Geometry in painting: the beauty of clear forms, the history of the origin of style, artists, titles of works, development and perspectives

2024 Author: Leah Sherlock | [email protected]. Last modified: 2023-12-17 05:25

Geometry in art was almost always present. Existing, however, in different eras, geometry in painting, sculpture and architecture took on different meanings. Sometimes it appeared in the role of perspective, being a tool for conveying volume on a plane, and later flowed into a literal concept, presenting geometric objects as objects of art. In paintings with abstraction, geometry becomes the main character of the plot, while on Renaissance paintings it is only responsible for the spatial image.

The concept of perspective

Perspective is a way of depicting objects on a certain plane, taking into account the visual contractions of their sizes, as well as changes in boundaries, shapes and other relationships that are seen in nature. Thus, this is a distortion of the proportions of bodies and the geometry of the picture during their visual perception.

Types of perspective in painting

Geometry inpainting and sculpture are fundamentally different from each other, although they go side by side, like science and art, and have been incessantly intertwined for many centuries. During the Renaissance, art sparked the study of geometry. Geometry in painting has enriched art, introducing new possibilities and fundamentally different qualities. At present, we have the opportunity to look at it from a new perspective. As a major branch of mathematics, geometry in painting is the link that runs through history.

There are three methods to reproduce 3D space on a 2D painting surface:

• perspective (forward and backward);
• orthogonal projection method;
• axonometry.

History

These fundamental foundations of geometry in painting were implemented at various stages of the formation of artistic culture, when each of the methods found the most appropriate expression. For example, the system of orthogonal projections became the basis of the art of Ancient Egypt, while axonometry, also called parallel perspective, became characteristic of the images of the era of medieval Japan and China. Reverse perspective became a typical method of depiction on the icons of Ancient Russia and Byzantium, and direct perspective became widespread during the Renaissance, becoming the basis of the monumental painting of European and Russian art of the 17th-19th centuries.

The idea of orthogonal projections was suggested to man by nature: the shadow cast by an object is the mosta simple analogy of the image of a three-dimensional object on a two-dimensional plane. But this projection is unable to convey the depth of the real world, so the first attempts of artists to move further into axonometry began to be noted in ancient Egypt.

Axonometry conveyed the frontal plane of the object without any distortion. It could give an idea of the volume of the depicted space, but the depth itself remained an obscure value. Mathematics interprets this geometry in painting as a central projection with an infinitely distant center. Nevertheless, the method of axonometry, also called free perspective, has been known since ancient times. From the 2nd to the 18th centuries, plans for settlements were presented in a similar way, as if from a bird's eye view.

The shortcomings of axonometry were made up for in the Renaissance, when ideas about perspective began to develop. Such a system acquired a set of rules based on calculations. This method was notable for its complexity, but at the same time it accurately reproduced the surrounding world. The Renaissance perspective expanded the scope of human worldview, opening up new opportunities and knowledge for people.

Developing perspective

Axonometry changed orthogonal projections, which then gave way to perspective. The origin of geometry in painting in stages occurred gradually, in strict sequence. The complexity of the method determined its position in this scheme: the method of orthogonal projections, as the most primitive, took first place in the history of development. He helped to reproduce the contours of real objects withoutdistortion.

Each of the methods of geometry became an important step in the development of painting. There was a search for the most perfect system for the transmission of visual images.

Objective and subjective spaces

Man is surrounded by two geometric spaces. The first is a real, objective space, the second is generated by the work of the brain and the eye. Its people see and perceive in their minds, which is why it is called the subjective or perceptual space.

The history of painting went from the image of the actual space to the visual, subjective. In the XIX-XX centuries, the creators intuitively approached the creation of a perceptual perspective, which was displayed in their works in the form of various deviations from the Renaissance system. The general theory of perspective, including both Renaissance and perceptual, was created by Academician B. V. Raushenbakh.

