Composition of geometric bodies with intersections of surfaces. Examples in painting

09.02.2019

On fig. 6.1 shows the simple geometric bodies that the examination composition should consist of. In addition to the bodies already familiar to you, dies and sticks are presented here. Dies - additional flat square, round and hexagonal elements, the height of which is equal to one-eighth of the edge of the cube. Sticks are linear elements of the composition, the length of which is equal to the edge of the cube. In addition, bodies of the same proportions, but of different sizes, can be used in the composition. These are the so-called compositions with scaling (since in this case there are identical bodies on the sheet, but, as it were, taken at a different scale). Consider compositions made by applicants in last years(Fig. 6.2-6.20).

The form of the examination composition, its size, placement on the sheet, the degree and nature of the interaction geometric bodies have been established for a long time. All these positions are reflected in the examination task to one degree or another. Of course, you should immediately make a reservation that we will talk about the exam task that exists today - it may be changed at the time when you read this section of the manual. However, let's hope that the essence of the task will be preserved, and you will be able to use our tips and recommendations.

First of all, we list the criteria by which your compositions will be evaluated:

Compliance of the completed drawing with the task;

The compositional idea as a whole, the harmony of the compositional solution and the complexity of the composition;

Leaf composition;

Competent image of individual elements of the composition, the correctness of perspective and frames;

In your work, choose a topic that is close to you. It can be a massive stability or a light, aspiring to some conditional distance or upward movement. The movement can be looped or extinguished, stopped. The mass may be dense or rarefied. The composition can be built on metric, uniform patterns, or, conversely, on a simple or complex rhythm. It may contain a uniform distribution of mass or sharp, highlighted accents. The listed properties can be combined (except, of course, those that exclude each other in one work). It should be remembered that the feeling of the complexity of the composition arises from the perception of the complex harmony of some non-trivial idea, and not only from the complexity of the inserts, and certainly not from the heap of many bodies.

Correct - a prerequisite for good composition. You have probably already noticed that when your composition consists of only a few geometric bodies, it is quite difficult to maintain the correct perspective on the sheet. Even if the basis of the work is almost perfectly built, the addition of each new body leads to a gradual increase in distortion.

Tracking them and correcting them is quite difficult, especially in the first compositions, when experience and practical skills are still small. That is why, to correctly determine the disclosure of all faces and the direction of all lines on the sheet, use various ways streamlining all these interrelated positions, bringing them into single system. One of these systems is described in detail in the next task. This is the so-called grid - a spatial structure that determines the opening of the faces of geometric bodies and the direction of lines throughout the sheet.

In the process of preparing for the exam, the "grid" will help you to bring together all the variety of problems associated with the process of building a composition, and at once, easily solve them. Of course, the "grid" is a useful thing, but it, of course, has its pros and cons.

On the one hand, when depicting compositions based on a "grid", you, of course, spend some (sometimes quite a lot) time on the preparatory stage (drawing the "grid" itself), thereby reducing the time spent working on the actual composition.

On the other hand, the "grid" can significantly reduce the time for solving purely technical problems related to determining the directions of horizontal lines and the disclosure of various surfaces. Of course, a certain skill will allow you to minimize the time spent on the "mesh", but if a mistake is made in the "mesh" (which is quite likely under the stressful conditions of the exam), then you can notice this error only by drawing the first geometric body.

What to do in this case - fix the grid or abandon it altogether to make up for lost time? It is only obvious that you should start working on the exam composition from the “grid” only if you have learned how to make the “grid” quickly and efficiently for the exam, bringing this process almost to automatism, and easily build a composition based on it.

Another question that often worries the applicant is the question of tie-ins: what tie-ins should be done, how difficult should they be, and even should they be done at all? To begin with, it is possible not to make frames in the exam composition - in the examination task, the use of frames is only recommended and is not prerequisite, however, it should be understood that the composition without tie-ins is significantly inferior in complexity and artistic expressiveness. Do not forget that your composition will be evaluated among others, and therefore, by making a composition without tie-ins, you will obviously reduce the competitiveness of your own (worries. Of course, the level of the exam composition grows from year to year, and this dictates the inclusion of complex tie-ins in the composition that make examination paper more expressive and interesting. However, their implementation requires additional time, which is limited under the conditions of the exam. In this situation, it all depends on your experience - if you have studied hard for your composition exam, most likely you already have your favorite frames, which can be quite complex, but, outlined many times, they are drawn easily and therefore quickly. But do not get carried away with complex frames, overcomplicate the work - remember that even a composition made using simple frames can be quite complex and expressive. It is also important to say how geometric bodies should crash into each other. Sometimes in the compositions geometric bodies are embedded so slightly that it seems as if they are not embedded into each other, but only barely touching. Such compositions tend to evoke a sense of instability, unsteadiness, and incompleteness. The viewer has an irresistible desire to make such a composition denser, to embed geometric bodies deeper into each other. Analyzing such a work, it is difficult to speak of it as a composition - a group of harmoniously subordinated volumes. In other compositions, the bodies are so deeply embedded in each other that it is no longer clear - what kind of bodies are they? Such a composition, as a rule, looks like a complex mass with parts of geometric bodies sticking out of it and does not create a sense of harmony in the viewer. The bodies in it cease to exist as independent objects, turning into a geometric mixture. If we do not consider such extreme cases (when geometric bodies almost do not crash into each other or when they turn into a single dense mass), to create a medium-density composition, one should adhere to next rule: a geometric body should crash into another (or other) geometric bodies by no more than half, better - by one third. In addition, it is desirable that the viewer can always determine the main dimensions of a geometric body from its visible part. In other words, if a cone cuts into any body, its top, a significant part of the lateral surface and the circumference of the base should remain visible in the figure. If it crashes into any body, then parts of the lateral surface of the cylinder and the circles of its bases should remain visible. Particular mention should be made of inserts of cubes and tetrahedrons - in the composition these geometric bodies form a background or, in a way, a framework for arranging and inserting other geometric bodies that are more difficult to construct. Therefore, inserts are allowed when the visible parts of cubes and tetrahedrons make up less than half of their volumes.



