Analysis of geometrical printing patterns formed by superposing the same two figures of dots arranged on intersections of triangle fretwork.
Sadao Hayashi, Masaru Kobayashi, Takashi Suzuki, Toshihiro Hirai, Morio Murayama · Sen i Gakkaishi · 1989
The geometrical moiré patterns which are formed by superposing two figures of dots arranged on intersections of triangle fretworks have been investigated by using a personal computer. When a moving angle between the two figures is small, the appearing patterns have a hexagonal form. In particular, when two figures of dots arranged on intersections of regular triangle fretwork are superposed at the moving angle (θ) chosen at m1=1, and n1=3, 9, 15, ...... (a multiple of three in an odd-number) according to the equation, tan (θ/2)=m1l2/n1l1, the hexagons in the moiré patterns at each n1 consist of all the same shape, where n1 and m1 are the abscissa and the ordinate of dot lines, l1 is the dot pitch of the abscissa, and l2 is the dot of the ordinate (double the high of triangle-dots). The appearance period of moiré patterns based on moving angle is 60° in the regular triangle-dot arrangement system, and is 180° in the equilateral triangle-dot arrangement system. Since the moiré patterns are very regularly constructed, the working technique will have a bright prospect of developing the new field of various printing patterns for cloths, papers and so forth.