Free technical library

Changing terrain and perspective. Encyclopedia of Visual Illusions

At leisure / Visual (optical) illusions

 Comments on the article

<< Back: Exaggeration of sharp corners

>> Forward: figure and background

Several interesting visual illusions take place under the conditions of changing the relief we see or the depth of the picture. The emergence of these illusions is associated, on the one hand, with the phenomena of accommodation and convergence of the eyes, that is, with their ability to see objects at different distances, with the ability to perceive space by the brightness of objects, by their shadows and by the number of intermediate objects. On the other hand, these illusions also arise in the process of comprehending the visible. A huge role in correcting spatial perception belongs to the brain. In this case, the work of the brain, clearly not conscious of us, is carried out in the same way as when turning over the reverse and straightening the curvilinear images obtained on the retinas of our eyes.

Examples of illusions of this kind are shown in fig. 79-87. When looking at Fig. 80-87 changes in the relief images we see can occur both at our will, and involuntarily, and sometimes even contrary to our desire.

Rice. 79. Separately drawn faces of a cube are unable to create the impression of a spatial figure.

Rice. 80. What is it? An open book with its spine towards us or its spine away from us?

Rice. 81. Is it either a plate with a notch (rear side of the notch AB), or three walls of the box to which the plate is pressed (the front side of the plate AB)?

Rice. 82. Is this either a ladder, or a niche, or an 'accordion' from a strip of paper? It is easy to see that the visibility of different objects here depends on how our gaze is directed. If you first of all direct your gaze to the left side of the picture, a staircase will be visible. If the eye slides over the drawing from right to left, a niche will be visible. If the gaze follows diagonally from the lower right edge to the upper left, a piece of paper folded in an 'accordion' will be visible.

Rice. 83. The right cube seems to be larger than the left, although all three cubes are the same. Converging lines we perceive as a hint of the depth of space

Rice. 84. Take a closer look! Are convex or concave figures depicted here?

Rice. 85. How many cubes are there and how are they arranged?

Rice. 86. How many cubes are there and how are they arranged?

Rice. 87. How is this prism located? Which edge, ab or vg, is closer to us? Which faces are labeled A and B?

For example, in fig. 87 shows a glass prism, and it depends on us to see the edge ab as the front, and vg as the back, or, conversely, to see A outside the prism, and B inside, or vice versa. The prism, finally, can be hollow, and face A or face B may be absent altogether. To resolve these issues, some tension of the visual apparatus is required, after which we are able to see in Fig. 87 whatever we please. If the parts of the edges hidden by the faces were not drawn on the prism, we would see only one, quite definite position of the prism in space. In the same way, if we consider only two projections of two transparent glass vases (Fig. 88), without seeing the third projection, it is difficult to imagine which of the vases is closer to us and whether these vases touch each other. After constructing the third projection, we confidently and strictly determine that the barrel vase is closer to us and that the vases are not touching.

Rice. 88. Having closed the lower part of the picture (dotted plan), try to determine how the vases are located in space. Do they touch each other?

We have developed the habit of assuming that the object depicted in the figure was illuminated from the left, and its shadows in the image are located on the right and below. On this basis, we take the image of the Maltese cross (on the left in Fig. 89) as a convex figure. But by mistake, the cliché of this drawing was turned upside down, and everyone, perhaps, will say that the cross on the right is a deepened figure.

Fig. 89

Our eyes accommodate in accordance with what we fix our attention on, and in accordance with this we see some parts of the figure closer, and others farther.

Objects that are far away from us seem small to us due to the fact that the angle formed by the rays falling from the extreme points of the object to the pupil of the eye decreases. This angle is called the angle of view.

Which of the vertical lines shown in Fig. 90, the longest? Seems to be on the far left. However, all vertical lines are the same length. This figure explains the formation of the angle of view, and the illusion is explained by the fact that the left line pulls together the largest angle of view, and other angles are only parts of it.