Choose one or two best sketch and enclose them in frames, the proportions of which correspond to the proportions of the future drawing. So, an A-3 sheet measuring 30 by 40 centimeters has a 3 to 4 prop (Figure 172). In search of the most successful composition of the sheet, you may have to correct the point of view, and in some cases even make changes to the setting itself.

When composing the sheet, you should also take into account the location of the illuminated and shadow surfaces, as well as the boundaries of the falling shadows. Remember that chiaroscuro can disrupt the compositional harmony of a line drawing.

Stage 1

Figure 173 Starting a drawing on a large sheet, try to accurately transfer to it the arrangement of objects fixed in the best sketch. Mark the location of each geometric body with light lines. Once again check the size of the entire composition, as well as its compliance with the size of the sheet. Make the necessary changes to the drawing and continue working, refining the size of each geometric body in relation to other bodies and to the entire composition as a whole.

Stage 2

Figure 174. Linearize all geometric bodies. In the course of work, pay special attention to the correspondence of the disclosure of squares and ellipses lying in horizontal and vertical planes.

Stage 3

Figure 175. At this stage, it is necessary to strengthen those lines that are closer to the viewer, so you will create the effect of the depth of space already in the linear-constructive drawing. Mark the lines of your own and falling shadows and cover all the shadows with a light stroke.

Stage 4

Figure 176. Continue working in the shadows, making them more intense towards the viewer and the light source, and the falling shadows also towards the subject that casts the shadow. Gradually move on to work in the light. Carefully model the shape using knowledge of the distribution of light and shade on geometric bodies. On round surfaces, create smooth light and shade transitions; on bodies formed by planes - sharp and clear.

Comparing the light and dark tones of gypsum in nature, one must strive to correctly convey their relationship in the drawing, however, one must also be aware of special techniques that help the draftsman create a sense of three-dimensional space on a flat sheet:

1. Separation of the tonal scale into light and shadow parts: in the figure, the lightest place in the shadow should be darker than the darkest place in the light, in other words, the shadow should always be darker than the light. In nature, this is not always the case. For example, when a sufficiently well-lit surface is near the production, the reflections from it in nature can be as bright as light. They need to be “dampened” by making them darker, otherwise they will destroy the shape of the objects depicted in your drawing.

2. "Aerial perspective". This phenomenon, which we have already mentioned, can be observed in nature at great distances, when objects that are far from the viewer look less contrasting due to the thickness air environment, weakening the shadows and darkening the light. If the size of the depicted production is small, this effect cannot be observed. It is created artificially in the drawing: geometric bodies in the foreground have a greater contrast between light and shadow than bodies in the background, while in nature the difference in illumination of near and far plans can be almost imperceptible.

The main task of an architectural drawing is not to convey the state of an object, but, if possible, to ver
new image of the form, creation of volume. That is why, when drawing, we do not copy nature, but try
trying to see, select and transfer into our work only certain features that help us to re-
sew this task.

Stage 5

Figure 177 Summarize the drawing. Once again, carefully follow the tonal solution of the illuminated and shadow surfaces. At the final stage, the painter does not work with a single object, detail, part of the image, but with the entire sheet at the same time, achieving the integrity of the work, the harmonious subordination of its parts. To do this, if necessary, increase the tone of the illuminated surfaces in the background and the shadow surfaces in the foreground.


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Chapter 74

Linear-constructive drawing of a composition of geometric bodies according to the representation.

Make a sketch of the composition, observing the given proportions of geometric bodies (Fig. 178). Determine the general nature of the future composition, the position of the horizon line, the direction of the horizontal edges, the main tie-ins. We will immediately warn you about a typical mistake that is often made by those who work on their first composition by submission. Placing geometric bodies on a sheet, a novice draftsman quite freely places round bodies side by side (for example, a ball and a cone) or round bodies and bodies that have inclined planes (for example, a ball and a hexagonal prism). The insertion of such bodies into each other is very complex. Taking into account the limited time for completing the examination task, it would be more correct to use simple inserts in the composition, when round bodies and bodies with inclined surfaces intersect horizontal and vertical planes.

Do not overly carefully draw a sketch - on a small scale, you still can not solve all compositional issues. Even a very detailed sketch cannot be accurately transferred to a large sheet. Secondary and insignificant elements will inevitably undergo quite serious changes, and therefore it is not worth paying attention to them. excessive attention at the sketching stage. Enclose the sketch in a frame of appropriate proportions (3x4), make the necessary adjustments to the composition and start working on a large format sheet, trying to keep the main idea defined in the sketch, the main patterns and movements of large masses.

Continuing work on the composition, specify the dimensions and proportions of geometric bodies. Follow the correspondence of the disclosure of squares and circles lying in the horizontal and vertical planes, as well as the uniform convergence of parallel lines in perspective. Carefully build insets of geometric bodies, depicting the intersection lines of not only visible, but also invisible to the viewer surfaces. When working on individual elements, try to subordinate them to the general compositional idea, achieve integrity and harmony in your work.

The drawing should be made with clear, expressive lines and easily worked out in a conditional tone: determine the position of the light source and cover the surfaces that are in shadow with several layers of strokes. Consider figures 179,180,181,182,183 depicting examples of such compositions.