He found out that there can be no single perspective in the image of visible space, just as there are no perfect methods for depicting three-dimensional space on the surface. The exact image of three-dimensional space is impossible in principle: with all his desire, the artist can only give an approximate geometric picture of the real world. In accordance with his goals, the artist can choose one or another method that will help him most accurately express his idea. Therefore, it would be incorrect to reproach the ancient Egyptian master for being too simple, the Japanese one for a lack of depth, the Old Russian one for distorting perspective, while at the same time praising the creator of the Renaissance. However, Renaissance artists can be blamed for being too photographic.

Orthogonal painting of Ancient Egypt

The whole philosophy of the ancient Egyptians is permeated by the idea of the eternal absolute of the pharaoh, revered as the son of God. This situation could not but be reflected in the art and painting of ancient culture. Each object of the image was comprehended in isolation from the surrounding space, the creator delved into the essence of the object, discarding everything momentary and insignificant, leaving only eternal and genuine images, independent of time and space - noun images. They were composed into whole messages and pictures-narrations. Ancient Egyptian painting was closely intertwined with writing, images mixed with hieroglyphs.

To embody the idea of the eternal in the image-noun, the method of orthogonal projections was used. The ancient Egyptian artists saw the only true way in this way: only in this way can the form be captured without unnecessary distortion. They provided the viewer with information about the real world.

Since the artist did not have the opportunity to convey all three projections of the object, he chose the most characteristic side of the object: that is why the profile view was chosen when depicting animals: it was so easy to convey the individual features of the species, as well as depict the legs, which are in depending on the situation, they could walk or remain at rest. The chest and shoulders were depicted turned towards the viewer. Defeated enemies were depicted as if from above - for the greatest information content.

Ancient Egyptian creators created their ownworks, relying not so much on vision as on speculation, it allowed the artist to combine several different points of view in one work. Speculation contributed to the development of a mathematical system of rules in the depiction of a human figure, which was called the canon. He confirmed the attitude of the painter to knowledge and power, being a symbol of initiation into the secrets of the priests. The stricter the framework of the canon was, the more skill the artist needed for the image.

The images were deliberately two-dimensional, but this did not bother the authors at all: the ancient Egyptians did not set themselves the task of displaying three-dimensional space, rather, pursuing the goal of transmitting valuable information. When there was an action in the picture, the event did not develop in depth, but along the plane of the canvas, moving along the lines.

However, the problem of depicting space gradually rose in the painting of Ancient Egypt. Sometimes the artist placed one figure behind another, but this technique was far from always successful. For example, in the image of Pharaoh Akhenaten, one could only guess about the wife sitting next to the image of her hand, which hugged her husband. The palm seemed to appear out of nowhere, and the second rested peacefully in the hand of the pharaoh.

But there were more successful examples of geometry in the paintings of artists, for example, when depicting archers. Each subsequent archer, standing behind, was depicted with a shift slightly up and to the right: this gave the impression of depth. In terms of geometry, this is already called frontal oblique axonometry.

Necessity to depict three-dimensional spaceleads to the development of geometric systems in painting - axonometry. Although its rudiments began to be found in the painting of Ancient Egypt, it received its real development later.

Parallel painting of the medieval East

Attempts to convey depth on a plane began to be found in the painting of Ancient Egypt, which prompted the creation of a new system - axonometry, which is also called parallel perspective. This system was called “fishbone” by art historians by analogy: it had a vanishing axis and gravitated towards linear perspective, but never developed into it.

"Fish bone" was found not only in Ancient Egypt, but also in the images of Ancient Rome and Ancient Greece. However, Rome soon fell, not having had time to sufficiently develop the system of geometry in the paintings of artists, and axonometry found its development only for several centuries, finding its place in the painting of medieval China and Japan.