Fig. 90

The phenomenon of the apparent convergence of parallel lines in the distance (railway bed, highway, etc.) is called perspective. In order to depict in a drawing a certain part of space filled with objects, and for this drawing to give the impression of reality, it is necessary to be able to use the laws of perspective. All the lines in this drawing, which are actually parallel to the earth's surface, should be shown converging at some point on the horizon, called the "vanishing point". The choice of the level of the earth's surface and the horizon, as well as the "vanishing point" can be arbitrary. Lines going at different angles should converge on one or the other side of the "vanishing point" the farther from it, the greater the angle to the line of direct vision they pass. Of these points, the most remarkable is the point where the lines converge at an angle of 45 ° to the line of direct vision; this point is called the "distance point". It is remarkable in that it is removed from the "vanishing point" at the distance at which the artist's eye was removed from the picture when he painted it.

To view the picture, it is most advantageous to place the eye at the "remote point". The importance of this can be easily seen from Fig. 91. If you look at this drawing from a distance, it gives the impression of being flat. If, however, the eye is placed against the "vanishing point" at a distance of 3,5 cm from the drawing (equal to the distance from the "vanishing point" to the "distance point"), then the drawing gives the impression of three-dimensionality*. The corridor depicted on it goes deep, its floor consists of regular squares, and the ceiling seems to be vaulted. The type of objects depicted in the figure and the realism of the whole picture depend to a large extent on the choice of the height of the horizon and the distance point. Known, for example, "frog perspective", when the vanishing point is very low, and known perspective "bird's flight".

* (If you use a magnifying glass, then it should be pressed tightly to the eye.)

Fig. 91

In addition to linear perspective, in painting they also take into account aerial perspective, that is, with different brightness of objects in the foreground, middle and background of the picture due to the absorption and scattering of light in the air.

A person transfers the perspective perception of space, developed by the centuries-old evolution of vision, to the paintings and photographs he examines, which depict objects at different distances (Fig. 92-94). Along with the normal perspective of modern painting, there is the so-called reverse perspective. It is easy to see that such a prospect exists by doing the following experiment. We place the matchbox in front of the Eyes at the level of the tip of the nose and at a distance of 10 cm from it so that the side with the pattern is facing up. Looking at the box in this position with both eyes, we note that its more distant end seems wider than the nearest one. This can be explained by the fact that the width of the object in this case is less than the distance between the eyes, and we are dealing with an illusion of vision.

Rice. 92. Due to non-compliance with the rules of perspective, the figure of an old man walking in front seems to be much higher than the figure of a boy walking behind, although the figures are the same

Rice. 93. Of all the figures, the tallest figure of a girl walking behind. Failure to comply with the rules of perspective in all details of the picture distorts the visible dimensions

Rice. 94. Which distance is greater: AB or AC? Isn't it true, the AC is bigger? Now measure

However, why is it that in the drawings and icons of the painters of Ancient Rus' all objects, regardless of their size, are depicted precisely in reverse perspective? This can be seen, for example, the image of the "Trinity" from the iconostasis of the Trinity Cathedral in the city of Zagorsk, now stored in the Tretyakov Gallery; This picture (Fig. 95) was painted by the great artist of Ancient Rus' Andrei Rublev. Here, the boards under the feet of the angels on the right and left are narrow in the foreground and wide in the background, the table is almost parallel to the plane of the picture and is wider in the background than in the foreground. Moreover, on the icon "Washing of the Feet", also painted by A. Rublev, even architectural structures are depicted in reverse perspective.

The Russian artist of the second half of the XNUMXth and early XNUMXth centuries, Dionysius, also paints many objects in his frescoes in reverse perspective. Some historians of painting point out that the artists of antiquity did not pay attention to perspective at all, and a new phase in this regard allegedly began in the XNUMXth century. It is known that the aerial perspective began to be used along with the linear one only in the XNUMXth century.