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Chapter 80

Chapter IV. drawing of architectural details

Architectural details include architectural profiles (gooseneck, heel, shaft, quarter shaft, fillet, scotia), geometric and floral ornaments, capitals, rosettes, vases, ionics, brackets, supporting and locking stones of arches, entablature. From all this variety, to complete educational drawings at evening preparatory courses MARCHI selected vase, capital and ionic.

When starting to draw an architectural detail, first determine its geometric basis, imagine a complex shape as a combination of simple geometric bodies. Having depicted a simplified diagram in perspective on a sheet, gradually complicate it, saturating it with details and carefully studying individual elements in a linear-constructive drawing. Plan paired symmetrical volumes at the same time, under this condition it is easier to follow the promising reductions. If the image of any part of the architectural detail causes you some difficulties, make small sketches of it in the margins of your drawing - perspective sketches with different points and orthogonal projections. Finishing the linear stage, enter into drawing easy tone, having previously outlined the lines of own and falling shadows: this will allow you to refine the main masses and reveal possible mistakes before starting tonal work.

Chiaroscuro on architectural details is also distributed according to the laws of drawing simple geometric bodies. On curved surfaces, the transitions from light to shadow are soft, gradual, on faceted surfaces - sharp, clear. The closer the light and shadow on the object to the drawing and the light source, the stronger the light-and-shadow contrast, and, conversely, the distant parts of the objects have a dimmer light and a faded shadow. Falling shadows are more saturated with tone, own ones are highlighted by reflexes, and therefore more airy and transparent. Both in a linear-constructive and in a black and white drawing, try to work evenly over the entire sheet, constantly comparing individual parts of the image with the whole. At the final stage, refine the tonal solution and summarize the work, striving for a sense of completeness and harmony.

Vase drawing.

As an object for drawing, you are offered a plaster cast from a Greek vase (amphora) dating from the 4th century BC. The masters of that time were distinguished by an amazing sense of proportions and constructive logic.

Start drawing a vase, as you would drawing any complex architectural detail, by analyzing its shape. Carefully examine the vase (Fig. 184). Mentally divide it into separate volumes and compare them with simple geometric bodies. The body of the vase has a complex drop-like shape, which can be conditionally represented as a combination of two balls and a cone, so the contour of the vase body can be divided into three parts in height, each of which has its own curvature. The neck of the vase is similar to a cylinder, which has a noticeable thinning in the middle, and is bounded above and below by narrow shelves. The vase is crowned with a massive neck in the shape of a quarter shaft. The supporting part (base) of the vase consists of two cylinders of different diameters, connected by a gooseneck profile. The handles of the vase have a complex three-part structure and thicken at the points of attachment to the neck and body of the vase.

Continuing the study of nature, make a drawing of the frontal projection of the vase. To do this, you will have to use not only the sighting method, but also a long strip of paper and even a ruler. The projection should be large enough, only then you will be able to reflect in it all the information you received: the proportional ratio of the main masses, the dimensions separate parts in height and width


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rine, their relationship, subordination and functional validity. Try to accurately convey the proportions of the vase, note how many times its width fits in height, how many times the neck fits in the body of the vase horizontally and vertically, etc. (Fig. 185).

When depicting the facade of the vase, you will notice that in this projection the neck of the vase looks too thick, the body is more massive, the base is lighter and more elegant than in nature. Of all the modes of depiction, perspective is the closest to real perception. human eye. The orthogonal projection of an object is always different from its perception in nature. But it is orthogonal projections, due to their accuracy and information content, that will help you now. the best way study a complex architectural form, and in the future will become a convenient and natural means of your professional communication.

Let's get back to nature. As you have already noticed, the main volume of the vase is a symmetrical shape. All its horizontal sections are circles of different diameters with the center lying on the same vertical (the axis of the vase). In a perspective drawing, these circles are depicted as ellipses of various sizes and openings. The minor axes of these ellipses coincide with the axis of the vase, while the major axes are perpendicular to it.

Changing your vertical position relative to nature (and, consequently, the level of the horizon line), follow the reduction in the vertical dimensions of individual elements and the entire vase, as well as how some parts of the vase overlap others.

Choose a point from which perspective vertical cuts are negligible (for example, when the horizon line is slightly above the mouth of the vase or below the base of the vase). The position when the horizon line passes through the body of the vase is not recommended due to some difficulties that a novice draftsman may have with determining the opening of ellipses. In addition, this position is the least successful for creating an expressive pattern.





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Stage 1

Figure 186. Determine the dimensions of the vase on the sheet, mark its axis in the middle of the sheet. Break the total vertical dimension into segments corresponding to the large parts of the vase: neck, neck, body, base. Mark the width of these elements.

Stage 2

Figure 187. Indicate the position and dimensions of the small parts of the vase in the figure.

Stage 3

Figure 188. Outline the outline of the vase in orthogonal projection. Such a contour does not take into account future changes, but is a clear constructive basis for further work.

Stage 4

Figure 189. On the horizontal axes, in the places of characteristic sections, draw ellipses. Remember that the ellipse expands the further it is from the horizon. Connect the ellipses with tangent arcs at the junctions of one shape with another. Sketch the handles of the vase, generalizing them to a simple rectangular shape, and only after making sure that the basic relationships are correct, work out their details.

Stage 5

Figure 190 Final stage- tonal work. Start as usual by defining the lines of your own and drop shadow. To do this, use nature and the knowledge already gained about the nature of chiaroscuro on simple geometric bodies. Own shadows on the neck of the vase, belts, shelves of the base, as well as handles - are similar to the shadows on the cylinder; the shadow on the neck is like the shadow on the ball; the shadow on the body of the vase can be represented as a complex combination of the shadow on two balls and a cone. Carefully consider the falling shadows on the vase. Analyze the forms from which shadows fall on the neck of the vase, its body, base, handles. Sometimes it is convenient to do this with a pencil. If you slowly move the tip of the pencil along the line of your own shadow on the vase, the shadow from the tip of the pencil will also move along the line of the falling shadow, fixing at each moment of this movement a certain pair: a point and a shadow from it.

