We will analyze with you the basics of classical composition.

Volumetric drawing geometric shapes associated with the laws of perspective.

1. Consider the drawing of a cube. Pay attention to the fact that its parallel horizontal sides in the figure, unlike the drawing, are not completely parallel, but slightly at an angle to each other, because. they are affected by prospective reduction. Even if you do not see this on a small object, say, in a still life, you still need to draw with this in mind, because. otherwise in the drawing, the viewer's eye will perceive it as a mistake.

2. On large objects, as in this figure (for example, on houses), the perspective reduction is clearly visible. Here you see the horizon line and the so-called vanishing points: points on the horizon line where parallel lines visually converge. In the drawing of small objects, we do not draw either a horizon line or a vanishing point, but we mean them and mentally build a perspective reduction "by eye" or, if it is difficult in a still life, for example, we build perspective lines to the very edge of the sheet, and the vanishing point - adjust mentally.

3. Let's draw a square in a horizontal plane. Segments C and W are equal, and segment A, which is farther from us, will be less than a segment AT.

4. Now we connect the vertices of the square. As a result, visually there is a feeling that it lies on a plane.

5. Let's draw a circle lying on a horizontal plane - according to the same principle. Visually, it is an oval. When you draw various cylindrical objects, for example, jugs, cups, you will need to start by building just such an oval. Its upper half is shorter than the lower. Pay attention to the left and right edges: they should be rounded, there should not be any corners.

Now let's draw a parallelepiped. We build a rhombus, from it we postpone the vertical axis of symmetry. On it we put another rhombus on top. If we look at the box from above, then the horizon line is above the object. Therefore, its lower horizontal plane will be visually wider than the upper one. Not by much if the subject is small, but still in a competent drawing this must be taken into account. That is, A< B, С < D.

7. Draw the sides of the figure.

8. We emphasize the volume with chiaroscuro: we shade one shadow plane, strengthening the stroke along the edge of the border with the illuminated plane.

9. If we draw a cube frontally, with the horizon line G running along the middle of the cube, then we will not see any perspective cuts, but we will see only one side of it.

In the sixteenth pencil drawing lesson, we will learn how to draw a cube and a pyramid correctly.

Simple drawing techniques using geometric shapes for preschool children

This master class is designed for children from 3 to 5 years old.

Targets and goals:

To develop elementary drawing skills in children, to learn to build the process of doing work in stages, using geometric shapes.

The study of geometric shapes in drawing, their location in space and scaling.

To instill in children an interest in drawing, creativity and artistic taste.

Development of thinking, attention and logical design in drawing.

Drawing at preschool age

Visual work is a safe and interesting activity for a child.

Trying to draw, the child does not try to depict the object as it looks, but depicts the main idea, the internal model. As a result, he schematically breaks the subject down into its main elements. The content of the picture is dominated by graphic templates borrowed from adults (house, sun, car, etc.)

drawing, especially childhood, makes it possible to expand the children's horizons, give the opportunity to compare what they saw, analyze, draw conclusions and try to independently transfer the result to paper, in the form of a drawing. With the help of a drawing, a child can convey not only visual characteristics (color, shape, size and placement in space), but also his vision of the image.

Drawing in childhood calms, arouses a keen interest in work and achieving the desired result, forms perseverance in children and, of course, develops artistic taste.

The process of doing work.

Step 1: Prepare a place for work and the tools necessary for its implementation. (A glass of water, a brush, gouache of the required color, a pencil and a blank sheet of paper).

I suggest you draw a pear, traditional techniques for beginners.

Step 2: On a blank sheet of paper, in its upper part, draw an oval in the center of our sheet. (You can choose the scale yourself, which one you need)

Step 3: Then, finding on the first oval, draw another one, but place it horizontally fig. 3 (as shown in the figure). Try to apply the lines with jerky movements and without pressing the pencil, so that in the future there would be an opportunity to correct the imperfections. (So ​​we explain to children)

Step 4: Then we connect the two ovals, with streamlined lines, giving the sketch a natural, natural shape.

Here we have something similar to a pear.

Step 5: Now we can erase the construction lines of our drawing (i.e. ovals) with an eraser and draw the missing elements.

Step 6: Now let's give our pear a natural, color shade.

Let's start with the background. To make our drawing look more expressive.

Step 7: We paint over the pear with yellow gouache, giving it a natural shade and adding a little green to create a volume effect.

Step 8: And at the final stage, we finish drawing additional elements (stalk, leaf, etc.).

Here's what we got!

With the presented drawing technique, you can draw a lot, and on different topics, here are a few options for works drawn using geometric shapes.

The drawings are shown below.

MBOUDO Irkutsk CDT

Toolkit

Picture geometric bodies

Teacher of additional education

Kuznetsova Larisa Ivanovna

Irkutsk 2016

Explanatory note

This manual "Drawing of geometric bodies" is intended for teachers working with children school age. From 7 to 17 years old. Can be used both when working in additional education, and in the course of drawing at school. The manual is compiled on the basis of the author's study guide"Drawing of geometric bodies" intended for first-year students of the specialty Arts and Crafts and Folk Crafts and Design (not published).

The drawing of geometric bodies is an introductory material for teaching drawing. The introduction reveals the terms and concepts used in the drawing, the concepts of perspective, the procedure for performing work on the drawing. 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 fine literacy, teaching a realistic depiction of nature, that is, understanding and depicting a three-dimensional form on a sheet plane. The main form of education is drawing from a stationary nature. He teaches to correctly convey visible objects, their features, properties, gives children the necessary theoretical knowledge and practical skills.

The tasks of teaching drawing from nature:

To instill the skills of consistent work on a drawing according to the principle: from general to particular

To acquaint with the basics of observational, i.e., visual perspective, the concept of light and shade relations

Develop technical drawing skills.

In the drawing classes, work is carried out on the education of a complex of qualities necessary for an artist:

- eye placement

The development of "firmness of the hand"

The ability to see clearly

Ability to observe and remember what is seen

The sharpness and accuracy of the eye, etc.

This manual examines in detail one of the first topics of drawing from nature - “Drawing of geometric bodies”, allowing you to study in detail the shape, proportions, structural structure, spatial relationships, perspective contractions of geometric bodies and the transfer of their volume using light and shade ratios. Learning tasks are considered - layout on a sheet of paper; construction of objects, transfer of proportions; from through drawing, to the transfer of volume by tone, the shape of objects to reveal light, penumbra, shadow, reflex, glare, full tonal solution.