Rice. 95. Image of 'Trinity' by A. Rublev, performed in reverse perspective

The "neglect" of perspective was also observed among Western European painters of antiquity. So, for example, a certain German painter in 1420 depicted in the painting "Garden of Eden" all objects in reverse perspective. However, having convinced ourselves of the existence of a reverse perspective, we still cannot conclude that the distance between the eyes of the ancient painters was greater than the size of the structures they depicted. Why did they still use reverse perspective? No one has yet given a satisfactory answer to this question.

Using the rules of perspective in painting makes it possible to obtain a fairly complete similarity of the pictorial relief on the flat surface of the picture with the apparent dimensions of objects and chiaroscuro in reality. Knowing and following the rules of perspective inevitably presupposes an astute observation of nature.

"Look at both," they say to a person, entrusting him with a responsible task. However, a person in determining large distances is capable of making mistakes. For example, an inhabitant of the plains mistakenly determines the distance in mountainous places, where, due to the high transparency of the air and the size of the mountains, unusual for the eye, all objects seem much closer.

Of decisive importance in the perception of relief and perspective is vision with two eyes, which can be easily seen using Fig. 96-99.

Rice. 96. Do the lines ab and cd seem vertical to you in both eyes?

Fig. 97

So, in fig. 96 line ab does not seem vertical to the right eye, but line cd to the left. Vertical and perpendicular to AB seem to be lines outlined by short segments ?? And ??.

This illusion comes from the fact that when we want to lower our gaze, the eye turns somewhat involuntarily somewhat inward; when we look upwards, the eye involuntarily turns outward. Therefore, the movement of the eye made in this way seems to us vertical, and if we are given a really vertical straight line, then it should seem to us somewhat inclined.

The action of each eye is also explained by such an experience, which also leads to a visual illusion. We connect the ends of the index fingers in front of us at a distance of 35-50 cm so that they form a continuation

one another, and look "through the fingers" at the remote wall. It will seem to us that a small "sausage" is squeezed between the fingers, which, if the fingers are slightly apart, hangs in the air (as shown schematically in Fig. 97). The length of the "sausage" will be the greater, the farther the object considered "through the fingers" is located. This illusion is explained by the fact that with the right eye we do not see the part of the wall bounded by the lines ABC and KLM, and with the left eye - the part of the wall bounded by the lines AB`C and KL`M. As a result, a completely invisible part of the wall looks like a "sausage". Finally, one more interesting observation. If you look with your right eye through the tube at some object, and with the palm of your left hand touching the tube, block the object from the left eye, then we get the impression that the object is visible with the left eye, but through the "hole in the palm" (Fig. 98 ).

Fig. 98

If in a flat drawing we distinguish to some extent the volume and remoteness of objects, then this is achieved thanks to side features associated with experience: the apparent size of objects, the fact that some objects block other objects, etc. Considering any drawing, we, quite consciously using the conditional image of the object, determine the shape of the details.

If there are two images of an object obtained separately "from the point of view" of the right and left eyes, then it is not difficult to obtain a three-dimensional image of the object. To do this, you need to consider these images by installing a partition (for example, a sheet of paper) between the eyes (from the plane of the picture to the very nose). After some training, the cube shown in Fig. 99 can be seen in bulk. It is known that the most distinct observation of perspective images in special drawings is carried out using a stereoscope - an optical device that combines two separate images of an object obtained as they are seen separately by the right and left eyes of a person.

Rice. 99. So this glass cube appears separately to the left and right eyes. After a certain training, you can learn to see the three-dimensional image of this cube. It is only necessary to put a partition, starting from the plane of the page (between images) and up to the nose

The mirror stereoscope was first built in 1838 by the English experimental physicist Wheatstone.

Let us pay attention to the following interesting phenomenon. What if you put rice in a stereoscope? 60? It would seem that the right and left halves of the picture will merge, and we will see a grid of horizontal and vertical lines. However, this will not happen. If we rotate the left half of Fig. 60 so that there are only horizontal lines on both halves, then the drawings will merge, and we will see some lines further and others closer, due to the inaccuracy of drawing. The pattern mismatch phenomenon observed in this way is referred to as "visual field dispute".