After determining the position of the lines of own and falling shadows, continue the tonal drawing in the usual sequence. First, gain enough tone in the shadows, separating them from the light. Then you need to strengthen your own shadows towards the viewer and the light source, and the falling shadows - also towards the source of the falling shadow. Continuing to work in the shadows, gradually go into the sowing, creating smooth light and shade transitions on spherical and cylindrical surfaces. Completing the drawing, generalize the light and shade relationships, trying to harmoniously subordinate all elements of the image to the general tonal design.

The proposed staging of work is not accidental: it contains important rule, obligatory for everyone, and especially for beginner draftsmen: drawing from the general to the particular and from the particular to the general. Always start drawing with the total mass and only then proceed to the details. But do not immediately work out one of the details to the end. Lead the drawing all over the sheet, moving from one part to another, comparing the parts with the general, constantly covering the whole with your eyes. This rule is true for both linear-constructive and black-and-white drawings.

Naturally, your desire is to see the final result as quickly as possible, to jump to the next stage without finishing the previous one. If you want - try to do it - and you will see how a logical and calm work turns into a chaotic throwing from one detail to another in an effort to put together a drawing that “crumbles” before your eyes.

Remember also that the design is the basis of any forms. Errors in construction cannot be hidden by the most virtuoso tonal study. Therefore, errors in construction and proportions discovered during the work must be corrected immediately.


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Chapter 86



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Chapter 88

Drawing of a Doric capital.

The capital is called the upper part of the column, which, in turn, is part of the architecture of the new order. Order - strictly verified art system, expressing the essence of the work of the post-and-beam structure. The name order comes from the Latin "ordo" - order, order. Classical orders - Doric and Ionic - were formed in ancient Greece. Somewhat later, in the architecture of Rome, they received their further development. The order consists of load-bearing and carried elements, the load is transferred from the overlying elements to those located below. From the entablature (bearing part) to the column (bearing), the load is transferred through the capital, which becomes one of the most important components of the entire order composition.

As an object for drawing, you are offered a capital of the Roman Doric order. Roman orders are somewhat drier in their forms than Greek ones, however, like all order systems, they are distinguished by a strict logic of shaping, well-balanced proportions and simplicity. Doric order- the most concise, strict and courageous of all. A novice architect needs to learn to understand and feel the logic of the structure, expressed in an artistic form, which is called tectonics in architecture. Try to feel in the drawing of the capitals how the shape changes from the upper, square parts to the lower, round ones, how each of the profiles is designed to support the elements located above and to transfer pressure from top to bottom.

Start your drawing by analyzing the shape of the capital (Fig. 191). The upper part of the capital is square in terms of abacus (abacus) - a plate with a heel and a shelf. Echin is a quarter of the shaft and mates with the neck of the column through three successively decreasing belts. Astragalus, consisting of a roller and a shelf, passes into the trunk of the column through a fillet. The trunk of the column is decorated with twenty long grooves, semicircular in plan, - flutes, which have semicircular ends.

Make a drawing of the frontal projection of the capital. The drawing should be large enough so that the details are clearly visible. Sign the names of all parts of the capital in the picture. This will make it easier for you to remember them. Analyze the main proportions of the capital, select the total height of the echinus and girdle as a unit of measurement. Compare your drawing with drawing 192.


Fig.191

Continuing to study the form, go around the capital around and examine it from different points. You will notice that the main volume, which is a round symmetrical shape, remains unchanged. Only the position of the square abacus changes. Choose a point of view for the drawing so that one side of the abacus is more open to you and the other side is less. The optimal ratio is 1/2-1/3. The horizon line should pass just below the capital, then its proportions will be close to orthogonal. If necessary, make a sketch to more accurately determine the composition of the sheet.


drawing of architectural details

Stage 1.

Figure 193. Place the future image on the sheet, determining its dimensions vertically and horizontally. Mark the corners of the abacus, the main axis, and also determine the dimensions corresponding to the main parts of the capital. It is very important at this stage of the linear drawing to find the correct ratio of the opening of the upper ellipse of the echinus and the square of the abacus. Traditionally, draughtsmen draw the abacus first, and then have considerable difficulty fitting the ellipse into it. Do it differently: having decided on the size and opening of the ellipse, draw it. Then describe a square around the ellipse, comparing the directions of its sides with nature. Stage 2

Figure 194. Mark all parts of the capital vertically and determine their horizontal dimensions. Draw the main masses, taking into account perspective reductions. Depicting the ellipses of the girdle, neck, astragalus and the lower section of the column, correlate their openings with each other and with the already drawn upper echinus ellipse. Stage 3

Figure 195. Draw flutes. Properly portray them will help you plan the trunk of the column. If you do not have the opportunity to place the plan on the drawing itself, then pin an extra sheet of paper to your work. The points transferred from the plan to the perspective image will make the drawing accurate and convincing. At this stage, the drawing is mostly linear, but when refining the main elements, it is possible to apply a tone that helps to graphically reveal the "movement" of the main surfaces. At the same time, the tone should be very light, suggesting further constructive elaboration of the form. Stage 4

Figure 196. Reveal the shape of the capital by means of chiaroscuro. A clear understanding of the mutual Location in space of the light source, the object and the painter makes it possible to understand the geometry of own and falling shadows, as well as to identify the main tonal relationships. When defining the lines of own and falling shadows, use the knowledge about the nature of chiaroscuro on simple Forms: mentally divide the capital into separate volumes and compare them with the geometric bodies already known to you.

Stage 5

Figure 197 Work out in detail the shapes in the shadows and in the light, generalize the light and shade relationships

images, harmoniously subordinate them to each other, taking into account the aerial perspective.