Introduction

Drawing from nature

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

The laws and rules of drawing are assimilated as a result of a conscious attitude to work from nature. Each touch of the pencil to the paper must be thought out and justified by the feeling and understanding of the real form.

An educational drawing should give, perhaps, a more complete picture of nature, its form, plasticity, proportions and structure. It should be considered, first of all, as a cognitive moment in learning. In addition, knowledge of the features 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 either sharp or obtuse, a circle sometimes looks like an ellipse; the pencil is larger than the house, and so on.

Perspective not only explains the mentioned optical phenomena, but also equips the painter with the techniques of spatial representation of objects in all turns, positions, and also at various degrees of remoteness 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 external view, the external outlines of the object.

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

For a better understanding of the form, before proceeding to the drawing, it is necessary to consider nature from various angles. The painter is encouraged 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 nature, which is more complex in design.

The construction, or structure, of an object means the mutual arrangement and connection of its parts. The concept of "construction" is applicable to all objects created by nature and human hands, starting with the simplest household items and ending with complex forms. A drawing person needs to be able to find patterns in the structure of objects, to understand their shape.

This ability develops gradually in the process of drawing from nature. The study of geometric bodies and objects close to them in their form, and then objects more complex in structure, obliges the painters to consciously relate to drawing, to reveal the nature of the design of the depicted nature. So, the lid, as it were, consists of a spherical and cylindrical neck, a funnel is a truncated cone, etc.

Line

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

It can be flat, monotonous. In this form, it mainly has an auxiliary purpose (this is the placement of a drawing on a sheet, a sketch of the general outline of nature, the designation of proportions, etc.).

The line can also have a spatial character, which the painter masters as he studies the form in lighting and environmental conditions. The essence and meaning of the spatial line is easiest to understand by watching the master's pencil in the process of his work: the line either intensifies, then weakens or completely disappears, merging with environment; then it reappears and sounds at the full power of the pencil.

Beginning draftsmen, not realizing that the line in the drawing is the result of complex work on the form, usually resort to a flat, monotonous line. Such a line, with the same indifference delineating the edges of figures, stones and trees, conveys neither form, nor light, nor space. Completely unaware of the issues of spatial drawing, such draftsmen pay attention, first of all, to the external outlines of the object, trying to mechanically copy it, in order to then fill the contour with random spots of light and shadow.

But the planar line in art has its purpose. It is used in decorative painting, wall paintings, mosaics, stained-glass windows, easel and book graphics, posters - 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 gives the ability to generalize the image.

The profound difference between planar and spatial lines must be learned from the very beginning, so that in the future there will be no confusion of these various elements of the drawing.

Beginning draftsmen have another characteristic feature of drawing lines. They put too much pressure on the pencil. When the teacher shows with his hand the techniques of drawing with light lines, they trace the lines with increased pressure. It is necessary from the very first days to wean from this bad habit. You can explain the requirement to draw with light, “airy” lines by the fact that at the beginning of the drawing we inevitably change something, move it. And erasing lines drawn with strong pressure, we spoil the paper. And, most often, there is a noticeable trace. The drawing looks messy.

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

Proportions

A sense of proportion is one of the main elements in the drawing process. Compliance with proportions is important not only in drawing from nature, 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 picture or parts of the depicted object in relation to each other. Violation of proportions is unacceptable. The study of proportions is given great importance. It is necessary to help the painter to understand the mistake he made or to warn against it.

A person drawing from life should keep in mind that with the same size, horizontal lines appear longer than vertical ones. Among the elementary mistakes of novice artists is the desire to stretch objects horizontally.

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

Since ancient times, great importance has been attached to educating the artist's sense of proportions and the ability to accurately measure the size by eye. Leonardo da Vinci paid much attention to this issue. He recommended games and entertainment invented by him: for example, he advised sticking a cane into the ground and, at one distance or another, trying to determine how many times the size of the cane fits into this distance.

perspective

The Renaissance for the first time created a mathematically rigorous doctrine of the ways of transmitting space. Linear perspective(from lat. Rers Ri ser e "I see through"“I penetrate with my eyes”) is an exact science that teaches to depict objects of the surrounding reality on a plane in such a way that an impression is created such as in nature. All construction lines are directed to the central vanishing point corresponding to the location of the viewer. 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 did not know this, so sometimes their work resembles a drawing.

Square perspective

a - frontal position, b - at a random angle. P is the central vanishing point.

Lines receding into the depth of the drawing seem to converge at the vanishing point. The vanishing points are 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 side vanishing points

circle perspective

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

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

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

Perspective of a cube and a parallelepiped.

P is the vanishing point lying on the horizon line.

Chiaroscuro. Tone. Tonal relations

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

This is how the concept of chiaroscuro arises.

Chiaroscuro implies a certain source of light and mostly the same light color of the illuminated object.

Considering the illuminated cube, we notice that its plane facing the light source will be the lightest, called in the figure light; the opposite plane shadow; semitone one should name the 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; highlight- a small part of the surface in the light, completely reflecting the strength of the light source (observed mainly on curved surfaces), and finally, drop shadow.

In order of decreasing light intensity, all light shades can be conditionally arranged in the following sequence, starting with the lightest ones: glare, light, semitone, reflex, own shadow, drop 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 has a faceted character, then even with a minimal difference in the luminosity of the surfaces, their boundaries will be certain (see the cube illustration).

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 been talking about the chiaroscuro of equally colored objects. Until the second half of the 19th century, they were limited to the means of this chiaroscuro when transmitting illuminated plaster casts and nude sitters.

In the end In the 19th and early 20th centuries, during the period of the development of a deeper understanding of color, demands of a picturesque nature began to be made to the drawing.

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

Therefore, the pictorial term entered the 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 appears lighter than burgundy, brown appears darker than blue, etc.

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

Draftsmen need to practice in developing the ability to subtly distinguish between gradations of lightness in natural productions. You need to learn to catch small tonal differences. Having determined where there will be one - two of the lightest and one - two of the darkest places, it is necessary to take into account the visual possibilities of materials.

While doing learning tasks must be respected proportional dependence between the luminosity of several places in nature and the corresponding several parts of the drawing. At the same time, it must be remembered 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 with relationships. In the process of drawing, you need to compare 2 - 3 areas in terms of lightness in kind with the corresponding places in the image. After applying the desired tones, it is recommended to check.

Drawing Sequence

Modern technique drawing involves the 3 most common 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 a detailed description of nature; 3) summing up. In addition, each drawing, depending on the tasks and duration, may have more or less common stages, and each stage may include smaller drawing stages.

