Composition of geometric figures drawing for architectural. Composition of geometric solids in the entrance exams to the Marhi

MBOUDO Irkutsk CDT

Toolkit

Drawing geometric bodies

Additional education teacher

Kuznetsova Larisa Ivanovna

Irkutsk 2016

Explanatory note

This manual “Drawing of Geometric Solids” is intended for teachers working with children school age. From 7 to 17 years. Can be used both in additional education and in a drawing course at school. The manual is compiled on the basis of the author's teaching aid"Drawing of geometric solids" intended for first-year students of the specialty Arts and Crafts and Folk Crafts and Design (not published).

Drawing of geometric bodies is introductory material when teaching drawing. The introduction reveals the terms and concepts used in drawing, the concepts of perspective, and the order of drawing work. Using the material presented, you can study the required material, teach children, analyze them practical work. Illustrations can be used both for your own deeper understanding of the topic, and in the lesson as visual material.

The purpose of teaching drawing from life is to instill in children the basics of visual literacy, teaching them to realistically depict nature, i.e., understanding and depicting a three-dimensional shape on the plane of a sheet. The main form of training is drawing from a still nature. It teaches how to correctly convey visible objects, their features, properties, and gives children the necessary theoretical knowledge and practical skills.

Objectives of learning drawing from life:

Instill the skills of consistent work on a drawing according to the principle: from general to specific

Introduce the basics of observational, i.e. visual perspective, the concept of light and shadow relationships

Develop technical drawing skills.

In drawing classes, work is carried out to develop a set of qualities necessary for an artist:

- “position of the eye”

Development of “steady hand”

The ability to “see completely”

The ability to observe and remember what you see

The sharpness and accuracy of the eye gauge, etc.

This manual examines in detail one of the first topics of drawing from life - “Drawing of geometric bodies”, allowing you to study in detail the shape, proportions, structural structure, spatial relationships, perspective reductions of geometric bodies and the transfer of their volume using light-and-shadow relationships. Are being considered learning objectives– layout on a sheet of paper; construction of objects, transfer of proportions; from end-to-end drawing to the transmission of volume in tone, the shape of objects to reveal light, penumbra, shadow, reflex, highlight, complete tonal solution.

Introduction

Drawing from life

Drawing is not only an independent form of fine art, but also the basis for painting, engraving, posters, arts and crafts and other arts. With the help of a drawing, the first thought of the future work is fixed.

The laws and rules of drawing are learned as a result of a conscious attitude towards working from life. Every touch of pencil to paper must be thought out and justified by a feeling and understanding of the real form.

An educational drawing should perhaps give a more complete idea of ​​nature, its shape, plasticity, proportions and structure. It should be considered, first of all, as a cognitive moment in learning. In addition, knowledge of the characteristics of our visual perception is necessary. Without this, it is impossible to understand why the objects around us in many cases do not appear to us as they really are: parallel lines seem to converge, right angles are perceived as acute or obtuse, a circle sometimes looks like an ellipse; a pencil is larger than a house, and so on.

Perspective not only explains the mentioned optical phenomena, but also equips the painter with techniques for spatially depicting objects in all rotations, positions, as well as at various degrees of distance from him.

Three-dimensionality, volume, shape

Every object is defined by three dimensions: length, width and height. Its volume should be understood as its three-dimensional value, limited by surfaces; under the form - the appearance, the external outlines of the object.

Fine art mainly deals with three-dimensional form. Consequently, when drawing, one should be guided by the volumetric form, feel it, and subordinate it to all the methods and techniques of drawing. Even when depicting the simplest bodies, it is necessary to develop this sense of form in children. For example, when drawing a cube, you cannot depict only its visible sides, without taking into account the sides hidden from view. Without imagining them, it is impossible to either build or draw a given cube. Without a sense of the entire form as a whole, the depicted objects will appear flat.

To better understand the form, before starting to draw, it is necessary to consider the nature from various angles. The painter is advised to observe the form from different points, but draw from one. Having mastered the main rules of drawing on the simplest objects - geometric bodies - in the future it will be possible to move on to drawing from life, which is more complex in its design.

The design, or structure, of an object means the relative arrangement and connection of its parts. The concept of “design” is applicable to all objects created by nature and human hands, starting with the simplest household items and ending complex shapes. The drawer must be able to find patterns in the structure of objects and understand their shape.

This ability develops gradually in the process of drawing from life. The study of geometric bodies and objects that are close to them in their form, and then objects that are more complex in their structure, obliges those who draw to consciously approach drawing and to identify the nature of the design of the depicted nature. So, a lid seems to consist of a spherical and cylindrical neck, a funnel is a truncated cone, etc.

Line

A line, or a line drawn on the surface of a sheet, is one of the main elements of a drawing. Depending on the purpose, it may have a different character.

It can be flat and monotonous. In this form, it mainly has an auxiliary purpose (this is placing a drawing on a sheet of paper, sketching the general outline of nature, indicating proportions, etc.).

The line can also have a spatial character, which the drawer masters as he studies the form under lighting and environmental conditions. The essence and meaning of a spatial line is most easily understood by observing the master’s pencil in the process of his work: the line either strengthens or weakens or disappears completely, merging with environment; then it appears again and sounds with all the power of a pencil.

Beginning draftsmen, not understanding that a line in a drawing is the result of complex work on a form, usually resort to a flat and monotonous line. Such a line, which outlines the edges of figures, stones and trees with equal indifference, conveys neither form, nor light, nor space. Having absolutely no understanding of the issues of spatial drawing, such draftsmen pay attention, first of all, to the external outlines of an object, trying to mechanically copy it in order to then fill the contour with random spots of light and shadow.

