平面圖形複雜度與面積錯視之關聯性研究－以不規則多邊形為例

The Association of Complexity of Figures and Dimensional Visual Illusion-A Study of Irregular Polygons

楊清田(Ching-Tien Yang) ； 魏碩廷(Shuo-Ting Wei)

《藝術學報》 77期 (2005/10) Pp. 13-23

https://doi.org/10.6793/JNTCA.200510.0004

摘要

本研究旨在探索不規則多邊形的複雜度與面積錯視之間的關係。過去研究中，多探討規則幾何圖形之面積錯視，對不規則圖形的面積錯視較少論及。30名大學生參與本研究，每位受試者必須進行兩次測驗，第一次實驗前僅告知測驗流程及方法，第二次實驗則再告知誘因，使其在第二次的實驗中能更用心調整。受試者在給定的基準圖形旁，逐次調整另外五個不同複雜度的不規則圖形，使其大小看起來與基準圖形相同。複雜度之計算採用D=P/A之公式，其中D為複雜度、P為周長、A為面積。結果發現，誘因與性別的因素對於圖形面積的誤差值影響皆不顯著，顯示一般人的面積錯視具有普遍性；圖形的複雜度與誤差值呈現高度相關，顯示圖形越複雜，越不易判斷準確。在過大視、過小視方面，兩次實驗的結果大多偏向同一捆傾向；圖形複雜度越大，越容易呈現過大視的現象。藉由複雜度的界定與不規則面積之算法，提供在形態與面積錯視研究上的參考。

關鍵字

面積錯視 ； 複雜度 ； 不規則形

並列摘要

The purpose of this study is to explore the relationship between the value of complexity of irregular polygon and the dimensional visual illusion. Many results of similar studies only mentioned the dimensional visual illusion of geometric figures, but rarely mentioned it of irregular figures. 30 college students joined this research. Each person had to do twice tests. At the first, they were informed the method of experiment only. Second, they were informed inducement in addition to the method of experiment, so that they could concentrate on the second test. In each test, each person had to adjust 5 irregular polygons one by one, which have different values of complexity, beside the standard figure. The function of value of complexity is 'D=P/A', where D is the value of complexity, P is the perimeter, and A is the area of a polygon. According to the result of experiment, factors of inducement and sex both didn't influence the errors between the areas of the standard figure and each irregular polygon. The values of complexity and errors are highly correlative. It means the higher value of complexity of a figure, the larger error we'll make. As to the phenomenon of viewing larger or smaller, almost every one was partial to the same tendentiousness in both tests. That is, it doesn't influence the tendency of human's dimensional visual illusion whether the factor of inducement was acceded to or not. The higher values of complexity of polygons, the more phenomenon of larger-seeing will happen. Besides, we also discovered that except the first sample of irregular polygon, the larger-viewing phenomenon was existed on the other 4. It might be relative to the factor of jogging condition of figures. By defining the value of complexity and the method of calculating areas of irregular polygons, we offer a reference material in studies of dimensional visual illusion.

並列關鍵字

Dimensional Visual illusion ； Complexity ； Irregular polygon

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