Let us consider in more detail these stages of work on the drawing.

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

Starting a drawing, first of all, they determine the ratio of the height and width of the nature, after which they proceed to establishing the dimensions 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 violated.

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 main, generalized character of the large form is revealed. If this is a group of objects, you need to equate them to a single figure - to generalize.

Having completed the compositional placement of the image on a sheet of paper, the main proportions are set. In order not to be mistaken in proportions, one should first determine the ratio of large values, and then select the smallest ones from them. The task of the teacher is to teach to separate the main 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 common spot, and the details disappear.

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

When drawing, it is necessary to clearly imagine the spatial arrangement of objects and the three-dimensionality of their constructive construction, since otherwise the image will be planar.

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

After choosing a point of view, a horizon line is drawn in the drawing, which is at the level of the drawing's eyes. You can mark the horizon line at any height of the sheet. It depends on the inclusion in the composition of objects or their parts that are above or below the eyes of the painter. For objects below the horizon, their upper sides are shown in the figure, and for those placed above the horizon, their lower surfaces are visible.

When it is necessary to draw a cube standing on a horizontal plane or another object with horizontal edges that is visible at an angle, then both vanishing points of its faces are on the sides of the central vanishing point. If the sides of the cube are seen in the same perspective cuts, then their upper and lower edges are directed outside the picture to the side vanishing points. In the frontal position of the cube, which is at the level of the horizon, only one side of it is visible, which looks like a square. Then the edges receding into the depth are directed to the central vanishing point.

When we see 2 sides of a horizontally lying square in the frontal position, then the other 2 are directed to the central vanishing point. The drawing of a square 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 side vanishing points.

In perspective cuts, the circles look like ellipses. This is how bodies of revolution are depicted - a cylinder, a cone. The higher or lower the horizontal circle is from the horizon, 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 shorter as they approach the horizon.

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

The lines in the figure depict the shape of the object. The tone in the drawing conveys light and shadows. Chiaroscuro helps to reveal the volume of the object. By building an image, such as 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 the ball remains unchanged during rotation. 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 away from the contour line. The light-to-shadow ratios are given as random spots - and the ball appears to be just a smudged 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 that carries the reflex, but will move somewhat 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 semitone in the light.

When drawing a group setting of geometric bodies located at different distances from a light source incident from the side, it should be borne 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 object's distance from the light source. Considering this law, when placing light and shadow, one should not forget the fact that the contrasts of light and shadow increase near the source of illumination, and weaken as they move away.

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

3). The third stage is summarizing. This is the last and most important stage of work on the drawing. At this stage, we sum up the work done: we check the general condition of the drawing, subordinating the details to the whole, clarifying the drawing in tone. It is necessary to subordinate lights and shadows, glare, reflections and halftones to the general tone - one must strive to bring to the present sound and completion those 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. At the final stage of work, it is desirable to return to a fresh, original perception again.

Thus, at the beginning of work, when the draftsman quickly outlines a general view of nature on a sheet of paper, he goes the way synthesis - generalizations. 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 the form for a novice draftsman presents rather great difficulties, because the details of the form attract his attention too much. Individual, insignificant details of an object observed by a draftsman often obscure a 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 the drawing develops from the definition of generalized parts of the subject through a detailed study intricate details to the figurative expression of the essence of the depicted nature.

Note: This manual describes the image of a composition that is quite complex for younger students from the frameworks of geometric bodies. It is recommended to first depict the frame of one cube, one parallelepiped or cone. Later - a composition of two geometric bodies of a simple form. 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 work on a drawing: 1) compositional placement of the image on the plane of a sheet of paper and determination of the general nature of the form; 2) construction of frameworks of geometric bodies; 3) creating the effect of the depth of space using different line thicknesses.

one). The first stage is the compositional placement of the image on the plane of a sheet of paper and the determination of 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 that, they proceed to establishing the dimensions 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 violated. The scale of the objects depicted in the drawing is also determined in advance, and not in the process of work. When drawing in parts, in most cases, nature either does not fit on the sheet, or is shifted up, down, or to the side.

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

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 eye level of the painter. The lower it is, the wider it appears. In accordance with this, all horizontal faces of geometric bodies and the circles of bodies of revolution look more or less wide for the painter.

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

Perspective of the box at a random angle.

Construction of a body of revolution - a cone.

Thus, all geometric bodies are built.

3) The third and last stage is the creation of the effect of the depth of space using different line thicknesses. The drawing person sums up the work done: checks the proportions of geometric bodies, compares their sizes, checks the general state 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 gypsum cube and a ball on one sheet. You can draw on two sheets. For tasks on cut-off modeling, illumination by a closely spaced lamp, soffit, etc. is highly desirable. on one side (usually on the side of the window).

Cube

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

The cube image is composited with a drop shadow in the center of the top half of the sheet. The scale is chosen such that the image is neither too large nor too small.

2). The second step is building the cube.

It is necessary to determine the location of the horizontal plane on which the cube stands and the horizontal faces relative to the level of the eyes, their width. How is the cube located - frontally or at an angle? If frontally, the cube has 1 vanishing point at the level of the painter's eyes - in the center of the cube. But more often the edges are located relative to the drawing at a random angle. Horizontal lines receding at an angle to the horizon converge atside vanishing points located on the horizon line.

Building a cube

The drawing must find out which of the side faces of the cube seems to be wider for him - for this face, the horizontal lines are directed to the vanishing point more gently, and the vanishing point itself is farther from the depicted object.

Having built a cube, according to the rules of perspective, we thereby prepared the borders for light and shadows. Considering the illuminated cube, we notice that its plane facing the light source will be the lightest, called light; the opposite plane - a shadow; semitones are called planes that are at angles to the light source and therefore do not completely reflect it; reflex - reflected light falling on the shadow sides. The falling shadow, the contour of which is built according to the rules of perspective, is darker than all the surfaces of the cube.

Black and white modeling of the cube

White can be left on the surfaces of the cube or the sheet of paper on which it stands, illuminated by direct, bright light. The remaining surfaces should be hatched with light, transparent hatching, gradually increasing it on the lines of the light division (the edges of the cube where the illuminated and shadow faces meet). In order of decreasing light intensity, all light shades can be conditionally arranged in the following sequence, starting with the lightest ones: glare, light, semitone, reflex, own shadow, drop shadow.

Summing up, we check the general condition of the drawing, clarifying the drawing in tone. It is necessary to subordinate lights and shadows, glare, reflections and halftones to the general tone, trying to return to the clarity, integrity and freshness of the first perception.