But the flat line in art has its purpose. It is used in decorative paintings, wall paintings, mosaics, stained glass, easel and book graphics, poster - all works of a planar nature, where the image is linked to a certain plane of the wall, glass, ceiling, paper, etc. Here this line makes it possible to convey the image in a general way.

The deep difference between plane and spatial lines must be learned from the very beginning, so that in the future there will be no mixing of these different elements of the drawing.

Beginning draftsmen have another characteristic feature of drawing lines. They put too much pressure on the pencil. When the teacher demonstrates light line drawing techniques with their hand, they trace the lines with increased pressure. It is necessary to wean from this from the very first days bad habit. The requirement to draw with light, “airy” lines can be explained by the fact that at the beginning of the drawing we inevitably change or move something. And by erasing lines drawn with strong pressure, we spoil the paper. And, more often than not, a noticeable mark remains. The drawing looks untidy.

If you first draw with light lines, in the process of further work it is possible to give them a spatial character, sometimes strengthening, sometimes weakening.

Proportions

A sense of proportion is one of the main elements in the drawing process. Maintaining proportions is important not only in drawing from life, but also in decorative drawing, for example, for ornament, appliqué, etc.

Compliance with proportions means the ability to subordinate the sizes of all elements of the drawing or parts of the depicted object in relation to each other. Violation of proportions is unacceptable. Great importance is attached to the study of proportions. It is necessary to help the artist understand the mistake he has made or warn against it.

A person drawing from life must keep in mind that when same size horizontal lines appear longer than vertical ones. Some of the elementary mistakes of beginning artists include the desire to stretch objects horizontally.

If you divide a sheet into two equal halves, then Bottom part will always seem smaller. Due to this property of our vision, both halves of the Latin S seem equal to us only because its lower part is made larger in the typographic font. This is the case with the number 8. This phenomenon is well known to architects; it is also necessary in the work of an artist.

Since ancient times, great importance has been attached to instilling in the artist a sense of proportion and the ability to accurately measure quantities by eye. Leonardo da Vinci paid a lot of attention to this issue. He recommended games and entertainment that he invented: for example, he advised sticking a cane into the ground and, at a given distance, try to determine how many times the size of the cane fits within this distance.

Perspective

The Renaissance was the first to create a mathematically rigorous doctrine of how to convey space. Linear perspective(from Lat. Rers Ri ser e “I see through”“penetrating with my gaze”) is an exact science that teaches how to depict objects of the surrounding reality on a plane so that an impression is created the same as in nature. All construction lines are directed to the central vanishing point, corresponding to the viewer’s location. The shortening of the lines is determined depending on the distance. This discovery made it possible to build complex compositions in three-dimensional space. True, the retina of the human eye is concave, and straight lines do not appear to be drawn along a ruler. Italian artists They didn’t know this, so sometimes their work resembles a drawing.

Square perspective

a – frontal position, b – at a random angle. P – central vanishing point.

Lines receding into the depth of the drawing appear to converge at a vanishing point. Vanishing points are located on the horizon line. Lines receding perpendicular to the horizon converge at central vanishing point. Horizontal lines receding at an angle to the horizon converge at lateral vanishing points

Circle perspective

The upper oval is above the horizon line. For circles lying below the horizon line, we see their upper surface. The lower the circle, the wider it seems to us.

Already in the first tasks of drawing geometric bodies, children have to construct the perspective of rectangular objects and bodies of rotation - cylinders, cones.

F 1 and F 2 – lateral vanishing points lying on the horizon line.

Perspective of a cube and parallelepiped.

P is the vanishing point lying on the horizon line.

Chiaroscuro. Tone. Tonal relationships

The visible shape of an object is determined by its illumination, which is a necessary factor not only for the perception of the object, but also for its reproduction in the drawing. Light, spreading across the form, depending on the nature of its relief, has different shades - from the lightest to the darkest.

This is how the concept of chiaroscuro arises.

Chiaroscuro presupposes a specific light source and predominantly the same light color of the illuminated object.

Examining the illuminated cube, we notice that its plane facing the light source will be the lightest, called in the figure light; opposite plane - shadow; halftone we should call planes that are at different angles to the light source and therefore do not completely reflect it; reflex– reflected light falling on the shadow sides; glare– a small part of the surface in the light, completely reflecting the strength of the light source (observed mainly on curved surfaces), and finally, falling shadow.

In order of decreasing light intensity, all light shades can be conventionally arranged in the following sequence, starting with the lightest: highlight, light, halftone, reflex, own shadow, falling shadow.

Light reveals the shape of an object. Each form has its own character. It is limited to straight or curved surfaces or combinations of both.

An example of chiaroscuro on faceted surfaces.

If the shape is faceted, then even with a minimal difference in the aperture ratio of the surfaces, their boundaries will be definite (see illustration of a cube).

An example of chiaroscuro on curved surfaces.

If the shape is round or spherical (cylinder, ball), then light and shadow have gradual transitions.

So far we have talked about chiaroscuro of equally colored objects. The means of this chiaroscuro were limited to the second half of the 19th century century in the transfer of illuminated plaster casts and nude models.

At the end XIX and early XX centuries, during the period of development of a deeper understanding of color, painterly demands began to be placed on drawing.

Indeed, all the colorful diversity of nature, especially festive elegant costumes, diffused lighting that excludes clear chiaroscuro, the rendering of the environment - all this puts before the draftsman a number of tasks, as if of a picturesque nature, the solution of which is impossible with the help of chiaroscuro alone.

