A study on the area of basic geometric shapes and its effects on Poggendorff illusion figures

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1 A study on the area of basic geometric shapes and its effects on Poggendorff illusion figures Tsu-Wu Hu * and Ku-Hsi Chu ** * Chaoyang University of Technology Graduate Institute of design Taiwan, hutw@cyut.edu.tw. ** Chaoyang University of Technology Graduate Institute of design Taiwan, s @cyut.edu.tw. Abstract: the basic optical elements used in designing include: square, equilateral triangle and circle. They are used extensively in both graphic design and product design. Therefore, it is understood that geometric shapes are used widely in designing. In order to probe into and explore Poggendorff geometric illusions and effects, and to understand the relationship between areas and lines in terms of illusion, so as to provide beneficial help in graphic design or geometric implications in terms of icon design of product. This research study discusses effects geometric areas have on illusions of lines. Experimental results show that it have no significant effects on area variables by the test of ANOVA. Also, in accordance with DUNCAN examination, geometry plays an essential role in affecting illusion. Area on the other hand does not. Therefore, this result provides an alternative option and consideration in icon designing to suit differentiating and operational needs for users. Key words: Poggendorff basic geometric figures optical illusion relativity 1. Introduction The phenomenon of illusion is a frequent occurrence in everyday conveyance of optical messages by humans. However, these optical and sensual judgments also cause errors and inaccuracy in the things we see. These inaccurate phenomena are bound to exist even if we deliberately try to distinguish them. The so-called illusion is an obvious optical diversion in which wrong stimuli are perceived leading to false judgments of actual objects. Poggendorff geometry figure is one of the frequently manifested geometric illusions. Through separation of the main line, two of its diagonal lines (i.e. control line) appear to converge into one. Therefore, erroneous judgments of observer result causing a phenomenon of optical illusion. Geometrically, basic figures based on mathematical principles include: square, equilateral triangle, regular pentagon and circle etc. these geometric shapes are largely used in graphic design, product design or even artistic works. Therefore, focusing on Poggendorff illusion figures, we aim to discuss the effects basic geometric shape areas have on optical illusion. In addition, we hope that our experimental results will contribute to graphic design and product icon design so that optical errors may be reduced. This research focuses mainly on our frequently used geometric shapes in designing and effects they have on Poggendorff figures and optical effects on lines. Therefore, this research is carried out in form of experimental operations. Hopefully, through the objective results, data utilization by 1

2 teachers and designers alike may be provided. In accordance with researches done by psychologists, simple figures draw more attention than complicated ones such as square, triangle and circle etc. the level of attention for these shapes are way higher than shapes like oval, and T-shape etc. (Lu, Ching-Hsiu,1996) However with respect to other research studies, there is a discrepant point of view. Triangles are simple figures and possess angles. Therefore, triangles are the most easily noticed shapes of all. (Charles& Cynthia, 1992) The optical illusion figures we see normally are named after their discoverers. As a result, there are no definite classifications and definitions up to now. They are however classified into three categories based on 3 main aspects: (1) Illusions of angle and direction (2) Illusions of straightness and curvature (3) Illusions of length, distance and area (Imai Shougo,1988) Directions of lines are affected by limitations of figures and optical deviations result. Poggendorff optical illusion is an example of this. As we observed a Poggendorff figure, we realize it consists of an oblique line interrupted by an area defined by two vertical parallel lines, which seem like a straight line judging objectively. However, in our subjective perception, the two separated but collinear oblique lines seem non collinear which is known as Poggendorff illusion (Fig.1). The larger the angle of Poggendorff geometric intercept line and parallel line, the lesser the extent of illusion; similarly, as the distance between the parallel lines gets longer, more extensive illusion results. The relationship between the distance between intercept angle condition (acute angle A) and parallel line condition (W) and extent of illusion can be summed up in this equation: i.e. I=0.162 (W/tanA) (Imai Shougo,1988) Poggendorff Fig.1 Poggendorff optical illusion In order to convey messages surrounding us in everyday life through perceptual and sensual channels as a means for message relay to us, messages enter the neural system and through sensual processes, various different cognitive experiences are produced. Sensations are combinations and analysis of message input and through the process of reception and output of various different experiences we can then clearly perceive and understand happenings around us.(chung, Sheng-Chiao,1990) Geometric shapes are results of mathematical principles. They are divided into two main types namely straight lines and curvature lines. Examples of straight lines include square, equilateral triangles and other equilateral polygons. As for curvature lines, examples include circles; ovals etc. definitions and calculations on area of the aforementioned 4 basic geometric shapes are as follows: (1) Equilateral triangle:a triangle with three equal sides is defined as an equilateral triangle.if its side length is set as a then its area is calculated as: (2) Square:a quadrilateral of right angles and 4 sides of equal length is defined as square. Its area is calculated 2