The culture and art of China were not shackled by religious dogmas: Taoism, Confucianism and Buddhism peacefully existed side by side in these parts. Against the background of cultural and philosophical teachings, two areas of art developed - secular and religious. The path of knowing the truth passed through the renunciation of worldly fuss, turning to nature for calm and spiritual purification. The geometry of the picture and visual perception were difficult for both the viewer and the artist. The Chinese artist perceived nature and its depiction as a spiritual space in which the personality of the beholder was dissolved. That is why it has become widespreadlandscape.

Axonometry as a central projection with an infinitely distant center of projection ideally suited this philosophy of contemplation. The artist's point of view, as it were, was removed to infinity, dissolving in the space of nature: the artist became a part of art itself. Axonometry knows neither the angle of view, nor the vanishing points, nor even the horizon line, because it seems to elude the observer, rising somewhere upward and dissolving in space and the beholder. Oriental landscape art was a look from infinity that passed through the picture and rushed further into infinity.

Parallel perspective is most revealing in Chinese painting in pictures with man-made buildings - parallelepipeds of houses and other human structures. The axonometry of geometry in oil paintings is obvious, but even here you can see that the scenes of human life are seen by the artist as if from afar, from infinity, which symbolizes the tinyness of human worries and problems: the world appears as an anthill.

Axonometry has three coordinates. If you choose such a point of view that the two axes will represent the frontal orthogonal projection, then distortion will be noticeable along the third coordinate. Such a projection is called frontal oblique axonometry, in which Chinese masters usually worked. The distortion factor along the third coordinate is not fixed, so it is not possible to judge the depth from the first two coordinates. The fuzziness of depth is enhanced by the parallelism of the lines, which do not tend to one point asaway from the observer. So in a parallel projection, two opposing principles arise: flat and deep. The picture has a deep beginning, but in fact it is a flat slice moving in depth without metric cuts.

Oriental artists cleverly used this contradiction, turning it into a kind of compromise between flat (Ancient Egypt) and deep (Renaissance). This dialectic of opposing opposites fits comfortably into the ancient Chinese philosophy of Yin-Yang. Yang for the Chinese painter symbolized bright places in the picture: mountains, snow, clouds. Yin filled the dark areas: waters and lowlands, where all the impurities flowed. The black-and-white Chinese landscapes were executed not only masterfully, but also soulfully and thoughtfully.

As for Japanese art, it comes from ancient Chinese culture. But still separated from the whole world by the seas, Japan has retained its original culture up to the present day. Throughout the history of Japanese art, painting has not known drastic changes. The geometric basis was the same parallel perspective. This is especially significant in the works of the famous Katsushika Hokusai. His work became the pinnacle of the geometry of parallel projections in painting.

Linear Renaissance perspective

The world began to change, and this could not but affect creativity: old canons collapsed, new thinking came, empirical knowledge triumphed over visual experience. Perspective has become the geometric language of art. Althoughthe germs of a new method were found in antiquity, only with the Renaissance this projection was fully developed.

Linear perspective is based on the laws of geometric optics, reflecting perceptual space in the picture. Vision becomes dominant over speculation. The perspective combined two main features of the Renaissance culture: rationalism and empiricism.

The main tools in the hands of the artists were the horizon line and the vanishing point. The vanishing point is the main point in the picture and the center of the composition, and the parallel lines tending to it are designed to lead the viewer to its semantic source. The composition of the painting has acquired strict vertical symmetry, passing through the main point.

Renaissance artists sought not only to convey the depth of space, but also to calculate it. That is why in the paintings it was often possible to observe squares of floor or ceiling tiles, because they were a coordinate system. Thus architecture in painting became the architectonics of the painting.

Together with geometry, new artistic thinking came to the art of the Renaissance. The Renaissance perspective was a revolution in artistic thinking and understanding of art. Painting began to reflect a deep interest in science.

Reverse perspective of the painting of Ancient Russia

Due to the strict alignment of geometric rules, this version of perspective seemed the only correct one of all possible. However, there was another system of perspective - the reverse.