Ball

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

Building a ball

2). The black-and-white modeling of a sphere 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 that carries the reflex, but rather moving 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 semitone in the light. Closer to the light source, the contrasts of light and shadow intensify, 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 generalization process begins: we check the general condition of the drawing, refining the drawing in tone. Again trying to return to the clarity, integrity and freshness of the first perception.

Topic 3. Still life drawing from plaster

geometric bodies (black and white modeling).

Note: this manual describes the image of a complex composition of plaster geometric bodies. 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 a simple shape. Later, you can move on to a more complex composition. For a task on cut-off modeling, illumination by a closely spaced lamp, spotlight, etc. is highly desirable. on one side (usually on the side of the window).

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

one). 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 that, they proceed to establishing the dimensions 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 main proportions are set. In order not to be mistaken in proportions, you should first determine the ratio of large values, 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 eye level of the painter. The lower it is, the wider it appears. In accordance with this, all horizontal faces of geometric bodies and the circles of bodies of revolution look more or less wide for the painter.

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

Geometric bodies can not only stand or lie on the horizontal plane of the table, but also be at a random angle relative to it. In this case, the direction of the 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 the direction of the inclination of the body, the other on the line perpendicular to it, belonging to the plane of the base of the given geometric body.

3). The third stage is modeling the form 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 the bodies facing the source of light will be the lightest, called light; opposite planes - a shadow; semitones are called planes that are at angles to the light source and therefore do not completely reflect it; reflex - reflected light falling on the shadow sides; and, finally, a falling shadow, the contour of which is built according to the rules of perspective.

White can be left on the surfaces of prisms, a pyramid or a sheet of paper on which they stand, illuminated by direct, bright light. The rest of the surfaces should be hatched with light, transparent hatching, gradually increasing it on the lines of the light division (edges of geometric bodies where the illuminated and shadow faces meet). In order of decreasing light intensity, all light shades can be conditionally arranged in the following sequence, starting with the lightest ones: glare, light, semitone, reflex, own shadow, drop shadow.

At the ball, light and shadow have gradual transitions, and the deepest shadow will not be on the edge of the shadow side that carries the reflex, but rather moving 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 semitone in the light. Closer to the light source, the contrasts of light and shadow intensify, as they move away, they weaken.

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

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

four). When all the details are drawn and the picture is modeled in tone, the generalization process begins: we check the general condition of the picture, refining the picture in tone.

It is necessary to subordinate lights and shadows, glare, reflections 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" v. 2, M. "Art" 1968

Trouble G.V. "Fundamentals of visual literacy" M. "Enlightenment" 1988

"School of Fine Arts" 1-2-3, "Fine Arts" 1986

"Fundamentals of Drawing", " Concise Dictionary artistic terms"- M. "Enlightenment", "Title", 1996

Additional:

Vinogradova G. “Drawing lessons from nature” - 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 by representation" - M., 19885

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

Applications

Topic 1. Building frames of geometric bodies

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

Topic 3. Drawing of 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 plaster geometric bodies: cube, ball (black and white modeling) _____________________________________________ 14

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

Applications ____________________________________________ 21

All objects and figures are placed in space. Even in simple drawing it is worth understanding completely different objects, but everything that is on it, and everything that we want to depict. It is worth considering this as one stream of shapes and lines, white and black, light and shadow.

The drawing must be perceived as a space on paper, where there is a plane and proportions of all objects, light and shadow, which is guided by the shape of the object.

Basic geometric shapes:

2D Plane Figures

3D shapes that have volume

Absolutely all objects are based on these figures.

A cube is a figure, the basis of which is a three-dimensional image in the spatial ratio of a sheet. The cube has all the geometric parameters, such as: vertical, horizontal and depth. The cube itself contains the concept of the picture as a whole.

To begin understanding the drawing, we will work with it. With the help of figurative-logical constructions, we are with you we will develop thinking through form analytics. For a better understanding and analysis of the drawing, there are several exercises.

Exercises

We sit down at the easel, take a large sheet of paper, it can be inexpensive, or even a piece of wallpaper (in this exercise, paper is not particularly important). We draw a square, naturally we try to make its sides even and the lines straight.

So - we see an ordinary square, completely uninteresting and not impressive, but this is only at the moment ...

We make a cube from a square with a pencil: draw lines from the faces with an angle of approximately 45 degrees. We finish the back part and ... we get a cube. But again, we do not see any space in our sheet. You can freely confuse the nearest and far faces. Now it's just a few lines on paper.

In order for us to feel space, we need to make the drawing smooth.. That is, to make it clear to us where the front of the picture is, and where the back is.

The side of the cube, which is closer to us, needs to be highlighted, made clearer and more active. We take our pencil and draw the front edges in a bold tone. Now we can already see where the near side is, and where the side is farther from us.

This is how we transferred the space in order to achieve the desired result. But that's not all. Now it is important to correctly convey smoothness in order to get three-dimensionality in the drawing.

We present to your attention a short video tutorial on the topic of optical illusions.

The study and drawing of geometric bodies in the educational academic drawing is the basis for mastering the principles and methods of depicting more complex forms.

Education fine arts requires strict adherence to the sequence of complication of learning tasks and multiple repetitions to master the technique. The most suitable form for mastering the principles of constructing a drawing are geometric bodies, which are based on clear constructive structures. On simple geometric bodies, it is easiest to understand and assimilate the basics of volumetric-spatial construction, the transfer of forms in perspective reduction, the patterns of chiaroscuro and proportional relationships.

Exercises in drawing simple geometric bodies allow you not to be distracted by the details that are available in more complex forms, such as architectural objects and the human body, and fully focus on the main thing - visual literacy.

Correctly understood and learned patterns in the image simple shapes should contribute to a more conscious approach to drawing complex shapes in the future.

In order to learn how to competently and correctly depict the shape of an object, it is necessary to realize the internal structure of the object hidden from the eyes - the design. The word "construction" (from the Latin construct) means "structure", "structure", "plan", that is, the relative position of the parts of the object and their relationship. This is important to know and understand when depicting any form. The more complex the shape (regardless of the material, texture and color of the object), the more and more seriously students will have to study the internal structure of a full-scale model. So, for example, when drawing living nature - the head or figure of a person, in addition to knowing general structural features, you should definitely know plastic anatomy. Therefore, without a clear understanding of the structure of the form and nature of the object, it is impossible to correctly master the drawing.