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Chapter 94



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Ionic drawing.

Ionic is an architectural ornamental element, consisting of an ovoid shape cut off from above, framed by a “shell”, a profiled roller, and lancet leaves pointing downwards. In architecture, ionics are widely used on capitals and cornices of the Ionic and Corinthian orders. Ionic has two axes of symmetry, one of them runs along the egg-shaped form, the other - in the middle of the lancet leaf. Studying the form, make a plan, facade and side facade (Fig. 198). This will help you better understand the structure of the ionic, and will also greatly facilitate further work on the drawing.

Stage 1

Figure 199. Outline the dimensions of the future image on the sheet. Draw in perspective a rectangular slab that is the basis for the ionic.

Stage 2

Figure 200. Draw the diagonals of the ionic base plate and draw a vertical middle line - the main axis of symmetry. Imagine the generalized form of the ionic as a solid quarter shaft with a beveled top, to which a small roller adjoins from below. Draw its plan on the upper surface of the ionic, separate the central egg-shaped volume from the lateral volumes, outline the axes of symmetry passing through the center of the lancet leaves, and specify the main axis. At this stage, pay special attention to the perspective reduction of horizontal segments of equal length.

Stage 3

Figure 201. Draw the details - egg, shells, profiled roller, leaves. Depicting the leaves, make them a large front view in the fields (Fig. 202). This will help you draw the leaves correctly in perspective.

Stage 4

Figure 203. Draw lines of own and falling shadows. Start, as usual, with shadow areas and stroke them several times, separating them from the light. Then you need to strengthen the falling shadows towards the object casting the shadow, the viewer and the light source. At the same time, strengthen the lines of your own shadows, forming zones of reflections. At this stage, do not get carried away with the details, "sculpt" general form in accordance with the law of aerial perspective and the basic principles of the distribution of chiaroscuro on simple geometric bodies.

Stage 5

Figure 204. Continuing work, go to the riveting large form in the light and then to the details. Complete the drawing with a generalization of the form, a harmonious subordination of all its parts.







Chapter 98



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Plaster head drawing

The human head is the hardest natural structure. This is due to its complex function in the human body. You can start drawing a head only if you have a sufficiently developed spatial representation, a thorough knowledge of general provisions drawing and good practice in depicting simpler shapes.

The practical section "Drawing a plaster head" begins with an examination of its external form in an "introductory drawing". This first experience will form the basis of further, more detailed analysis. In the drawing of the skull, the structure of the bone base of the head is analyzed. In Houdon's ecorche drawing, the location and principle of operation of the main muscles, as well as cartilaginous tissues, are studied. For detailed consideration skull and muscles, it would be advisable to refer to anatomical atlases and manuals. AT the following figures special attention is paid to the main details of the head: nose, lips, eyes and ear. And, finally, returning to drawing a plaster head at a new level of understanding of its architectonics (i.e., the relationship between the internal structure and external form), you will be able to consolidate and gradually improve your skills in drawing plaster casts from ancient sculptures: Caesar, Aphrodite, Doryphorus, Diadumen, Socrates, Antinous and Apoxyomenos, traditionally offered for drawing at the entrance exams at the Moscow Architectural Institute.

Drawing "antiques" is a continuation of the old academic traditions. The plastic perfection of classical sculpture, its static nature and extraordinary expressiveness will allow you to quickly understand the general three-dimensional structure of the head, understand its details and basic proportions.

24. Introductory drawing. Head of Doryphorus.

The sculpture of Doryphoros was created in the 5th century BC by the Greek sculptor Polykleitos, a representative of the Peloponnesian school. Polikleitos was not only a sculptor, but also an art theorist. He created the treatise "Canon", where they developed in great detail ideal proportions human body. The figure of Doryphorus - a young hoplite warrior (spearman) - was the embodiment of this canon. At the same time, she was to become the personification of the ideal citizen of the Greek polis: a man like the immortal gods, equally beautiful in body and spirit, a courageous defender of his native city. The face of Doryphoros is schematic, it is devoid of individual traits and expressions, which is why the head of Doryphoros is offered for the first "introductory" work, as a result of which you will receive an initial, largely simplified idea of ​​​​the shape of the head.

The head has a brain and facial parts. Its external plasticity is known with the help of a number of anatomical points - nodes ( reference points or lighthouses) and lines. So, on the head are clearly visible: the chin tubercles, the line of the lower jaw, the corners of the mouth, the lines limiting the area of ​​the mouth, the line of the incision of the lips, the filter, the base, the tip and wings of the nose, the bridge of the nose, the cheekbones, the zygomatic arches, the orbital edges, the tear ridges, the eyebrow arches , lines limiting the eyebrow arches, frontal tubercles, temporal lines, crown, auricles, auditory openings, mastoid processes of the temporal bones, parietal and occipital tubercles, nuchal line, border of the neck and chin, jugular fossa and protrusion of the seventh cervical vertebra. Find all these points and lines in figures 205 and 206, and then on the plaster head.

Knowing the anatomical points - beacons and characteristic lines, you will never get confused in the details and will always be able to distinguish the main from the accidental. For a better understanding of the external spatial relationships of the points of the head, a simplified diagram is often used, representing its structure in the form of an irregular polyhedron. It is impossible, however, to abuse such schemes in the drawing. They are only needed as visual aids for a competent and convincing representation of the human head.



Chapter 100


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Draw from the drawing by P.I.Churilin

from the textbook "The structure of the human head"


Chapter 102

Draw from PIChurilin's drawing

from the textbook "The structure of the human head"

It is also customary to study the human head by analyzing its sections in three mutually perpendicular planes: sagittal, horizontal and frontal (Fig. 207).