Therefore, the pictorial term entered into drawing - "tone".

If we take for example yellow and Blue colour, then being in the same lighting conditions, they will appear one light, the other dark. Pink seems lighter than burgundy, brown seems darker than blue, etc.

In a drawing it is impossible to “fully” convey the brightness of the flame and deep shadows on black velvet, since the tonal differences between pencil and paper are much smaller. But the artist must convey all the various tonal relationships using modest means of drawing. To do this, take the darkest thing in the depicted object or still life at full pencil strength, and leave the paper as the lightest. He places all other shadow gradations in tonal relationships between these extremes.

Drawers need to practice developing the ability to subtly distinguish gradations of lightness in full-scale productions. You need to learn to pick up small tonal differences. Having determined where there will be one or two lightest places and one or two darkest places, it is necessary to take into account the visual capabilities of the materials.

When completing training assignments, you must comply proportional dependence between the aperture ratio of several places in nature and the corresponding several parts of the drawing. At the same time, you need to remember that comparing the tones of only one place in nature with its image is the wrong method of work. All attention should be given to the method of working relationships. In the process of drawing, you need to compare 2 - 3 areas in terms of lightness in nature with the corresponding places in the image. After applying the desired tones, it is recommended to check.

Drawing Sequence

Modern drawing techniques provide for the 3 most general stages of working on a drawing: 1) compositional placement of the image on the plane of a sheet of paper and definition general forms; 2) plastic modeling of the form with chiaroscuro and detailed characterization of nature; 3) summing up. In addition, each drawing, depending on the tasks and duration, may have more or fewer overall stages, and each stage may also include smaller drawing stages.

Let's take a closer look at these stages of working on a drawing.

1). The work begins with the compositional placement of the image on a sheet of paper. You need to examine the nature from all sides and determine from which point of view it is more effective to place the image on the plane. The painter must familiarize himself with the nature and mark it characteristics, understand its structure. The image is outlined with light strokes.

When starting a drawing, first of all, they determine the ratio of the height and width of the model, after which they proceed to determine the sizes of all its parts. During work, you cannot change the point of view, since in this case the entire perspective construction of the drawing will be disrupted.

The scale of the objects depicted in the drawing is also determined in advance, and is not developed in the process of work. When drawing in parts, in most cases the nature does not fit on the sheet, it turns out to be shifted up or down.

Premature loading of the sheet with lines and spots should be avoided. The form is drawn very generally and schematically. The basic, generalized nature is revealed large shape. If this is a group of objects, you need to equate them to a single figure - generalize.

Having completed the compositional placement of the image on a sheet of paper, the basic proportions are established. In order not to be mistaken in proportions, you should first determine the ratio of large quantities, and then select the smallest ones from them. The teacher’s task is to teach how to separate the important from the secondary. So that the details do not distract the beginner’s attention from the main character of the form, you need to squint your eyes so that the form looks like a silhouette, like a general spot, and the details disappear.

2). The second stage is plastic modeling of the shape in tone and detailed elaboration of the drawing. This is the main and longest stage of work. Here, knowledge from the field of perspective and the rules of cut-off modeling are used.

When drawing, it is necessary to clearly understand the spatial arrangement of objects and the three-dimensionality of their structural structure, since otherwise the image will be flat.

While working on a perspective construction of a drawing, it is recommended to regularly check by comparing the abbreviations of the surfaces of volumetric forms, comparing them with the verticals and horizontals, which are mentally drawn through characteristic points.

After choosing a point of view in the drawing, a horizon line is drawn, which is at the eye level of the person drawing. You can mark the horizon line at any height of the sheet. This depends on the inclusion in the composition of objects or parts thereof that are located above or below the eyes of the painter. For objects located below the horizon, their upper surfaces are depicted in the figure, and for objects placed above the horizon, their lower surfaces are visible.

When you need to draw a cube or other object with horizontal edges standing on a horizontal plane, which is visible at an angle, then both vanishing points of its faces are located on the sides of the central vanishing point. If the sides of the cube are visible in the same perspective cuts, then their upper and lower edges are directed outside the picture to the lateral vanishing points. When the cube is in a frontal position, located at the horizon level, only one side of it is visible, which has the shape of a square. Then the ribs receding into the depth are directed to the central vanishing point.

When we see 2 sides of a horizontally lying square in a frontal position, then the other 2 are directed to the central vanishing point. The square pattern in this case looks like a trapezoid. When depicting a horizontal square lying at an angle to the horizon line, its sides are directed towards the lateral vanishing points.

In perspective contractions, circles look like ellipses. This is how bodies of rotation are depicted - a cylinder, a cone. The higher or lower the horizontal circle is from the horizon line, the more the ellipse approaches the circle. The closer the depicted circle is to the horizon line, the narrower the ellipse becomes - the minor axes become increasingly shorter as they approach the horizon.

On the horizon line, both squares and circles look like one line.

The lines in the drawing depict the shape of the object. The tone in the drawing conveys light and shadows. Chiaroscuro helps to reveal the volume of an object. By constructing an image, for example a cube, according to the rules of perspective, the painter thereby prepares the boundaries for light and shadows.

When drawing objects with rounded surfaces, children often experience difficulties that they cannot cope with without the help of a teacher.

Why is this happening? The shape of the cylinder and ball remains unchanged when rotated. This complicates the analytical work of a novice draftsman. Instead of the volume of a ball, for example, he draws a flat circle, which he then shades from contour line. Light and shadow relationships are given as random spots - and the ball appears to be just a dirty circle.