Special devices have been built on the principle of using deep stereoscopic vision, with the help of which distances are now measured with high accuracy. At present, with the help of special (raster) lens screens, stereopairs of film frames are shown in stereoscopic cinemas, where for all viewers the impression of relief and perspective images is created.

Much earlier than the stereoscope appeared, the so-called panoramas were built. These are paintings that present landscapes or scenes to the viewer as if the viewer himself were among them. To do this, the canvas on which they are applied is stretched in a round building and thus surrounds the viewer from all sides. The perspective of the image in this case is designed for the viewer to consider it, being in a certain position (point of distance). If we consider the picture from a different position, then the images of many objects may seem greatly distorted. The degree of distortion of a planar drawing can be so great that we consider this drawing to be mysterious or not reflecting real objects. For example, let's look at Fig. 100. Here the house is depicted in such a way that under ordinary conditions one never sees it: it has unusually long pipes, it is narrow at the foundation and unusually wide at the roof. The gazebo in the picture is falling, the trees are growing obliquely and in different directions, the woman on the left falls forward, and the couple walking on the right falls back. However, this enigmatic appearance is due to the fact that this planar drawing does not give us the impression of a "bird's flight" perspective.

Fig. 100

In this figure, using a pencil and a ruler, you can find the vanishing point. To do this, continue until the intersection, for example, two lines depicting the edges of the corners of the facade - the vanishing point will be at the bottom. Instead of looking for a distance point by construction, you can use the figure shown on the right in Fig. 100. If such a figure is cut out of thick paper (the distance from the center of the hole D to the line AB is 53 mm, to point C is 58 mm, the diameter of the hole D is 6 mm), bend it along the line AB, and then put it in fig. 100 so that the vanishing point is at the top of the recess C, and look with one eye into the hole D, then ... the whole visible picture will change.

The mysteriousness of the building will disappear, the trees and the gazebo will appear to be standing vertically in relation to the ground, the walking people will assume a normal position. Moreover, the drawing will become embossed, and we will say that this is not just an image, but a panorama. Looking at the drawing, we will be convinced that the artist depicted the view that presented itself to him from the balloon - the "remote point" was higher than the house. The position of the figures, the shadows and individual lines of this drawing can be perceived by us as real only when observed from the position in which the artist was.

The American writer Edgar Poe in his story "The Sphinx" describes how the hero of this story saw through the window a monster descending from a hill into the forest. In fact, it was a butterfly, descending on a cobweb near the window pane against the backdrop of a treeless hill.

The main source of error in many studies is the tendency of a person to attach insufficient or excessive importance to the object under study, depending on the distance to this object, and this distance is very often incorrectly determined.

A person sees quite clearly only those objects that are in the central part of his field of vision. Thus, the field of clear vision is contracted for the macula by an angle of only 6-8 °, and for the central part of the retina - by an angle of no more than 40 °. Other objects that are outside this angle, the eye perceives indistinctly - peripheral vision. But it is peripheral vision that gives us the opportunity to "feel" the surrounding space.

Recently, the so-called "panoramic" cinema has appeared in our cities, in which films shot by several devices are projected onto a cylindrical screen, arranged so that their viewing angles are sectors of the same circle. These pictures fill not only the central, but also the peripheral part of the field of view, due to which the so-called “presence effect” is created, that is, the viewer gets the impression that he himself is present at the events that are played out on the screen.

Author: Artamonov I.D.