When depicting spatial forms, in addition to knowing the laws of the structure of a structure, knowledge about the laws of perspective, proportion, and light and shade is necessary. Issues relating to perspective and proportion are covered in detail in the sections "Proportions" and "Fundamentals of Perspective".

For the correct image of a full-scale model, students need to be reminded once again of the need to accustom themselves to always analyze nature, to clearly represent its external and internal structure. Unfortunately, as practice shows, many students limit themselves to only a superficial impression, without delving into the essence of the structure of the object's form. In art, as in any science, the study of a natural subject must be approached with scientific point vision. Approach to work should be conscious, not content with copying the external forms that the eye sees. Such drawing will not contribute to the successful completion of work on the image of both simple and complex forms.

Drawing geometric shapes to inexperienced draftsmen seems at first glance quite easy. But this is far from true. Without sufficient experience in drawing, students easily get used to mechanical copying. Therefore, when depicting more complex shapes, you can easily get confused. For a more confident mastery of the drawing, first of all, it is necessary to master the methods of analysis of forms and the principles of the geometric construction of simple bodies.

Fig.34

Any form consists of flat figures: rectangles, triangles, rhombuses, trapezoids and other polygons that delimit it from the surrounding space. The challenge is to correctly understand how these surfaces fit together to form a shape. For its correct image, students need to learn how to draw such figures in perspective, in order to easily select three-dimensional bodies on the plane, limited by these flat figures. Flat geometric figures serve as the basis for understanding constructive construction bulk bodies. So, for example, a square gives an idea of ​​building a cube, a rectangle - about building a parallelepiped prism, a triangle - a pyramid, a trapezoid - a truncated cone, a circle is represented by a ball, a cylinder and a cone, and elliptical figures - spherical (ovoid) shapes (Fig. 34).

All objects have three-dimensional characteristics: height, length and width. Points and lines are used to define and depict them on a plane. The points define the characteristic nodes of the design of objects, they establish the mutual spatial arrangement of the nodes, which characterizes the design of the form as a whole.

The line is one of the main visual means. Lines indicate the contours of objects that form their shape. They denote height, length, width, constructive axes, auxiliary lines that define spaces, construction lines, and much more.

For a thorough study, geometric shapes are best viewed as transparent wireframe models. This allows you to better trace, understand and assimilate the basics of the spatial construction of structures and the perspective reduction of the shapes of geometric bodies: a cube, a pyramid, a cylinder, a ball, a cone and a prism. At the same time, such a technique greatly facilitates the construction of a drawing in which all spatial angles, edges, and edges of the body are clearly traced, regardless of their rotations in space and in perspective contraction. Wireframe models allow students to develop three-dimensional thinking, thereby contributing to the correct representation of a geometric shape on a paper plane.

For a thorough consolidation in the minds of students of a three-dimensional representation of the structure of these forms, it would be most effective to perform them with your own hands. Models can be made without much difficulty from improvised materials: ordinary flexible aluminum, copper or any other wire, wooden or plastic slats. Subsequently, in order to assimilate the laws of light and shade, it will be possible to make models from paper or thin cardboard. To do this, it is necessary to make blanks - appropriate scans or separately cut out planes for gluing. No less important is the modeling process itself, which will be more beneficial for students to understand the essence of the structure of one form or another than the use of a ready-made model. It will take a lot of time to make wireframe and paper models, so in order to save it, you should not make models big size- it is enough if their dimensions do not exceed three, four or five centimeters.

By turning the manufactured paper model at different angles to the light source, you can follow the patterns of light and shadow. At the same time, attention should be paid to the change in the proportional relations of the parts of the object, as well as to the perspective reduction of forms. By moving the model closer and further away from the light source, you can see how the contrast of lighting on the object changes. So, for example, when approaching the light source, the light and shadow on the form acquire the greatest contrast, and as they move away, they become less contrasting. Moreover, the nearby corners and faces will be the most contrasting, and the corners and faces located in the spatial depth,

Less contrast. But the most important thing at the initial stage of drawing
- this is the ability to correctly display the volumetric-spatial design of forms using points and lines on a plane. This is a fundamental principle in mastering the drawing of simple geometric shapes, as well as in the subsequent study of more complex shapes and their conscious representation.

For a consistent study, analysis of forms and execution of a drawing of geometric bodies, one should consider the techniques and principles of their construction on a plane.

In order to follow the sequence in the work on the drawing, based on the principle "from simple to complex", you must first study simple geometric bodies: a cube, a prism, a pyramid, a cylinder.

cube drawing

The cube is one of the simplest geometric solids. To better understand the geometric shape of the cube, its spatial constructive scheme (structure), consider the cube frame. This makes it possible to clearly present the volumetric and spatial characteristics of its shape, allows you to see its structural nodes - points invisible on ordinary bodies.

Fig.35

The cube is characterized by eight points at the corners and twelve lines of edges. The aspect ratio of the cube is 1:1:1. In order for the cube to look credible in 3D, students should determine a point of view that makes the object look convincing enough in volume. The image of the cube frame is made taking into account its proportions, according to the laws of perspective. When viewed from above (from a perspective), the base of the cube frame (square) looks like a rhombus. The perspective construction of the cube in accordance with its rotation should begin with the square of the base, i.e. from its plan, which lies in a horizontal plane, extending in depth to the horizon line (Fig. 35). To get the lower base (rhombus), you need to mark four points and connect them with four lines. From the points of the base, vertical lines are drawn - ribs. To complete the construction, as in the first case, four points are designated and, connecting them with four lines, the upper base of the cube (rhombus) is obtained. It is necessary to note one important detail regarding the nature of the lines when constructing an image on a plane. In addition to maintaining proportion and perspective, the lines that define the spatial depth must be drawn in varying degrees of contrast. The lines of nearby ribs should be drawn in more contrast than those that are in perspective removal. Moreover, the difference between the lines should be extremely distinguishable in accordance with the spatial depth.

Fig.36. Measurement of proportional values

A perspective drawing of a cube can be constructed relatively easily and verified in a variety of ways. One of these methods are techniques that have long been used in practice by the old masters - this is comparison and sighting. To determine the main large sizes of an object in a drawing, it is the visible, perspectively changed ratios that are important, and not the actual dimensions of the object and its parts. So, for example, the ratio of the width of a face to the height of the front edge is measured with a pencil on an outstretched arm, perpendicular to the line of sight, aligning the back of the pencil with the edge of the shape of the object of the measured part of the model. In this case, the visible dimensions of the parts of the object are marked with the thumb. Without changing the position of the thumb on the outstretched hand and turning the pencil in a vertical position, correlate this segment of the pencil with the vertical edge of the cube, visually determining their differences (Fig. 36).

