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

我们通过测量斜线的角度和长度以及计算视觉光线的方法，分析了12至15世纪创作的42幅Emaki（叙事画卷）的三维空间图像表现形式。我们发现(1)928座建筑中65.5%采用水平线、垂直线和右侧向上倾斜的线条（R型），22.7%采用左侧向上倾斜的线条（L型），11.1%采用垂直线和左右向上倾斜的线条（B型），(2)475个场景中25.9%采用“Fukinuki-Yatai”（从上方绘制房间的方法，去掉天花板和屋顶）。47.2%的福之雅台场景是用“单品”（浪漫和世俗故事卷轴）绘制的，34.1%的福之雅台场景是用“单品”（佛教和神道教主题的说教卷轴）绘制的，(3)上斜线的角度按时间顺序逐渐变小，(4)B型的上斜线的角度比R型和L型的小，B型的上斜线的角度比R型和L型的小。(5)单目画卷的平均画角大于佛经画卷、传说画卷和画卷的平均画角；(6)在R、L两种画卷中，单目画卷的视光凹陷角小于其他画卷；(7)在B两种画卷中，单目画卷的视光凹陷角大于其他画卷。青竹竹的凹陷角小于其他品种，青竹竹的方位角范围比其他品种宽。

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.