<< Back: Exaggeration of sharp corners

>> Forward: figure and background

Latest news of science and technology, new electronics:

Machine for thinning flowers in gardens 02.05.2024

In modern agriculture, technological progress is developing aimed at increasing the efficiency of plant care processes. The innovative Florix flower thinning machine was presented in Italy, designed to optimize the harvesting stage. This tool is equipped with mobile arms, allowing it to be easily adapted to the needs of the garden. The operator can adjust the speed of the thin wires by controlling them from the tractor cab using a joystick. This approach significantly increases the efficiency of the flower thinning process, providing the possibility of individual adjustment to the specific conditions of the garden, as well as the variety and type of fruit grown in it. After testing the Florix machine for two years on various types of fruit, the results were very encouraging. Farmers such as Filiberto Montanari, who has used a Florix machine for several years, have reported a significant reduction in the time and labor required to thin flowers. ... >>

Advanced Infrared Microscope 02.05.2024

Microscopes play an important role in scientific research, allowing scientists to delve into structures and processes invisible to the eye. However, various microscopy methods have their limitations, and among them was the limitation of resolution when using the infrared range. But the latest achievements of Japanese researchers from the University of Tokyo open up new prospects for studying the microworld. Scientists from the University of Tokyo have unveiled a new microscope that will revolutionize the capabilities of infrared microscopy. This advanced instrument allows you to see the internal structures of living bacteria with amazing clarity on the nanometer scale. Typically, mid-infrared microscopes are limited by low resolution, but the latest development from Japanese researchers overcomes these limitations. According to scientists, the developed microscope allows creating images with a resolution of up to 120 nanometers, which is 30 times higher than the resolution of traditional microscopes. ... >>

Air trap for insects 01.05.2024

Agriculture is one of the key sectors of the economy, and pest control is an integral part of this process. A team of scientists from the Indian Council of Agricultural Research-Central Potato Research Institute (ICAR-CPRI), Shimla, has come up with an innovative solution to this problem - a wind-powered insect air trap. This device addresses the shortcomings of traditional pest control methods by providing real-time insect population data. The trap is powered entirely by wind energy, making it an environmentally friendly solution that requires no power. Its unique design allows monitoring of both harmful and beneficial insects, providing a complete overview of the population in any agricultural area. “By assessing target pests at the right time, we can take necessary measures to control both pests and diseases,” says Kapil ... >>

Random news from the Archive Milk quenches thirst better than other drinks 01.02.2024 A study conducted by scientists from Scotland reveals which drinks are most effective at quenching thirst. The results open up new perspectives in understanding the body's needs. Milk, due to its composition, turns out to be the best drink to quench thirst, providing a long-term feeling of fullness. The study highlights the importance of drink selection to maintain optimal levels of hydration in the body. Researchers at the University of St. Andrews analyzed the effects of various drinks on the body and found that water, although considered the standard, is not always the best choice. The results of the work showed that milk is superior to water in quenching thirst. Due to the presence of sugar lactose, fat and protein in its composition, it helps the body retain fluid, which reduces the need to drink for the longest time. Coffee also shows positive effects in fighting thirst, especially when consumed in moderation. However, be aware that caffeine may have a diuretic effect. On the other hand, alcohol, including beer, is not an effective thirst quencher, as it contributes to dehydration of the body. New research allows us to make more conscious decisions about our drink choices and understand their effects on the body.

Other interesting news:

▪ Bloodhounds of mercury

▪ Digital camera in lighter housing

▪ Fern against arsenic

▪ Sea of ​​garbage

▪ Prototype of the first electric motorcycle

News feed of science and technology, new electronics

Interesting materials of the Free Technical Library:

▪ section of the Antenna website. Article selection

▪ Article Alpha and Omega. Popular expression

▪ article The melody of what world-famous hit did its author dream about? Detailed answer

▪ article Operator of hydraulic systems. Job description

▪ article Watering machine for flowers. Encyclopedia of radio electronics and electrical engineering

▪ article Motor control device. Encyclopedia of radio electronics and electrical engineering

Leave your comment on this article:

All languages ​​of this page

Arabic	Hebrew	Polish
Bengali	Hindi	Portuguese
Chinese	Italian	Spanish
English	Japanese	Turkish
French	Korean	Ukrainian
German	Malay	Vietnamese

Home page | Library | Articles | Website map | Site Reviews

www.diagram.com.ua
2000-2024