The sagittal plane is the plane of symmetry of the body. Its name comes from the Latin "sagttta" - an arrow. A cut in this plane gives us the midline, which is the basis of the professional line of the face and is very important for the drawing of the head.

The horizontal plane passes through the base of the occiput and the base of the nose.

Frontal plane perpendicular to the first two and "cuts" the head at its widest point. It passes through the top of the head, the parietal tubercles and the fulcrum of the skull on the spine. The study of these sections, as well as orthogonal projections of the head: front, back, side and top views will help to you better understand the external plasticity of the head and more accurately convey it in your drawing.


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The task of the “introductory” drawing is a good composition on the sheet, the total volume correctly conveyed, as well as the exact location and size of each detail of the head.

Stage 1

Figure 208. Starting work, determine the position of the horizon line and the angle. To do this, mentally enclose your head in a cube. Find the overall dimensions and place the future image on the sheet using short serifs. Remember that if you draw the head in front - the spaces on the left and right should be equal so that the image does not “fall over”, but if you draw the head in profile, in 3/4 or 7/8 - the sheet space in front of the head (from the side face) should be larger than from the back of the head. With light lines outline the outline of the head (outline).

Stage 2

Figure 209. Draw the main large parts: separate the mass of the head from the neck, outline the front part, its front plane and easily draw an axial profile line. Specifying the profile line, find the characteristic points lying on it: the point of the top of the forehead (on the hairline), the point between the eyebrows, the point of the base of the wings of the nose and the point of fracture of the chin. These points determine the main canonical proportional relations of the parts of the head. According to the Greek classical canon, the distances between these points must be equal. Draw horizontal lines through these points (in the figure extending to the vanishing point on the horizon) and mark on them, respectively, the width of the forehead, the base of the nose and the chin. For right choice directions of these lines, use the sighting method.

In accordance with the ancient canon, along the line of the eyes, the ancient head is divided into two equal parts - from the top of the head to the line of the eyes and from the line of the eyes to the base of the chin. The segment from the superciliary arches (the point between the eyebrows) to the base of the wings of the nose is divided into three equal parts - the line of the eyes passes along the upper division line, and the base and wings of the nose are separated along the lower line. The segment between the point of the base of the wings of the nose and the fracture of the chin is also divided into three equal parts. The middle line of the mouth passes along the upper division line, which is also called the lip cut line, the lower line divides the chin in half. The distance between the eyes is equal to the length of the eye, i.e. the eye line is also divided into three equal parts. The height of the ear is equal to the length of the nose.


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What thoughts, what concepts come to your mind first of all when you think of photographic composition? Many will say: balance in the frame, the rule of thirds, rhythm, guiding lines ... Yes, all this is true. All this affects the composition of the frame. All this works and works great. But not only that! There is also the angle, perspective, the relationship of tones, colors, contrasts ... All this the photographer needs to know and be sure to study the composition, the laws of constructing an image on a plane. Those who have recently decided to seriously engage in photography, who have just come into photography and are still discovering it for themselves, getting acquainted with the rules and laws of composition, sometimes cannot even imagine how many interesting things this most interesting art includes. The laws of composition are much deeper than it might seem at first glance. But starting to study the composition, you should not worry in any way. It is not so difficult. Just gradually getting acquainted with its laws, mastering them, you need to train. How? As the famous movie character used to say, “Elementary. Watson! Take more photos! Fortunately, the current technology allows you to photograph a lot. In film and expensive consumables today there is practically no need.

Today we decided to talk with you about geometry in composition. Yes Yes! Do not wonder! Geometry is one of the most important aspects of composition. And in this article we will try to prove it to you.

The bulk of those who have a camera, without thinking about it themselves, unconsciously use their knowledge of geometry when photographing, introducing various geometric shapes into a particular frame. Don't believe? Read the article further - and you will see that we are right. I would like to think that the information below will give you an impetus to further development mastery of the composition, to further improve your skills in photography.

Rectangles

Using these, perhaps the most popular figures in geometry, in the composition of a photograph is akin to using the rule of thirds. But, unlike this known rule, the frame is divided not into three imaginary equal parts, but into imaginary rectangles of various sizes. Just take a look at this picture. The bottom of the photo, the bank and the grass, form a horizontal rectangle. And the left side of the picture, where there is a large blue spot of the water surface, is a vertical rectangle. These two rectangles in the composition of the picture very well highlight the lantern standing on the shore. It looks like an isolated, independent object.

Circles

Circles have their own energy. They seem to concentrate a certain energy in themselves, and thereby direct the viewer's gaze into the depth of the frame. In order to create a spectacular composition, experienced photographers and good artists often use not only circles, but also semicircles. Here in this photo, which we have given as an example, this is very clearly visible. The circles in her composition focus the viewer's attention and gradually lead him to the main thing in the frame - to the beautiful mountain peaks in the distance.

triangles

A triangle is probably the most common geometric element in the composition of any image on a plane. Take a close look at your own photos. Pay attention: triangles are everywhere! They are literally scattered over your pictures! Here is an example for you - the most ordinary mountain landscape. The triangles in this photo create an imaginary, but quite natural way, which leads the eye of the viewer looking at the picture from the fence in the foreground towards the mountains themselves. And the mountains themselves, take a closer look, also have the shape of a triangle!

