Study on the Pictorial Representation of 3-Dimensional Space in Japanese Paintings from the Graphic Scientific Point of View

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We analyzed pictorial representations of 3-dimensional space in 42 Emaki (narrative picture scrolls), which were created from twelfth to fifteenth century, by means of measuring the angles and the lengths of the inclining lines and by means of calculating the visual rays.We found that (1) 65.5% of the 928 buildings were drawn by a horizontal line, a perpendicular line, and a right-side upward-inclining line (type R), 22.7% used a left-side upward-inclining line (type L), and 11.1% used a perpendicular line and both left-and right-side upward-inclining lines (type B), (2) 25.9% of the 475 scenes were drawn by the method of "Fukinuki-Yatai" (drawing method of rooms from above, whose ceilings and roofs were removed), and 47.2% of the fukinuki-yatai scenes were drawn in monogatari-emaki (scrolls of romantic and secular tales ) and 34.1% of those were drawn in engi-emaki (didactic scrolls with Buddhist and Shinto topics), (3) the angles of upward-inclining lines were became smaller bit by bit in chronological order, (4) the angles of upward-inclining lines used in type B were smaller than those in type R and L, (5) the mean angle drawn in monogatari-emaki is larger than that in kyousetu-emaki (didactic scrolls of the doctrines of Buddha), setuwa-emaki (scrolls of legendary stories) and engi-emaki, (6) with regard to type R and L the angles of depression of the visual rays in kyousetu-emaki were smaller than those in the others, and (7) with regard to type B the angles of depression in monogatari-emaki were larger than those in others, the angles of depression in kyousetu-emaki were smaller than those in others, and the range of azimuth angles in kyousetu-emaki was wider than those in others.