On the cylinder and the ball, light and shadow have gradual transitions, and the deepest shadow will not be on the edge of the shadow side, which carries the reflex, but slightly moved away in the direction of the illuminated part. Despite the apparent brightness, the reflex must always obey the shadow and be weaker than the halftone, which is part of the light, that is, it must be lighter than the shadow and darker than the halftone. For example, the reflex on the ball should be darker than the halftone in the light.

When drawing a group setting of geometric bodies located at different distances from a light source incident on the side, one should keep in mind that as they move away from it, the illuminated surfaces of the bodies lose their luminosity.

According to the laws of physics, the intensity of light is inversely proportional to the square of the distance of the object from the light source. Taking into account this law when placing light and shadow, we should not forget the fact that close to the light source the contrasts of light and shadow intensify, and with distance they weaken.

When all the details are drawn and the drawing is modeled in tone, the process of generalization begins.

3). The third stage is summing up. This is the last and most important stage of working on the drawing. At this stage, we summarize the work done: we check the general condition of the drawing, subordinating the details to the whole, and clarify the drawing in tone. It is necessary to subordinate lights and shadows, highlights, reflections and halftones to the general tone - we must strive to bring to real sound and completion the tasks that were set at the very beginning of the work. Clarity and integrity, the freshness of the first perception should already appear in a new quality, as a result of long and hard work. On final stage work, it is advisable to return again to a fresh, original perception.

Thus, at the beginning of work, when the draftsman quickly outlines on a sheet of paper general form nature, he goes through synthesis - generalization. Further, when a careful analysis of the form is carried out in a generalized form, the draftsman enters the path of analysis. At the very end of the work, when the artist begins to subordinate the details to the whole, he again returns to the path of synthesis.

The work of generalizing a form is quite difficult for a beginning draftsman, because the details of the form attract his attention too much. Individual, insignificant details of an object observed by the draftsman often obscure the holistic image of nature, do not make it possible to understand its structure, and, therefore, interfere with the correct depiction of nature.

So, consistent work on a drawing develops from defining the generalized parts of an object through a detailed study of complex details to a figurative expression of the essence of the depicted nature.

Note: This manual describes the image of a composition made from frames of geometric bodies that is quite complex for younger schoolchildren. It is recommended to first draw the frame of one cube, one parallelepiped or cone. Later - a composition of two geometric bodies of simple shape. If the training program is designed for several years, it is better to postpone the image of a composition of several geometric bodies for subsequent years.

3 stages of working on a drawing: 1) compositional placement of the image on the plane of a sheet of paper and determining the general nature of the form; 2) construction of frames of geometric bodies; 3) creating the effect of depth of space using different line thicknesses.

1). The first stage is the compositional placement of the image on the plane of a sheet of paper and determining the general nature of the form. Starting the drawing, determine the ratio of the height and width of the overall composition of all geometric bodies as a whole. After which they move on to establishing the sizes of individual geometric bodies.

During work, you cannot change the point of view, since in this case the entire perspective construction of the drawing will be disrupted. The scale of the objects depicted in the drawing is also determined in advance, and not during the work. When drawing in parts, in most cases the nature either does not fit on the sheet, or turns out to be shifted up, down or to the side.

At the beginning of drawing, the form is drawn very generally and schematically. The basic, generalized nature of the large form is revealed. A group of objects needs to be equated to a single figure - generalized.

2). The second stage is the construction of frames of geometric bodies. It is necessary to clearly imagine the spatial arrangement of objects, their three-dimensionality, how the horizontal plane is located on which geometric bodies stand relative to the level of the drawer’s eyes. The lower it is, the wider it appears. In accordance with this, all the horizontal edges of geometric bodies and the circles of bodies of rotation look more or less wide to the painter.

The composition consists of prisms and bodies of rotation - a cylinder, a cone, a ball. For prisms, it is necessary to find out how they are located relative to the drawer - frontally or at an angle? A body located frontally has 1 vanishing point - in the center of the object. But more often, geometric bodies are located at a random angle relative to the person drawing. Horizontal lines receding at an angle to the horizon line converge atlateral vanishing points located on the horizon line.

Perspective of a parallelepiped at a random angle.

Construction of a body of rotation - a cone.

All geometric bodies are constructed in this way.

3) Third, final stage- creating the effect of depth of space using different line thicknesses. The drawer sums up the work done: checks the proportions of geometric bodies, compares their sizes, checks the general condition of the drawing, subordinating the details to the whole.

Topic 2. Drawing of plaster geometric bodies:

cube, ball (black and white modeling).

Note: This manual describes the image of a plaster cube and a ball on one sheet. You can make a drawing on two sheets. For tasks involving cut-off modeling, illumination by a closely located lamp, spotlight, etc. is highly desirable. on one side (usually the window side).

Cube

1). The first stage is the compositional placement of the image on the plane of a sheet of paper. The plaster cube and ball are drawn sequentially. Both are illuminated with directional light. The upper half of the sheet of paper (A3 format) is reserved for the cube, the lower half for the ball.

The image of the cube is composed together with the falling shadow in the center of the upper half of the sheet. The scale is chosen so that the image is neither too large nor too small.

2). The second stage is building a cube.

It is necessary to determine the location of the horizontal plane on which the cube stands and the horizontal edges relative to eye level, their width. How is the cube positioned - frontally or at an angle? If viewed from the front, the cube has 1 vanishing point at the eye level of the drawer - in the center of the cube. But more often the edges are located at a random angle relative to the person drawing. Horizontal lines receding at an angle to the horizon converge atlateral vanishing points located on the horizon line.