Polygons

Looking into the camera viewfinder, most photographers, especially beginners, hardly think that now, mentally working on the composition of the future frame, they will imagine some kind of polygons. But then, when they see their pictures already on the monitor screen, they will be very, very surprised: there will be a huge number of polygons on them! They are what give photographs visual sense. Take a look at these pictures here. They clearly show that geometric polygons appear in the plane of the frame not only due to the shape of the objects themselves. They are also well seen due to the contrast of individual sections, due to light spots and shadows.

squares

The square is considered perfect figure not only in geometry, but in general in the visual arts as a whole. Remember, at least, the famous "Black Square" by Kazimir Malevich. And for the photo square - perfect shape. Look at this illustration. main object photos easily and naturally fit into the square. And this square, in turn, is in perfect harmony with other squares - squares formed from books and bookshelves in the background.

arches

Arches in their manifestation in the composition of building an image on a plane somewhat repeat the “work” of circles. But, unlike circles, arches are more of a background element than an independent geometric shape. Here in this photo, for example, women's hands holding a rose and folded in the shape of a heart form three whole arches! And these imaginary arches form, as it were, a frame framing a beautiful and delicate flower.

Converging and parallel lines

Any experienced photographer or artist will tell you that it can be very difficult to correctly use various kinds of lines in a composition. However, it is quite possible. Both converging lines and parallel ones can, and even more than that, should be effectively used in the composition of the frame! Such lines work especially effectively when composing the background. Look at this picture. It is easy to see both converging and parallel lines on it. They are very good at directing the viewer's eye to the main subject of the photo - to a person sitting on the grass. Plus, these lines visually seem to be reflected from each other.

Attitude and balance of space

If you want to add to your photo works make more sense, in some way increase their emotional impact on the viewer, then try to understand the understanding of space. In some cases, compositionally photographs can be quite simple at first glance. Like these, for example. What is the most important thing here? Correctly. The proximity of the viewer to the bench shown by the author and the presence of space, or rather, even emptiness directly behind it. This kind compositional construction frame allows the viewer to mentally, at the subconscious level, recreate in his mind the history of this plot, based on his experiences, on his personal experience on your emotions.

Take your time to deal with everything that we have told you today. Try to understand how they affect geometric elements on the composition of the image on the plane. Perhaps this understanding will not come to you immediately. But it's not scary at all. The main thing is that it seems to us that we, so to speak, have sown our seed. You just have to wait for shoots first, and after a while, fruits.

DRAWING AS REPRESENTED: COMPOSITION FROM GEOMETRIC BODIES. STEP-BY-STEP GUIDE. REVIEW

Volumetric composition of geometric bodies. How to draw?

A composition of geometric bodies is a group of bodies of a geometric nature, the proportions of which are regulated according to the table of modules cut into each other and thereby forming a single array. Often such a group is also called architectural drawing and architectural composition. Although the formation of the composition, like any other production, begins with a sketch idea - where you can determine the overall array and silhouette, front and background plans, the work must be "built" sequentially. In other words, to have as its beginning a compositional core, and only then, by means of the calculated sections, to “acquire” new volumes. In addition, this allows you to avoid accidental flaws - "unknown" sizes, too small indents, ridiculous cuts. Yes, we must immediately make a reservation that such topics raised by almost every drawing textbook as “Organization of the workplace”, “Varieties of paints, pencils and erasers”, and so on, will not be considered here.

Composition from geometric shapes, picture

Before proceeding to the examination exercise - “Composition of three-dimensional geometric shapes”, you must obviously learn how to depict the geometric bodies themselves. And only after that you can go directly to spatial composition from geometric bodies.

How to draw a cube correctly?

On the example of geometric bodies, it is easiest to master the basics of drawing: perspective, the formation of a volumetric-spatial design of an object, the patterns of chiaroscuro. The study of the construction of geometric bodies does not make it possible to be distracted by small details, which means that it allows you to better learn the basics of drawing. The image of three-dimensional geometric primitives contributes to a competent image of more complex geometric shapes. Depicting the observed object competently means showing the hidden structure of the object. But in order to achieve this, the existing tools, even leading universities, are not enough. So, on the left side, a cube is shown, checked by the "standard" method, widely used in most art schools, schools and universities. However, if you check such a cube using the same descriptive geometry, presenting it in plan, it turns out that this is not a cube at all, but there is some geometric body, with a certain angle, probably the position of the horizon line and the vanishing points only resembling it.

Cuba. Left is wrong, right is right

It is not enough to put a cube and ask to depict it. Most often, such a task leads to proportional and perspective errors, among which the most famous are: reverse perspective, partial replacement of the angular perspective by the frontal one, that is, the replacement of a perspective image by an axonometric one. There is no doubt that these errors are caused by a misunderstanding of the laws of perspective. Knowing the perspective helps not only to warn against blunders at the very first stages of building a form, but also stimulates you to analyze your work.

Perspective. Cubes in space

Geometric bodies

Here, combined orthogonal projections of geometric bodies are shown, namely: a cube, a ball, a tetrahedral prism, a cylinder, a hexagonal prism, a cone and a pyramid. In the upper left part of the figure, lateral projections of geometric bodies are shown, in the lower - a top view or plan. Such an image is also called a modular scheme, since it regulates the sizes of bodies in the depicted composition. So, it can be seen from the figure that at the base all geometric bodies have one module (the side of the square), and in height the cylinder, pyramid, cone, tetrahedral and hexagonal prisms are equal to 1.5 cube sizes.

Geometric bodies

Still life of geometric shapes - we go to the composition in stages

However, before moving on to the composition, a couple of still lifes consisting of geometric bodies should be completed. The exercise “Still life drawing from geometric bodies in orthogonal projections” will be even more useful. The exercise is quite difficult, which should be taken with due seriousness. Let's say more: without understanding the linear perspective, it will be all the more difficult to master a still life according to orthogonal projections.

