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constructive analysis:
Constructive analysis of objects in space 
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Constructive analysis of objects in space
So, all objects are in space. Space and objects are three-dimensional and three-dimensional. They can be circumvented, viewed from different angles, carried out a constructive analysis and reflected, using methods, in the form of a picture on the plane of the graphic sheet.
The question is not how to reflect objects in the form of a drawing (because this is a matter of technique and methods, which is secondary so far), but how to see these objects. Learning to see is the number one task for anyone mastering a drawing.
So, the dog hears ultrasound, but the person does not. The artist sees in volume not from birth, this is the quality he acquired. Drawing and sketching are polar concepts. They draw with the head, or rather, with consciousness, and draw with hands. But consciousness must be taught to see with the help of a constructive drawing. Yes, a constructive drawing, at first glance, looks a little rude. But this is the foundation, a complex mathematical calculation in a column with numerical memos in the fields (especially when you study). And as soon as lightness and confidence appear in it, this will mean that the main load of knowledge has reached the goal, that is, the subconscious.
Even with little experience and shallow knowledge in the theory of drawing, one can mentally imagine such a geometric figure as a cube. Close your eyes and mentally try rotating this form to examine it from different angles. You do it because you are aware of the whole integrity of this simple form in space. You can also imagine the space that is divided into an infinite number of cubes. But this is not so important, since these cubes are similarities of the big one, and you can already move the big one, rotate it, transform it, “wander” inside in any direction.
Now imagine the shape of the skull of a human head. Vaguely? And they must have a clear idea of this form, be able to mentally rotate it in space no worse than a cube. But why is this happening? Just instead of a large and solid shape (cube), composed of a certain number of smaller forms (cubes), you saw a scattering of some mosaic, flat set.
Work on the educational drawing of a still life of geometric bodies is the first step in the knowledge of the whole drawing. At this stage, a new consciousness is being formed to understand volume and space. Through the drawing of geometric bodies (primitives), we learn to see the world around us and understand that any object of the world around us is composed of simple geometric bodies and inscribed in a cube. At this stage of cognition lies the key to the whole picture.
Take a closer look at still life objects, what reminds you of their shape? Geometric bodies. A jug, a mug, a glass, a cup, fruits consist of the sum of several geometric bodies, such as a cone, cylinder, ball. The table and the plane behind it resemble the planes of a cube, a rectangular prism. Drapery, located on these planes, repeats their direction, has a thickness and relief, something similar to the elements of such geometric shapes as a cone, cylinder, hexagonal prism. And all this is subject to a single space.
How to see in the subject its simple components? This must be learned. The cube faces - not only structural elements, but also the boundaries of spaces. Pay attention to the illustration with jugs where these boundaries of spaces are defined along a contour line. A line cannot just change its position in space, it is the boundary of the form.
The point at which a change in position occurs is necessarily located at the boundary of the change in the plastic form or the joining of two forms. If at this point there are changes in two dimensions, that is, up, down, right or left, there will be a third, that is, on us and from us. Add depth to the drawing and you get the volume and position of the shapes that make up the jug in space.
Failure to understand this leads to the following example (it is borrowed from the manual). In the figure, which gives an idea, it seems, about the construction of the nose of a person, there is no understanding that the shape of the nose is three-dimensional. The design has a height and width, but has no depth. In any case, it is absent in the places indicated by arrows.
To make it absolutely clear what is at stake, we compare this with the following constructive drawing. And another example from the same textbook, which shows the location of the constructive axial lines of the human head - and again the same misunderstanding. True, the author of the textbook has a significant trump card: this is a drawing of Dürer, where Dürer discusses the construction of the human head and which cannot be taken as dogma. But, alas, this drawing formed the basis for a constructive understanding of the human head by a whole generation of students of art and graphic departments.
Look at the person’s head as we just saw the jug, and you will see that some constructive center lines change their position. For example, on the borrowed figure there is no axial line of the cheekbones, and yet it corresponds to the widest part of the face. On it are two symmetrical zygomatic points that lie on the border of four spaces. They will be our beacons when building the shape of the human head in space. There is no similar center line corresponding to the widest part of the cranium and also having two symmetrical reference points.
In this case, it is not clear what meaning is put into the constructive lines by the authors of these publications. Perhaps everything is simpler. You can talk a lot about drawing and not understand what is the design of the object, and, in the end, not to understand what is the design of the drawing itself as an object.
