CG Image Generation of Four-Dimensional Origami
Akira Inoue, Ryouko Itohara, Kuniaki Yajima, Keimei Kaino · The Journal of the Society for Art and Science · 2005
To produce four-dimensional (4-D) origami, we fold a solid material along flat planes in a 4-D space. A 4-D space has a fourth axis that is perpendicular to a three-dimensional space. Because a computer graphics (CG) image of a 4-D origami must be drawn on a three-dimensional screen to visualize it, we will produce its CG image using a 4-D painter′s algorithm with a stereogram. First, we will show how to fold a solid material in a 4-D space. After defining front and a back sides of this solid in a 4-D space, we will make mountain and valley folds and thereby produce a "4-D Noshi" CG image. Secondly, we will show how to fold a regular tetrahedron flat by bisectors of its dihedral angles and make a 4-D bird base from a double tetrahedron. Finally, we will produce CG images of this 4-D bird with opened wings using a stereogram.