3 as: a² (3) Regular pentagon:a polygon with all sides and all angles equal are called regular n polygon. One with 5 sides is called regular pentagon, one with 6 sides is called regular hexagon so on and so forth. If its side length is set as a then its area is calculated as: (4) Circle:A plane curve everywhere equidistant from a given fixed point is called a circle. Its fixed point is called center and its radius is set as r. the area is calculated as: πr² 2. Method 2.1 Subject The subject for this experiment was set to be the 20 students of Designing Department, Chaoyang University Of Technology. Student age range were between 22~40 with an average age of 26.9 years old (SD=5.52). Among which, 13 were male and 7 were female. These subjects all had background in designing and had normal eyesight (including after correction of vision) 2.2 Materials The main materials used in this experiment include 4 basic geometric designs namely: square, equilateral triangle, regular pentagon and circle. Respective figures were enlarged proportionally and area units were in mm². Therefore, these 4 types of figure areas were: 20*20mm² 25*25mm² and 30*30mm² respectively with 12 samples in total. (Fig.2) All figure-fill-in color was white. Beside poggendorff illusion shapes were two oblique straight lines. Objects being interrupted were in straight lines. The lines were tilted 45 degrees with line width of 0.75 points and were all colored in black. All experimentally set up samples were presented on a white background of 1024* 768 pixel. Experimental material presentation media was a laptop 14 LCD monitor. Experimental figures were drawn by Corel Draw 12 software. 2.3 Procedure Prior to experimental testing of subjects, experiment objects and experimental procedures were explained first. Subject was asked to fill-in forms of personal data. When the experimentally officially began, each subject was to directly key-in the right positions through a keyboard through experimental pattern presentation. Positions in which subjects believed to be the most suitable were to be located. Each subject was required to complete experimental combinations of 4 types of figure areas that are of equal distance in 12 samples (3 squares, 3 equilateral triangles, 3 regular pentagons and 3 circles.) the original position was being set up as point of origin, point above that was positive, and below it was negative. Experimental results of subjects were measured and recorded using the installed software(unit: mm) and the values obtained were being numerically analyzed. This experiment was under no time constraint. Therefore, during experimentation, subjects made the best judgments based on personal preferences. Breaks were allowed in between the experiment. The estimated time to completion was approximately 5 minutes. The venue in which the experiment was carried out was the research lab of the university. Each subject was given the same amount of illumination. According to Grandjean, the most optimum indoor standard of illumination was 700 Lux(Grandjean, 1985) 3

4 Fig.2 12 samples of figure areas 3. Results and Discussions Distributions of respective experimental illusion samples are as follows: (1)square 20*20 pattern: 45% of subjects were able to locate the correct connection point. (2)square 25*25 pattern: 35% of subjects were able to locate the correct connection point. Fig.3 square 20*20 sample of (3)square 30*30 pattern: 25% of subjects were able to locate the correct connection point. Fig.4 square 25*25sample of 4 Fig.5 square 30*30 sample of

(4)equilateral triangle 20*20 pattern: 40% of subjects believed that the

6 equilateral triangle 20*20 sample (5)equilateral triangle 25*25pattern:

(6)equilateral triangle 30*30 pattern: 40% of subjects believed that the

8 equilateral triangle 30*30 sample (7)regular pentagon 20*20 pattern: 25%

5 (4)equilateral triangle 20*20 pattern: 40% of subjects believed that the correct Fig.6 equilateral triangle 20*20 sample (5)equilateral triangle 25*25pattern: 40% of subjects believed that the correct Fig.7 equilateral triangle 25*25 sample (6)equilateral triangle 30*30 pattern: 40% of subjects believed that the correct connection point was located 1.0mm above Fig.8 equilateral triangle 30*30 sample (7)regular pentagon 20*20 pattern: 25% of subjects believed that the correct Meanwhile, 25% of subjects were able to locate the correct connection point Fig.9 regular pentagon 20*20 sample 5