When working on the constructive construction of a cube, one must carefully monitor its perspective contraction. To do this, it is necessary to mentally imagine the form from a given point of view in terms of, i.e. see it from above. This representation makes it possible to better understand how the planes are consistent with each other and in general. In drawing from nature, it is important to correctly convey not only the visible ratios of magnitudes, but also the magnitudes of the angles between the bases of two visible faces, i.e. perspective perspectives.

For their correct determination, a mechanical inspection should be done. Holding the pencil by the tip on an outstretched hand, you need to combine the line of the pencil itself with the top of the front lower corner of the base of the object and determine by eye the angle of the object in perspective. Remembering what you saw, draw an appropriate auxiliary horizontal line in your drawing. By comparing the amount of inclination (angle) of the right and left sides of the model, refine the figure. If further clarification is needed, the check should be repeated. Figure 36 clearly shows how to measure the dimensions and check the perspective slope of the horizontal edges of the cube. Note that when drawing from nature, one should not abuse the method of sighting, since it is purely mechanical in nature for determining dimensions and does not contribute to the development of the eye. It is used at the initial stage of learning to draw from nature, and it should serve only for auxiliary control and verification of work already completed.

When a cube is positioned with a front vertical edge slightly shifted to the right from the center, the horizontal edges of its left face will approach the horizontal in perspective, and the edges of the right, on the contrary, will deviate from it. Therefore, the more the right side is reduced, the smaller the reduction of the left will be and vice versa. This is due to the mutual rectangular arrangement of the planes of the cube.

For a better assimilation of the material on the study of geometric bodies, it is necessary to complete an academic task on drawing a cube. Assimilation of the laws of the structure of the shape of the cube, it should be borne in mind that their observance must be monitored throughout the entire process of drawing from nature. Working on a long drawing requires adherence to a methodical sequence both in the analysis of the structure of the form and in the process of constructing an image. This makes it possible to consolidate the individual stages of the educational drawing, without which it is impossible to understand the main meaning. educational material. At the same time, it should be noted that the division of the process of working on a drawing into separate stages is rather arbitrary. This is due to errors in solving problems that could have been made at the previous stage, and the need to correct them in the process.

Fig.37. The sequence of work on the cube drawing

Consider the sequence of execution of the cube drawing (Fig. 37).

1. The drawing begins with the compositional placement of the subject on the sheet. The image is outlined with light lines from the sides, top and bottom. Taking into account the angle, proportions and perspectives, the main constructive points of the vertices of the corners of the cube are found and determined.
2. Taking into account the perspective reductions on the constructive points of the vertices of the corners, they outline general form cube designs.
3. Clarify the proportions and perspective construction of the volume-spatial form of the cube. Defines the boundaries of own and falling shadows.
4. With the help of light-tonal relations, the three-dimensional shape of the cube is revealed. Apply own and falling shadows. Define the background.
5. Full tonal study of the form. Work with light-tonal relationships: light, shadow, penumbra and reflex.
6. Summing up. .Checking and summarizing the drawing (integrity).

Rice. 38. Perspective construction of a cube

Prism drawing

Continuing to consider the principles of constructing the construction of volumetric bodies, it is necessary to familiarize yourself with the image of the geometric shapes of faceted objects (trihedral and hexagonal prisms).

A trihedral prism is characterized by six points of spatial angles of the bases and three lines of edges. The axis of the prism is determined by lines drawn from the spatial angles of the bases perpendicular to its opposite sides. From the points of their intersection, a vertical line is drawn, which will be the axis of the prism. When constructing a trihedral prism, it is necessary to choose the right point of view. The subject should be depicted in such a way that it looks three-dimensional, with two visible planes and a front edge slightly offset to the side. A trihedral prism with such a rotation will be the most expressive, voluminous and expedient, provided that the object is located in the optimal perspective.

Students experience great difficulties in determining the dimensions of the segments of the faces in a perspective perspective on the basis of a prism. To avoid errors, it is recommended to use an additional circle (in plan, top view), on which, in accordance with the apparent position of the object, the spatial angles of the base of the prism are precisely determined. Thus, for the correct representation of prismatic forms, it is necessary to construct a cylindrical scheme with the subsequent construction of faceted forms in it.

Rice. 39-41

The construction of a trihedral prism should begin with a horizontal line (it must be drawn strictly horizontally). This makes it possible to correctly determine the position of the surface of the bases of the prism with respect to the axis of the body. Then you should draw a vertical center line. Marking the radius of the base, draw a circle (ellipse) in perspective (Fig. 39). To correctly determine the spatial points of the corners of the base on the ellipse, it is necessary to draw a circle above it, in accordance with the radius of the ellipse, along one axis. When drawing it, check how correctly it is drawn, since on a distorted circle it will be impossible to accurately determine the spatial points and sizes of the segments of the faces. The correctness of the image of the surface of the base of the prism and the entire object as a whole will largely depend on how correctly they are defined on the circle.

Having accurately determined the apparent position of the points of the spatial angles of the base of the prism on the circle, transfer them to the ellipse. To determine its upper, base, it is necessary to repeat the drawing of the ellipse, after which, connecting the spatial points of the bases with vertical lines of edges, an image of a trihedral prism is constructed. On a perspective image of a prism, the circle (ellipse) of the lower base should be somewhat wider than the upper one.

When constructing an object on a plane, proportions and perspective should be strictly observed. For greater expressiveness of its volume-spatial characteristics, the near edges of the form should be highlighted with more contrasting lines, weakening and softening them as they move away. During a long, many hours of drawing, you can gradually get rid of all auxiliary lines. The drawing in the process of construction should be done by lightly pressing the pencil on the paper, so that as the image is refined, it is possible to correct and remove the unnecessary.

A hexagonal prism is characterized by twelve points of spatial angles of the base and six lines of edges. Its axis is determined by lines drawn from opposite spatial angles of the base, where their intersection point will be the center through which the axis of the prism passes. To correctly determine its spatial angles, as well as when constructing a trihedral prism, it is necessary to start work with constructing an ellipse and a circle under it. In accordance with the apparent position of the object at a given point of view, it is necessary to correctly determine the points of the spatial angles of a regular hexagon on a circle. It is necessary to pay attention to the rotation of the prism, you should not draw a hexagonal prism with a symmetrical arrangement of its planes. Therefore, when choosing a drawing place, you need to sit down so that the object looks the most expressive, voluminous, as, for example, shown in Fig. 40.