Methods for the implementation of constructive analysis methods in sheet space
We know that the space around us and objects in it are three-dimensional. As we have already said, the shape of the picture is the image on the plane, and the plane is two-dimensional. It has a height, a width, but no depth. In the figure, there is a method of transmitting the illusion of the depth of space, which is called "perspective". What it is?
Perspective (French perspective - to penetrate with the gaze, see through) is a way to build space on the sheet plane. Any image on a plane can be considered as a projection of a real or imaginary object onto a given plane (this is a look through a transparent picture plane onto an object).
Creating a three-dimensional image on a plane is carried out in various ways. There is a direct and reverse perspective. The laws of direct and reverse perspective arise from the objectively existing features of visual perception. They can be used by the artist to create a convincing spatial image.
In pure form, the forward and reverse perspectives are only abstract geometric schemes. It should be noted that if the direct perspective still has scientific mathematical justification and is one of the methods of projecting real space onto a plane, then the reverse perspective is not such a method (that is, it is the diametrically opposite perspective with respect to the direct).
We use the direct perspective method. It has two features: all parallel lines extending into the depth of the plane converge at one point (which is on the horizon); all objects decrease in size as they are removed in depth. The horizon line, whether you are sitting or standing, is always at the level of your eyes.
This method has another name - linear perspective. Here is the time to recall the line, because it is an expressive means of drawing. And the drawing does not have many of these means, only two: a point and a line.
A line is an abstract concept, and in its pure form does not exist in nature. There is a form in space that we separate from this space with a line. When drawing an object in the space of a sheet with a line, creating a third dimension, we must take into account that the line itself is also in this space.
As you move farther away from us in the depth of the picture plane — that is, the sheet plane — the line becomes less active and thinner (this is the “fog effect”). Applying such an effect to the line, we get the stage of constructive drawing with the state of aerial perspective; linear drawing will gain depth. So, the lines of the first plan, as you get closer to you, are strengthened with a pencil, and the lines of the second plan, as you move away from you, are weakened by an elastic band.
It is very important to pay attention to the nature of the lines in the figure: there are two types of lines. This is a contour line (outline) that closes a form or a set of forms and separates them from space, and a line of borders or faces of a form, giving an idea of the position of the sides of the form in space. The line of faces of the form has a wide graphic range.
It can be either very soft or very hard, like a cube face. The cube has a sharp line between the sides and a sharp contrast between light and shadow, enhancing this effect with chiaroscuro (this is the border of light and shadow). Which, as we can see, coincides with the border of the parties.
Chiaroscuro is one of the most important concepts of the foundations of the picture after the concept of three-dimensionality of space (these are the most related and most mysterious terms). As teaching practice shows, in order to master the first, a student - at best - requires 1-2 years of practical training. We have already said that the artist does not see in volume from birth - this is an acquired skill. Without three-dimensional vision, chiaroscuro is not visible.
In existing drawing tutorials, the term "chiaroscuro" defines lighting in general, and this lack of specificity causes some chaos in the concept of drawing. We will understand it this way: “light” is light, “shadow” is shadow, and “chiaroscuro” is the boundary between light and shadow. Thus, much in the picture becomes simple and understandable: the borders of light and shadow are always darker than the shadow itself; on bodies of revolution, chiaroscuro is soft and blurry, on hull objects - hard.
Look at the picture. At the cube (in the upper row) we rounded the edges. The question of the presence of vertical lines instead of missing faces causes students to panic, because the cube has no edges! But the sides of the cube continue to be in the same position and still have different orientations in space. So, between them there are spatial boundaries. Take a closer look at nature, and you will see them: this is a glare or chiaroscuro, the border of light and shadow.
In the constructive drawing (that is, while there are no tone relations), the glare at the boundaries of the fracture of forms in space is also replaced by a line. If you do not learn to distinguish between these boundaries, you cannot draw a volume in space - that is, you simply will not see it.
For the first time, a student is seriously confronted with this in tasks when he performs constructive drawings of a human head and a skull of a human head. The shape of the human head is in space, has all its sides. This shape can be compared with a cube in space, but only this cube has no sharp edges.
But borders are necessary to create a three-dimensional volume. Where are they? How to see them? Remember the constructive analysis of the jug: look at the shape of the head and you will see chiaroscuro. To see chiaroscuro means to see the boundaries of spaces.