Old Russian painting, alas,almost never reached our days. The drying oil, which was used to cover the painting for better preservation, had the property of darkening with time, so that over the centuries it turned into a black impenetrable coating. It was customary to dispose of such blackened boards either by rafting down rivers, or burning, or renovating along barely readable contours.

This continued until the end of the last century, when under one black layer another was discovered, followed by a second, and a third, and a fourth, and a fifth, until suddenly piercing bright colors emerged from the depths of the centuries. This discovery marked the return from oblivion of an entire era of Russian culture.

Thanks to this look, a new perspective, different from the Renaissance, was opened, which art critics immediately dubbed primitive, naive and wrong. Old Russian painting combined many contradictions, but it soon becomes clear that this is not a set of inconsistencies, but a system of perspective different from all others, which was called reverse.

The origins of the reverse perspective are in Byzantine art, from which ancient Russian culture grew. Surprisingly, it was the reverse that became the basis for creating a direct perspective, familiar to Europeans.

But one way or another, neither ancient Russian nor Byzantine painters adhered strictly to the rules of reverse perspective. Masters relied on their own sense of beauty and measure. Many wonder what caused the divergence of parallel lines in reverse perspective. Following one of the points of view, its roots go back to religious tasks: images on icons shouldwere to convince the believer of the reality of what he was unable to explain. Reverse perspective places the viewer, as it were, at the point of convergence of parallel lines, and everything that he sees in front of him seems to increase with distance from his point of view. So there is a sense of the reality of the unreal, the impression of the insignificance of one's own person in front of the one depicted in the picture. This is what emphasized the meaning and significance of the icon through the display in the reverse perspective system.

Modern Art

Today, geometry in painting, sculpture and architecture has taken on a literal meaning. Times are changing, and in contemporary art, projections and perspectives are no longer always so important. Now geometry in painting is a style that stands out in real life.

Its beginnings arose as early as 900-700. BC e. Art critics single out the proto-geometric style. It was typical for various arts and crafts. But closer to the 20th century, geometry acquired a new meaning not only for painting, but for art in general.

Geometry in painting has no name, at least one that would suit every creator. Styles such as cubism, abstractionism, suprematism, futurism, and many others began to stand out, where geometry itself became a kind of art object. Figures in these styles of painting and sculpture created a huge number of innovative subjects that excite the minds of viewers to this day. Controversial, but compositionally accurate and harmonious worksarts inspire contemporaries to new creative achievements.

Among the well-known artists with geometry in painting are, for example, Malevich, Kandinsky, Picasso and many others. Their work is known even to those who are new to art. Geometry in the paintings of modern artists is much more pronounced than in the works of old masters, which makes such examples easy to remember. Recall at least the "Black Square", discussions about which still do not subside.

Manifestations of such creativity can be both paintings with abstract geometry, where circles meet triangles and lines, forming a single ensemble with a well-balanced composition and specific meaning, as well as amazing sculptures, consisting of the simplest figures, but in which you can read a deep understanding of the structure of the world and surrounding objects. Modern works are often veiled, but at the same time they look to the very essence, pulling out the original idea of the subject, sometimes in the most unexpected form. Geometry in modern painting is no longer a tool for creating art, but the means itself, the essence of the idea.

Earlier, people studied perspective and its varieties in order to come to the most complete and accurate image of the world around them. Now, geometry in painting in pictures has led people to a fundamentally new understanding of the world around them, its non-literal component. People looked at the paintings in a new way.

Geometry in the paintings of modern artists is manifested much more clearly than in the works of old masters. Today, it is important for artists notthe perfection of reproduction of the outer shell of three-dimensional objects in the plane, and the exact transfer of the essence of objects with the help of a minimum of means and a maximum of expression.

One can conclude the conclusion: geometry in sculpture and painting returns to its beginning. Once upon a time, it was important for creators to fix the idea of the depicted object, and only later did they move on to the desire to depict the world around them as accurately as possible. Now the geometry of the picture and visual perception are returning to the beginning, when the accuracy and alignment of the perspective is not so important as the clarity of thought is valuable.