Building a cube

The drawer must find out which of the side faces of the cube seems wider to him - on this face, the horizontal lines are directed towards the vanishing point of the hollower one, and the vanishing point itself is located further from the depicted object.

By constructing a cube according to the rules of perspective, we thereby prepared the boundaries for light and shadows. Examining an illuminated cube, we notice that its plane facing the light source will be the brightest, called light; the opposite plane is a shadow; halftone refers to planes that are at angles to the light source and therefore do not fully reflect it; reflex - reflected light falling on the shadow sides. The falling shadow, the contour of which is constructed according to the rules of perspective, is darker than all the surfaces of the cube.

Black and white cube modeling

You can leave the surfaces of the cube or the sheet of paper on which it stands, illuminated by direct, bright light, white. The remaining surfaces need to be shaded with light, transparent shading, gradually intensifying it on the light separation lines (edges of the cube where the illuminated and shadow edges meet). In order of decreasing light intensity, all light shades can be conventionally arranged in the following sequence, starting with the lightest: highlight, light, halftone, reflex, own shadow, falling shadow.

To summarize, we check the general condition of the drawing, clarifying the drawing in tone. It is necessary to subordinate lights and shadows, highlights, reflexes and halftones to the general tone, trying to return to the clarity, integrity and freshness of the first perception.

Ball

1). The first stage is the compositional placement of the image of the ball along with the falling shadow in the center of the lower half of the sheet of paper. The scale is chosen so that the image is neither too large nor too small.

Construction of the ball

2). The light and shadow modeling of a ball is more complex than that of a cube. Light and shadow have gradual transitions, and the deepest shadow will not be on the edge of the shadow side, which carries the reflex, but slightly moved away in the direction of the illuminated part. Despite the apparent brightness, the reflex must always obey the shadow and be weaker than the halftone, which is part of the light, that is, it must be lighter than the shadow and darker than the halftone. For example, the reflex on the ball should be darker than the halftone in the light. Close to the light source, the contrasts of light and shadow intensify, and as they move away, they weaken.

Black and white modeling of the ball

3). When all the details are drawn and the drawing is carefully modeled in tone, the process of generalization begins: we check the general condition of the drawing, refining the drawing in tone. Trying again to return to the clarity, integrity and freshness of the first perception.

Topic 3. Drawing a still life from plaster

geometric bodies (black and white modeling).

Note: This tutorial describes the image complex composition from gypsum geometric solids. If the training program is designed for several years, it is better to postpone the image of such a composition for subsequent years. It is recommended to first depict the composition of two geometric bodies of simple shape. Later you can move on to a more complex composition. For a task on cut-off modeling, illumination by a closely located lamp, spotlight, etc. is highly desirable. on one side (usually the window side).

3 stages of working on a drawing: 1) compositional placement of the image on the plane of a sheet of paper and determining the general nature of the form; 2) construction of geometric bodies; 3) modeling of forms with tone.

1). The first stage is the compositional placement of images of geometric bodies on the plane of a sheet of A3 paper. Starting the drawing, determine the ratio of the height and width of the overall composition of all geometric bodies as a whole. After which they move on to establishing the sizes of individual geometric bodies.

The scale of the objects depicted in the drawing is determined in advance. Premature loading of the sheet with lines and spots should be avoided. Initially, the shape of geometric bodies is drawn very generally and schematically.

Having completed the compositional placement of the image on a sheet of paper, the basic proportions are established. In order not to make mistakes in proportions, you should first determine the ratio of large quantities, and then smaller ones.

2). The second stage is the construction of geometric bodies. It is necessary to clearly imagine the spatial arrangement of objects, how the horizontal plane is located on which geometric bodies stand relative to the level of the drawer’s eyes. The lower it is, the wider it appears. In accordance with this, all the horizontal edges of geometric bodies and the circles of bodies of rotation look more or less wide to the painter.

The composition consists of prisms, pyramids and bodies of rotation - a cylinder, a cone, a ball. For prisms, it is necessary to find out how they are located relative to the drawer - frontally or at an angle? A body located frontally has 1 vanishing point - in the center of the object. But more often, geometric bodies are located at a random angle relative to the person drawing. Horizontal lines receding at an angle to the horizon line converge at lateral pointsright away located on the horizon line. In bodies of rotation, horizontal and vertical axial lines are drawn, and distances equal to the radius of the depicted circle are laid out on them.

Geometric bodies can not only stand or lie on the horizontal plane of the table, but also be at a random angle in relation to it. In this case, the direction of inclination of the geometric body and the plane of the base of the geometric body perpendicular to it are found. If a geometric body rests on a horizontal plane with 1 edge (prism or pyramid), then all horizontal lines converge at the vanishing point lying on the horizon line. This geometric body will have 2 more vanishing points that do not lie on the horizon line: one on the line of direction of the body’s inclination, the other on a line perpendicular to it, belonging to the plane of the base of this geometric body.

3). The third stage is modeling the shape with tone. This is the longest stage of work. Here, knowledge of the rules of cut-off modeling is applied. By constructing geometric bodies according to the rules of perspective, the student thereby prepared the boundaries for light and shadows. The planes of bodies facing the light source will be the lightest, called light; opposite planes - shadow; halftone refers to planes that are at angles to the light source and therefore do not fully reflect it; reflex - reflected light falling on the shadow sides; and, finally, a falling shadow, the contour of which is constructed according to the rules of perspective.