The perspective construction of a hexagonal prism is carried out in the same way as when depicting a trihedral prism. The difficulty lies in the correct determination from the visible position of the perspectively reduced faces, their proportional relationships. In this case, you should also use the auxiliary circle in the plan at the lower base of the prism, as shown in Fig.40. Having built the circle of the base of the prism, you need to determine six spatial angles along the circle. In this case, it is important to correctly set aside equal segments, taking into account the rotation of the prism, i.e. from a visible position. Connecting the points with light lines, it is necessary to follow the parallelism of opposite sides. Having received the points of the spatial angles of the base, in the same way as in the first case, they should be transferred to the lower base of the ellipse. It should be noted that when transferring the spatial angles to the base of the ellipse, the perspective reduction of its far half is taken into account, although these changes are not significant. The main thing is not to allow a reverse perspective.

Having connected all the points on the bases with lines, they begin to check the work performed. Errors found are corrected without delay. In order to achieve the greatest expressiveness of the image of a spatial form, it is necessary to strengthen the near vertical and horizontal lines of the ribs, and weaken the far ones. If you need to continue working on the drawing, you should get rid of the auxiliary construction lines with the help of an eraser.

A trihedral pyramid (Fig. 41) is characterized by three points of the spatial angles of the base, a point of the top and six lines of edges.

For the correct image of the pyramid, the drawing should begin with the construction of its base, which is similar to the construction of a prismatic shape. By connecting the points of the spatial angles of the base with lines, it is necessary to find the constructive axis of the pyramid and the point of its top.

The position of the structural axis is determined by lines drawn from the spatial corners of the base perpendicular to its sides. A vertical line is drawn from the intersection point. Then it is necessary to determine the position of the point of the top of the pyramid on the axial line, which is carried out in accordance with the proportional value of the height of the full-scale model. Then you should connect the top with the spatial corners of the base.

A tetrahedral pyramid (Fig. 42), in contrast to a trihedral one, is characterized by four points of the spatial angles of the base, a vertex point and eight lines of edges. The constructive axis of the pyramid, similarly to the trihedral one, is determined by the connection of lines of their opposite spatial angles. A vertical (axial) line is drawn from the intersection point, on which the point of the top of the pyramid should be indicated.

When constructing a pyramid in a horizontal position, attention should be paid to the position of the axis of the pyramid in relation to the center of its base (Fig. 43). In this case, the plane of the base of the pyramid with respect to its constructive axis must be strictly at a right angle, that is, perpendicular, regardless of the position of the object at a given point of view. The structure of the body structure also remains unchanged.

Drawing Solids of Revolution

The bodies of revolution are characterized by the axis, the radii of the bases and the constructive points of the generatrix of the surface of the bodies. To better understand the principles of constructive construction of the shape of a cylinder and a cone, you should pay attention to Fig. 44, where they are shown as transparent wire patterns. The drawings clearly express the constructive basis and volume-spatial characteristics of the shape of objects. The task is to learn how to competently and correctly depict them on a plane. To do this, it is necessary to learn the basic principles and methods for the constructive construction of such images.

Fig.44	Fig.45

Before proceeding to the construction of bodies of revolution, it is necessary to pay attention to one circumstance. In the representation of bodies of revolution, one of the most difficult elements is drawing the circles of their bases in perspective. For clarity, Fig. 46 is shown, which shows typical mistakes allowed by students when drawing the bases of cylinders. So, the base of the first one is a figure of two arcs, forming sharp corners at the edges when crossing, which is why there is no impression of a circle in perspective. To avoid such errors, let's try the following work. Cut out a circle from cardboard, insert two buttons with a plastic head symmetrically along its edges. Then, holding big and index fingers button heads, consider the circle in different inclined positions. Rotating it along the axis, we will see how the circle changes shape, turning from a circle into a narrower figure. But no matter how we turn the circle, it never forms corners, but takes the form of a closed curve with a smooth bend in the outlines of the side contours. For example, consider the drawing of rings located in different perspectives (see Fig. 45). Depending on the position of the rings in the foreshortening, their shape gradually changes. The higher the horizon line, the more the ring (circle, circle) expands and, conversely, as it approaches the horizon line, the ring narrows, gradually turning into a straight line shape when the horizon line (eye level) is at the same level with the ring.

When the horizon line is low, the change in the shape of the rings occurs in exactly the same way as in the first case. The position of the ring at the level of the observer's eyes, when it is a straight line, deserves special attention. In this case, not only the ring, but also any horizontal plane will be visible as a straight line, and not only in a horizontal, but also in a vertical and inclined position.

Having examined and studied the circles and their changes in a perspective perspective, you can move on to the methods and techniques for depicting circles on a plane.

A circle is a closed geometric line, all points of which are equally spaced from the center.
An ellipse is a closed curved line, which is built on two mutually perpendicular axes: a large one - horizontal and a small one - vertical, dividing each other in half at the point of intersection. In the drawing, an ellipse should be understood as a perspective image of a circle, where there are no corners, but there is a smooth transition from the near part to the far part.

Fig.48

For the correct perspective construction of an ellipse, it is necessary to consider methods and techniques for depicting a square with a circle on a plane, using a perspectively lying square and its diagonals, on which additional points are marked (Fig. 48). The construction of an ellipse is First stage work on the construction of a cylinder and other bodies of revolution in a vertical position on a horizontal plane. As an example of a perspective construction of a circle, let's take an object whose shape is a circle - a sports hoop. For optimal consideration of the object from the perspective, we put the hoop on the floor at a distance of 6-7 meters. The image should begin with the definition of the horizon line and the vanishing point on it. In this case, the vanishing point of the circle of the hoop will be at the level of your eye (horizon line). Having determined the horizon line, mark the vanishing point on it, and draw a perpendicular line from it, on which you want to mark the center of the circle of the hoop. Through this point, draw a horizontal line parallel to the horizon line, plot the radii of the hoop to the right and left on it, and connect the resulting points with the vanishing point. Having the vanishing lines, taking into account perspective cuts, proceed to determine the length of the minor axis of the ellipse by eye.

