. 4.
Fig. 4.

Spherical image volume of regular-polyhedrons; (a) hexahedron, (b) octahedron, (c) dodecahedron, and (d) icosahedrons.

Fig. 5.
Fig. 5.

Radius of spherical image volume as a function of facet viewing angle and observation distance for (a) hexahedron (viewing angle cut-off θ = 56(deg.) at infinity R), (b) octahedron (viewing angle cut-off θ = 56(deg.) at infinity R), (c) dodecahedron (viewing angle cut-off θ = 40(deg.) at infinity R), and (d) icosahedron (viewing angle cut-off θ = 43(deg.) at infinity R).

Equations (5)

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R v ' ( θ , R ) = min R i ( θ , R , d ) for d .
cos ψ = sin 2 θ + cos θ R 2 sin 2 θ R .
R v ' = R tan ( θ ψ ) ,
R v = sin θ .
R v / R ' v = sin θ / [ R tan ( θ ψ ) ] .

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