The surfaces of the prisms, pyramids, or sheets of paper on which they stand, illuminated by direct, bright light, can be left white. The remaining surfaces need to be shaded with light, transparent shading, gradually intensifying it on the light separation lines (edges of geometric bodies where the illuminated and shadow edges meet). In order of decreasing light intensity, all light shades can be conventionally arranged in the following sequence, starting with the lightest: highlight, light, halftone, reflex, own shadow, falling shadow.

In a ball, light and shadow have gradual transitions, and the deepest shadow will not be on the edge of the shadow side, which carries the reflex, but slightly moved away in the direction of the illuminated part. Despite the apparent brightness, the reflex must always obey the shadow and be weaker than the halftone, which is part of the light, that is, it must be lighter than the shadow and darker than the halftone. For example, the reflex on the ball should be darker than the halftone in the light. Close to the light source, the contrasts of light and shadow intensify, and as they move away, they weaken.

White is left with only a highlight on the ball. The remaining surfaces are covered with light and transparent shading, applying strokes to the shape of the ball and the horizontal surface on which it lies. The tone builds up gradually.

As they move away from the light source, the illuminated surfaces of bodies lose their luminosity. Close to the light source, the contrasts of light and shadow intensify, and as they move away, they weaken.

4). When all the details are drawn and the drawing is modeled in tone, the process of generalization begins: we check the general condition of the drawing, clarifying the drawing in tone.

It is necessary to subordinate lights and shadows, highlights, reflexes and halftones to the general tone, trying to return to the clarity, integrity and freshness of the first perception.

Literature

Main:

Rostovtsev N. N. “Academic drawing” M. 1984

“School of Fine Arts” vol. 2, M. “Iskusstvo” 1968

Beda G.V. “Fundamentals of visual literacy” M. “Enlightenment” 1988

“School of Fine Arts” 1-2-3, “Fine Arts” 1986

"Drawing Basics", " Brief dictionary artistic terms" - M. "Enlightenment", "Title", 1996

Additional:

Vinogradova G. “Drawing lessons from life” - M., “Enlightenment”, 1980

Library " Young artist»Drawing, tips for beginners. Issue 1-2 – “Young Guard” 1993

Kirtser Yu. M. “Drawing and painting. Textbook" - M., 2000

Kilpe T. L. “Drawing and Painting” - M., Publishing House “Oreol” 1997

Avsisyan O. A. “Nature and drawing from idea” - M., 19885

Odnoralov N.V. “Materials and tools, equipment in fine arts" - M., "Enlightenment" 1988

Applications

Topic 1. Construction of frames of geometric bodies

Topic 2. Drawing of plaster geometric bodies: cube, ball

Topic 3. Drawing a still life from plaster geometric bodies

Explanatory note _____________________________________ 2

Introduction ________________________________________________ 3

Topic 1. Construction of frames of geometric bodies _____________ 12

Topic 2. Drawing of gypsum geometric bodies: cube, ball (black and white modeling) __________________________________________ 14

Topic 3. Drawing a still life from plaster geometric bodies (black and white modeling) _____________________________________________ 17

Applications _____________________________________________________ 21

84

Rice. 90. Drawing of a composition of geometric bodies specified in orthogonal

projections

Topic 2. Drawing a composition from geometric shapes by imagination

The applicant is asked to come up with a set of simple geometric bodiescomposition and depict it on a sheet of paper. A set of 4-5 figures, their proportions and scales the ratios are given. The task program is highlighted at the beginning of the exam in the form drawing of two orthogonal projections of the bodies from which the composition. It is allowed to cut one body into another, add and repeat 1- 2 tel.

6 hours are allotted to complete the task. The work is carried out on an A3 sheet of paper (30x42cm), issued admissions committee and supplied with a stamp. Surnamethe author is not written on the sheet, and works with the surname and any notes are not evaluated.

PERFORMANCE EVALUATION CRITERIA

The main purpose of this task is to assess the level of development of volumetric-spatialimagination of the applicant, that is, the ability to imagine complex volumes in variousangles, under different lighting and transfer this to the plane of the sheet. Should focus not on searching for a particularly complex compositional idea, but on expressive and competent presentation of an idea in the form of a finished drawing.

When evaluating work, the following is taken into account:

1. Correct compositional placement of the drawing on the sheet.

2. Competent representation of geometric bodies and their joints, taking into account
linear perspective.

3. Tonal reproduction of proportions.

4. Tonal elaboration - identification with the help of well-constructed
shadows of the shape of objects, transmission by enhancing (decreasing) contrasts
the degree of distance of objects from the viewer, general graphic culture.

5. The artistic quality of the composition, the integrity of the author's plan.
You need to understand that the drawing is evaluated as an artistic whole, and not

its individual components, and these criteria are used synthetically, complementing each other.

At the beginning of work on the same examination paper where the final one will bedrawing, several search sketches are made. Preferably immediatelydetermine the place of the final large drawing and sketches, that is, think about composition of the sheet as a whole,

In 2-4 small sketches, options for combining given bodies are outlined.It is important to understand that the composition is not interesting due to its complex intersectiontwo bodies (for example, a cone and a cylinder) with random adjacencies of other figures, and the organization of all elements is one whole. In sketches there is a search for commonality expressive silhouette, possible compositional ideas are identified -the formation of a composition around the core - one of their bodies, the development of a composition according toaxis - vertical or directed away from the viewer, the intersection of twocompositional axes at right or other angles, etc. The composition can stand on an imaginary plane or “hang” in space. 86

P. Refinement of the composition

Choosing the most interesting option, you need to imagine it with different sides Andfind the most expressive point of view for him in such a way that from one the sides of the objects, without overly obscuring one another, were clearly legible, their places incisions or abutments were clearly visible and emphasized the shape of objects, and with on the other side, the interesting silhouette and rhythm of the planes were preserved, expressing the main compositional concept. It is advisable to avoid random coincidencescontours of objects.