Build a square in perspective so that its sides pass through the resulting serifs. To do this, you need to circle the already outlined auxiliary lines that go into the depth of the vanishing point. The correct drawing of the circle is facilitated by the definition of its center, for which the opposite spatial corners of the square are connected with two diagonal lines. Their intersection will give the center of the circle, through which the major axis of the ellipse passes horizontally. Moreover, the major axis of the ellipse on the horizontal plane is always horizontal, its length corresponds to the horizontal diameter of the circle. Its minor axis determines the vertical width of the ellipse and is at right angles to the major axis.

It should be clarified that when two diagonals intersect, the intersection point must lie on a vertical line, and not to the side. When defining the major axis of the ellipse, mark the points at the intersection with the lines going to the vanishing point, as well as the points along the middle line - at the intersection with the horizontal sides of the square, since these points will be the basis for the correct drawing of the circle in the square. However, they are necessary to determine the points of contact of the circles with the sides of the square. Having correctly identified them, proceed to drawing a circle (ellipse). As it is completed, the near part should be strengthened, and the far part should be weakened. This gives the drawing the impression of a spatial form.

As pedagogical practice shows, building a circle (ellipse) in a square is a great difficulty for students, especially when depicting architectural details (capitals) and other complex shapes associated with a combination of cylindrical bodies with square ones. So, for example, when constructing a capital of the Doric order, inscribing a circle in a rhombus of a square abacus, its horizontal position is often incorrectly determined - the major axis of the ellipse, which leads to a distortion of the image of the ellipse circle and the picture as a whole. Regardless of the position of the corners of the rhombus of the capital, the ellipse, as mentioned above, must always be in a horizontal position. Therefore, in order to simplify, it is recommended to start the construction of such objects with the correct construction of an ellipse of a circle. Having built a circle, taking into account the apparent position and angle, one should build an element of the abacus on its basis. This will be discussed in more detail below.

Perspective construction of circles leads students to the correct image of objects related to bodies of revolution. So, for example, exercises on drawing a cylinder will help in the future when depicting objects that are complex in shape, in which the circle is an important constituent element. Observing the methodical principle of the sequence of performing educational tasks, one should move from constructing circles to constructing an image of a cylinder and a cone.

cylinder drawing

A cylinder is a geometric body, the shape of which consists of three surfaces: two flat circles of the same shape and one cylindrical surface that forms the shape. In order to better understand and understand the structural basis of the structure of the cylinder shape, as visual aid consider its wireframe model. It is not difficult to make such a model-frame. To do this, you can use wire - aluminum, copper, steel or soft alloy. The length of the large side of the frame can be in the range of 7-10 cm.

The study of wireframe models in the drawing allows students to better master the constructive essence of the subject, its relationship and the spatiality of the form.

Fig.49. Perspective construction of the circles of the bases of the cylinder: a - with one vanishing point; b - with two vanishing points

The image of a geometric body located on a horizontal plane in the usual vertical position should begin with the construction of its base. As you can see, on the bases of the cylinder there are surfaces that are round in shape, bounded by a circle. We have already familiarized ourselves with the circle and know the methods and ways of constructing it on a plane. Based on the method of linear-constructive construction of the image of wireframe models, we should proceed to consider the image of a cylinder.

The image of a cylinder should begin with the definition of the main proportional quantities - the diameter of the bases and the height.

The construction of the planes of the circles of the bases is carried out in the same way as when depicting circles - by fitting into a square (Fig. 48).

Fig.50

The axis of rotation of the body (axis of the cylinder) is always perpendicular to the planes of the base circles. When drawing a circle in squares, their vertical and horizontal axes end up in the midpoints of the sides of the square, i.e. at the points of contact of the circle with the sides of the surface of the cylinder (Fig. 48,49).

Considering the shape of the cylinder frame, we see that the lower base is wider than the upper one, therefore, the near height of the cylinder surface is greater than the far one. Their differences are due to a perspective regularity. At the same time, it should be noted that an excessively wide lower base of the cylinder does not contribute to the correct and convincing construction of the cylinder pattern. Therefore, the width of the lower ellipse relative to the upper one should be slightly larger, as well as when observing the cylinder from a far point of view, and not from a near one.

When depicting the circles of the bases of an ellipse on a plaster cylinder, its lower base should be drawn through, i.e. visible, with its subsequent removal to continue working with the help of chiaroscuro. This will make it possible to trace the differences in the size of the bases.

Having completed the perspective construction of the circles of the bases of the cylinder, proceed to drawing the edges of the shape of the generatrix of the surface connecting both circles. In this case, the lines should not be excessively contrasting, since they are further than the nearest surfaces of the cylinder - the near edges of the ellipse and its depicting surface. However, without strengthening the lines of the near edges of the bases, it is impossible to obtain a sufficient impression of a three-dimensional shape in the drawing.

Upon completion of work on the construction of the drawing of the cylinder, it is necessary to proceed to its verification. You should check, moving away from your place at a distance of at least 2-4 m, depending on the size of the picture. The larger its size, the more distance it should be viewed.

Having carefully checked the mistakes made in the process of work, they should be corrected without delay.

The image of a cylinder in a horizontal position has its own characteristics in contrast to the construction of a cylinder in a vertical position. This is due to its cylindrical generating surface, which connects both round bases of the cylinder. For example, consider the frame of a cylinder (Fig. 52).

Fig.51. Cylinder Drawing Sequence

A cylinder in a horizontal position can be built on the basis of a rectangular prism. This facilitates the volume-spatial and constructive construction of the cylinder, allows you to correctly determine the axis of rotation with respect to the axis of the ellipse and, therefore, correctly build base circles (ellipses). Having determined the horizon line and the position of the object in space relative to the angle of view (in this case, the cylinder is somewhat to the side, and the point of view is higher than the cylinder), you need to outline its location. When constructing, it is very important to correctly determine the angles of the horizontal directions of an object on a plane, therefore, the image of a prism begins with the construction of its base, in which all sides are pairwise equal to the height of the cylinder and the diameter of the bases of the circles. Subsequently, this prism will serve as a frame for building a cylinder in a horizontal position.

The construction of a prism is carried out from the points closest to us at the intersection of the sides of the parallelepiped. In accordance with the position of the object, it is necessary to outline a horizontal line of the base of the sides of the prism extending towards the vanishing points. The directions of these two main lines leading to the vanishing points should determine the basis for the correct construction of the prism, and then the cylinder. After that, a construction is made taking into account the perspective. To determine the points of the axial line of the prism, one should draw diagonals of opposite corners of its front face. The intersection point of the diagonals will be the center of the axis of the prism and the cylinder. In order to correctly inscribe the circle of the base of the cylinder (ellipse) into the front face of the prism, it is necessary to accurately determine the right angle between