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Chapter 4  Types of Geometrical Optical Illusions:

Illusions of Perspective.  As the complexity of figures is increased the number of possible optical illusions is multiplied. In perspective we have the influences of various factors such as lines, angles, and sometimes contour and contrast. In Fig. 21 the suggestion which is caused by the perspective of the cube makes the oblique angles appear to be right angles and the right angles appear to be oblique. This figure is particularly illusive. It is interesting to note that even an afterimage of a rightangle cross when projected upon a wall drawn in perspective in a painting will appear oblique.
Fig. 21.  Owing to perspective the right angles appear oblique and vice versa. 
A striking optical illusion involving perspective, or at least the influence of angles, is shown in Fig. 22. Here the diagonals of the two parallelograms are of equal length but the one on the right appears much smaller. That AX is equal in length to AY is readily demonstrated by describing a circle from the center A and with a radius equal to AX. It will be found to pass through the point Y. Obviously, geometry abounds in geometricaloptical illusions.
Fig. 22.  Two equal diagonals which appear unequal. 
The effect of contrast is seen in a in Fig. 23; that is, the short parallel lines appear further apart than the pair of long ones. By adding the oblique lines at the ends of the lower pair in b, these parallel lines now appear further apart than the horizontal parallel lines of the small rectangle.
Fig. 23.  Apparent variations in the distance between two parallel lines. 
The influence of perspective is particularly apparent in Fig. 24, where natural perspective lines are drawn to suggest a scene. The square columns are of the same size but the further one, for example, being apparently the most distant and of the same physical dimensions, actually appears much larger. Here is a case where experience, allowing for a diminution of size with increasing distance, actually causes the column on the right to appear larger than it really is. The artist will find this optical illusion even more striking if he draws three human figures of the same size but similarly disposed in respect to perspective lines. Apparently converging lines influence these equal figures in proportion as they suggest perspective.
Fig. 24.  A striking optical illusion of perspective. 
Although they are not necessarily illusions of perspective, Figs. 25 and 26 are presented here because they involve similar influences. In Fig. 25 the hollow square is superposed upon groups of oblique lines so arranged as to apparently distort the square.
Fig. 25.  Distortion of a square due to superposed lines. 
In Fig. 26 distortions of the circumference of a circle are obtained in a similar manner.
Fig. 26.  Distortion of a circle due to superposed lines. 
It is interesting to note that we are not particularly conscious of perspective, but it is seen that it has been a factor in the development of our visual perception. In proof of this we might recall the first time as children we were asked to draw a railroad track trailing off in the distance. Doubtless, most of us drew two parallel lines instead of converging ones. A person approaching us is not sensibly perceived to grow. He is more likely to be perceived all the time as of normal size. The finger held at some distance may more than cover the object such as a distant person, but the finger is not ordinarily perceived as larger than the person. Of course, when we think of it we are conscious of perspective and of the increase in size of an approaching object. When a locomotive or automobile approaches very rapidly, this "growth" is likely to be so striking as to be generally noticeable. The reader may find it of interest at this point to turn to illustrations in other chapters.
The foregoing are a few geometrical illusions of representative types. These are not all the types of optical illusions by any means and they are only a few of an almost numberless host. These have been presented in a brief classification in order that the reader might not be overwhelmed by the apparent chaos. Various special and miscellaneous geometrical illusions are presented in later chapters.
Chapter 4  Types of Geometrical Optical Illusions: Illusions of Contrast 
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