Having clarified your option based on this and chosen the most convincing angle,You can move on to the main drawing.

///. Construction of the main drawing (Fig. 92, 93)

First of all, you need to clarify the size of the future image. The drawing should not be too small, “get lost” in the sheet, which creates the impression of randomness and uncertainty, and should not be too large, “climbing” onto the edges;the imaginary center of gravity of the depicted composition should be placed approximately at the geometric center of the sheet. Outlining the extreme points with light lines general outline, let's move on to drawing the details.

It is advisable to immediately clarify the ratios of milestone volumes specified in the assignment,designate large divisions of the composition and the location of the main axes - this iswill save the further course of the drawing from strong corrections. To get it rightto convey the relative position of the figures, you need to imagine not only the visible ones, but also invisible parts of objects - therefore, the image of invisible lines and construction lines. It is important to know the laws of linear perspective - imagine a line horizon, vanishing points of parallel lines, picture plane. At the figuresrotation, you need to outline the axes and carefully draw the ellipses, rememberingtheir “opening” increases as they move away from the horizon. Special attentionyou need to pay attention to the cutting lines of the figures, in order to draw them correctly, you should represent the planes and surfaces that form the form, and the laws of their intersection. Despite all the care in drawing visible and invisible lines, it is impossible forget that we are not drawing lines, but volumes, and we need to constantly monitor and clarify the proportions of objects (for example, the faces of a cube should appear to be located at least from different angles, but identical squares; the slab shouldlook the same thickness everywhere, etc.) and check the relationships of objects.To do this, you should, highlighting the visible lines, often move away and compare objects between themselves.

IV. Final work (Fig. 94)

The main task of this stage is to achieve a solid and vivid perception of the drawing.First of all, you need to enhance the impression of volume and convey the degreedistance of objects from the viewer. While maintaining the construction lines, you need to strengthenvisible lines so that their contrast weakens from the foreground to rear

Light and shadow elaboration should be conditional and, subject to author's intention, emphasize the main thing in the composition. Own boundaries

shadows will help reveal the nature of bodies of rotation, and general light or shadow unitesparallel or perpendicular planes of rectangular shapes. BasedThis is why you should choose the direction of the light. Light can come from above, emphasizing horizontal planes, or slide along the side surfaces of the composition, revealing all the protrusions. Falling shadows are optional and are done only if the drawing is not clear without them.

The boundaries of own shadows must be built on spherical volumesIt is desirable to imagine the invisible part of these boundaries. No need to strive forcomplex gradations of tone, tonal elaboration should maintain a conventionalcharacter, maintaining large light-shadow relationships. The tone of the shadows should belight, intensifying only towards the boundaries of chiaroscuro, emphasizing the edges of objects.

When finishing work, you should consciously place emphasis - check the generalimpression of the sheet and, if necessary, weaken the preliminary sketches by highlightingmain drawing; in the main drawing, to more clearly indicate the distance of objects from the viewer, enhancing the contrasts in the foreground.

"4H":.,. ■

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Rice. 91

68

Rice. 93

B. Construction of bodies with a regular hexagon at the base

Rice. 95

B. The composition is formed according totwo perpendicular axes - vertical and horizontal

D. The composition is formed according to twohorizontal axes;intersecting at an angle of 45

Rice. 97. Examples of various compositional ideas

Rice. 101

Rice. 103

Section III . Drawing of a human head from a sculptural model.

The human head is a very interesting subject to draw. On the one side,this is a plastically complex volumetric form, and on the other hand, the portrait nature of the model makes it easy to spot errors in similarity.

The shape of the head combines the volumetric design common to all models, due to the unified anatomical structure of the skull and muscles, and portrait individuality. In the first stages of learning how to draw a head, the main focus is should be given to the general scheme for constructing a symmetrical volume, the generalproportional structure, general anatomical patterns (drawing of the skull,anatomical head, sketches of heads), and at the final stage of trainingThe emphasis is on identifying the individual characteristics of a particular head. Topic 1. Anatomical structure of the human head

In general, the head has a symmetrical ovoid shape, paired partswhich (eyes, ears, cheekbones, etc.) can be mentally connected with spicyparallel lines. When viewed from above or below, these lines will go to a common vanishing point on the horizon line. If you mentally draw horizontal section lines, you will get ellipses, the opening of which will also depend onperspective (Fig. 106). ■

The shape of the head can be divided into a larger brain region andfacial section (the so-called “mask”) (Fig. 105). Skull being the basehead, consists of six main bones: the frontal, two parietals, two temporal andoccipital At the places where they connect, the frontal and parietal tubercles protrude. The frontal bone forms the upper edge of the eye sockets, above which the brow ridges are located.and brow ridges. The lower edge of the borders is formed by the auditory bones withextending back to the ear openings, auditory arches. At the base of the cranialbox contains the horseshoe-shaped bone of the lower jaw. In the anatomical headyou should pay attention to the powerful chewing muscles coming from the cornerslower jaw under the auditory bones.

Analysis anatomical structure head, characteristic turns and protrusionsbones allows you to imagine the general design scheme with the front, twolateral (temporal), occipital, parietal and lower chin sides. Such a scheme should not replace complex head plastic surgery, but should help to see the directions of the main planes and subordinate the parts to them (Fig. 107).