(8)regular pentagon 25*25 pattern: 30% of subjects believed that the correct Fig.

that the correct Meanwhile, 30% of subjects were able to locate the correct connection

6 (8)regular pentagon 25*25 pattern: 30% of subjects believed that the correct Fig.10 regular pentagon25*25 sample (9)regular pentagon 30*30 pattern: 25% of subjects believed that the correct Fig.11 regular pentagon 30*30 sample (10)circle 20*20 pattern: 30% of subjects believed that the correct Meanwhile, 30% of subjects were able to locate the correct connection point Fig.12 circle20*20 sample of (11)circle 25*25 pattern: 25% of subjects were able to locate the correct connection point. Fig.13 circle 25*25 sample 6

7 (12)circle 30*30 pattern: 20% of subjects believed that the correct connection point was located -0.5mm below Fig.14 circle 30*30 sample of In order to understand whether basic geometric shape areas and obtuse lines that cause the illusion phenomena show significance, this research based on by One-Way ANOVA. The result is shown on table 1 with the following result analysis: Table 1 Tests tabulation of central illusion figures with area (1)from Table 1, we get the results that the area of P value>0.05,showed no significant difference; which means subject was not affected by area. (2)another results that the shape of P value<0.05, showed have significantly difference ; which mean subject was affected by shape. Also, in accordance with DUNCAN, examination results are shown on table 2 and table 3: Table 2 DUNCAN examination on area Table 3 DUNCAN examination on shape (1)With respect to areas there was no grouping, which means significance was not apparent. (2)With respect to shape, 1 and 4 were grouped; 4 and 3 were grouped, 2 formed a group on its own, which means shape had apparent significance. 7

8 4. Conclusion In accordance with result analysis of this experiment, It have no significant effects on area variables by the test of ANOVA and DUNCAN. However we can realize when subjects determined by these fours geometric figures illusion testing which have no apparent significance. In addition, experimental results also show that although there were no significant effects in terms of area, shape on the other hand, had very apparent significance. Furthermore, for parts that are not explained in detail in this research such as undifferentiated subject set up and subjects with no designing background can be worked on. In terms of experimental design, parts such as thickness of straight lines, color of central area are still open for discussion, reviews and improvements may be carried out after this research activity. References [1]Lu, Ching-Hsiu, 1996, constitution and form of design lay out -foundations in design and actual practice, Liu ho, Taipei City. [2]Lee, Chiang-Shan,etc, 1999, Vision and Cognition: visual perception and visual locomotion system, Yuan liu, Taipei City. [3]Chung, Sheng-Chiao, 1990, Cognitive psychology, XinLi Publishing Co., Taipei City. [4]Chang, Shao-Hsun, etc, 1994,SPSS For Window elementary statistical tabulation and analysis, advance statistic tabulation, SongGang Computer library, Taipei City. [5]Imai Shougo, Sha, Hsing-Ya translates, 1988, " look at the figure by illusion ", Yuan liu, Taipei. [6]Gerald Westheimer, Scott Brincat, Christian Wehrhahn, Contrast dependency of foveal spatial functions: orientation, vernier, separation, blur and displacement discrimination and the tilt and Poggendorff illusions, 1999,Vision Research 39, [7]M.J Morgan, The Poggendorff illusion: a bias in the estimation of the orientation of virtual line by secondstage filters, 1999,Vision Research, 39, [8]Yen, Ching-Chen, Lee, Chang-franw, Hsieh, Cheng-Hsun, Reseach on features of different figures and their effects on perpendicular, parallel line illusions, 2002 the Republic of China designs Association For Research And Development Of Teaching Materials, pp [9]Huang, Hsin-Fu, Cai, Deng-Chuan, effects of angle on basic geometric shape area and perceptio, 2004 the Republic of China designs Association For Research And Development Of Teaching Materials, pp [10]Hsieh, Cheng-Feng, Hsu, Yu-Chen, Lin, Fang-Sui, Discussion of different geometric shapes and their effects onpoggendorff illusion figures,2001 the Republic of China designs Association For Research And Development Of Teaching Materia,pp

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