To understand the design of the head, you should draw a skull and anatomical head, as well as their generalized models (cuts), where the planes forminghead, accentuated (Fig. 109-110).

In order not to make serious mistakes, you need to know the general proportionalhead structure and average canonical proportions. The ratio of brain andThe facial sections determine the position of the bridge of the nose. Horizontal linepassing through the bridge of the nose usually divides the head into two parts of equal height.The face is divided into three equal parts: the first - from the hairline to the ridges of the eyebrows,the second - from the eyebrow to the base of the root of the nose, the third - from the base of the nose to the bottom chin In this case, you need to focus on the skeleton, since eyebrows can be thick, drooping or raised, and the tip of the nose may be higher or lower grounds. At a third of the distance from the eyebrow to the base of the nose there is an eye line, 102

and at a third of the distance from the base of the nose to the chin there is a cut line for the mouth.The distance between the eyes is equal to the length of the eye. Between the ear and the edge of the eye you can fit almost two ears in width. The ear lies horizontally on the same level asnose and approximately equal to it in height. Knowing the proportional structure, it is easy to outline the divisions of the head, and comparing with the canonical proportions - the proportions of the specific head being drawn, it is easier to see it individual characteristics, (Fig. 108).

The graph on the left represents growth. The graph on the right means a fall. It just so happened. And, accordingly, in a composition, a diagonal line drawn from the lower left corner to the upper right is perceived better than a line drawn from the upper left corner to the lower right.

Closed and open composition

In a closed composition, the main directions of the lines tend to the center. This composition is suitable for conveying something stable and motionless.

The elements in it do not tend to go beyond the plane, but seem to be locked in the center of the composition. And the gaze from any point in the composition tends to this center. To achieve this, you can use a compact arrangement of elements in the center of the composition, a frame. The arrangement of elements (in the image - geometric shapes) so that they all point to the center of the composition.

An open composition, in which the directions of the lines emanate from the center, gives us the opportunity to mentally continue the picture and take it beyond the plane. It is suitable for conveying open space and movement.

Golden ratio rule

Different arrangements of elements on a plane can create a harmonious or inharmonious image. Harmony is a feeling and concept of correct location elements are very intuitive. However, there are several rules that are not at all intuitive.

The arrangement of simple geometric shapes in the image on the left looks much more harmonious. Why?

Harmony- this is coherence. A single whole in which all elements complement each other. Some kind of unified mechanism.

The largest such mechanism is the world around us, in which all elements are interconnected - animals breathe air, consume oxygen, exhale carbon dioxide, plants use its carbon and solar energy for photosynthesis, returning oxygen. Some animals feed on these plants, others regulate the number of plants that feed on them, thereby saving the plants, the water evaporates to fall as precipitation and replenish the supplies of rivers, oceans, and so on...

There is nothing more harmonious than nature itself. Therefore, the understanding of harmony comes to us from her. And in nature, a huge number of visual images obey two rules: symmetry And golden ratio rule.

I think you know what symmetry is. What is the golden ratio?

Golden ratio can be obtained by dividing a segment into two unequal parts in such a way that the ratio of the entire segment to the larger part is equal to the ratio of the larger part of the segment to the smaller one. It looks like this:

The parts of this segment are approximately equal to 5/8 and 3/8 of the entire segment. That is, according to the rule of the golden ratio, the visual centers in the image will be located like this:

Three thirds rule

This drawing does not follow the rule of the golden ratio, but creates a feeling of harmony.

If we divide the plane on which our geometric figures are located into nine equal parts, we will see that the elements are located at the intersection points of the dividing lines, and the horizontal stripe coincides with the lower dividing line. In this case, the three-thirds rule applies. This is a simplified version of the golden ratio rule.

The perspective of the composition is carried out according to individual instructions. Number individual assignment corresponds to the serial number according to the list in the group journal. Individual tasks in table No. 3

Table No.

Instructions for completing SHEET 1

Before making a perspective image of a composition of geometric bodies, you must first draw up the composition itself, that is, determine the relative position of the objects, their position relative to the main line of the picture, and the distance from the plane of the picture. Depending on the composition you have created, you can choose the position of the point of view (height of the point of view and distance). The point of view distance is chosen equal to one size of the composition. The height of the point of view is chosen to be either slightly lower or slightly higher than the height of the tallest object.

The individual task determines the shape of the objects, their size, the angle of rotation to the picture plane, and the distance from the picture plane. It is required to construct a perspective composition of faceted bodies, one of which is located frontally in relation to the picture plane, the other with a given angle of rotation to the picture, and one body of rotation.

When making a perspective image of a composition of geometric bodies, it makes sense to carry out preparatory work - to build a plan for the future composition. You can simply draw this plan or, by cutting out the contours of the plans of geometric bodies from paper and moving them along the plane, you can choose the best compositional solution, as well as determine the position of objects on the object plane and the distance between them. This will determine the overall overall size of the composition, which will determine the position of the height of the point of view, and the distance (the distance from the observer to the picture).

An example of SHEET 1 - a perspective image of a composition of geometric bodies is shown on ( rice. 91)

Interior perspective

The interior is the internal view of the room as a whole or its individual parts. In the practice of building interiors, various ways of depicting interiors are known, depending on the task that the artist sets for himself. This manual discusses one of the ways to build an interior using perspective scales. Depending on the location of the walls of the room relative to the painting, the image of the interior can be frontal or angular. If one of the walls of the room is located parallel to the picture, then such an image is called a frontal perspective of the interior. If the walls of the room are at an angle to the picture plane, then such an image is called an angular perspective of the interior.