Still life of geometric bodies

Geometric body frames

Inserts of geometric bodies - this is such a mutual arrangement of geometric bodies, when one body partially enters another - it crashes. The study of frame variations will be useful for every draftsman, because it provokes the analysis of one form or another, architectural or living in equal measure. Any depicted object is always more useful and efficient to consider from the standpoint of geometric analysis. The tie-ins can be conditionally divided into simple and complex, but it should be noted that the so-called "simple tie-ins" require great responsibility in the approach to the exercise. That is, in order to make the cut-in exactly simple, you should decide in advance where you would like to place the cut-in body. by the most simple option there is such an arrangement when the body is displaced from the previous one in all three coordinates by half the size of the module (that is, half the side of the square). General principle search for all cuts is the construction of the cut body from its inner part, that is, the cut of the body, as well as its formation itself, begins with a section.

Section planes

Composition of geometric shapes, phased implementation exercises

It is widely believed that the arrangement of bodies in space through the “chaotic” imposition of their silhouettes on each other makes it easier and faster to form a composition. Perhaps this is what prompts many teachers to demand the presence of a plan and a facade in the conditions of assignments. So, at least, the exercise is already presented in the main architectural domestic universities.

Volumetric-spatial composition of geometric bodies considered in stages

Chiaroscuro

Chiaroscuro is the distribution of illumination observed on an object. In the figure, it manifests itself through tone. Tone is a visual means that allows you to convey natural relationships of light and shadows. It is relationships, since even such graphic materials like a charcoal pencil and White paper, are usually not able to accurately convey the depth of natural shadows and the brightness of natural light.

Basic concepts

Conclusion

It should be said that geometric precision is not inherent in the drawing; So, in specialized universities and schools, using a ruler in the classroom is strictly prohibited. Trying to correct the drawing with a ruler leads to even more errors. That's why it's hard to underestimate practical experience- since only experience can train the eye, consolidate skills and enhance artistic flair. At the same time, only with the help of sequential execution of the image of geometric bodies, their mutual inserts, acquaintance with perspective analysis, aerial perspective- it is possible to develop the necessary skills. In other words, the ability to depict simple geometric bodies, the ability to represent them in space, the ability to connect them with each other and, no less important, with orthogonal projections, opens up broad prospects for mastering more complex geometric shapes, whether they are household items or a human figure and head, architectural structures and details or cityscapes.

Creativity & Hobbies

Learn the basics of architectural drawing

The cornerstone in architectural education is the knowledge of the fundamentals of architectural drawing. Even though I didn't get into architecture this year, I didn't give up the idea of ​​becoming an architect and I will slowly but surely move towards my goal.

So, in front of me is the book "Drawing by Representation. From Geometry to Architecture". Starting today, I will begin to study this book thoughtfully and diligently, practicing drawing every day. I commit to spend 1.5-2 hours a day drawing from a book (exceptions: unforeseen circumstances, days off, travel and situations where I can't use the tools and tutorial) and show the community my work. I will not rush much, and I will set the deadlines approximately, with a large margin. The deadline is March 6 next year.

Goal Accomplishment Criteria

The book has been studied: all tasks have been completed, photos of the work have been posted on the site.

personal resources

Time every day, paper, tools, book.

  1. Part 1. Initial exercises

    Section 1 Drawing Straight Lines

    • Straight line pattern
    • Drawing parallel straight lines
    • Drawing straight lines "from point to point"
    • Division of straight lines into equal segments
    • Division of angles into equal parts
    • Line drawing

    Section 2 Drawing curved lines

    • curved line pattern
    • Draw curved lines by anchor points
    • Ornament pattern based on a circle
    • Ellipse drawing
    • Ellipse pattern
  2. Part 2. Perspective of a square and a circle

    • Perspective diagram
    • Drawing a square in perspective
    • Drawing of a square circumscribed around a circle in perspective
  3. Perspective of simple geometric solids

    Section 5. Perspective drawing of a cube and a tetrahedral prism

    • Perspective cube drawing
    • Drawing of nine cubes
    • Linear-constructive drawing of a composition of cubes according to the plan and facade in frontal and angular perspectives
    • Linear-constructive drawing of a composition of cubes in perspective
    • Linear-constructive drawing of a composition of cubes and tetrahedral prisms in perspective

    Section 6. Pyramid and Hexagon Perspective

    • Linear-constructive drawing of a pyramid
    • Linear-constructive drawing of a hexagonal prism

    Section 7. Cylinder, Cone, and Ball Perspective

    • Linear-constructive drawing of a cylinder
    • Linear-constructive drawing of a cone
    • Section of a cylinder and a cone by planes parallel to the bases
    • Section of a cone by parallel planes perpendicular to its base
    • Drawing of cylinders of different diameters stacked on top of each other
    • Linear-constructive drawing of the ball
    • Section of a ball by parallel planes
    • Drawing of a ball standing on a cube
    • Drawing of a cube circumscribed inside a sphere
  4. Part 4. Tonal drawing

    Section 8. Tone. Initial exercises

    • Hatching tonal spots
    • Hatching flat figures
    • Tonal scale made in hatching technique
    • Shading flat figures
    • Hatching in the technique of "wide stroke"
    • Planar composition of polygons

    Section 9. Black and white drawing of simple geometric bodies

    • Tonal drawing of a cube
    • Tonal drawing of a tetrahedral prism
    • Tonal drawingpyramid
    • Tonal drawing of a cylinder
    • Tonal drawing of a cone
    • Tonal ball pattern
    • Tonal drawing of a stepped cone
    • Tonal pattern of illuminated surfaces
    • Tonal pattern of shadow surfaces
    • Tonal drawing of a composition of four cubes
  5. Part 5. Inserts of geometric bodies

    Section 10

    • Inset cube and tetrahedral prism
    • Inset cube and pyramid
    • Inset cube and hexagonal prism
    • Cube and Cylinder Inset
    • Cube and Cone Inset
    • Insertion of a sphere and a cube according to given orthogonal projections
    • Cube and ball with a common center
    • Insertion of a sphere and a cube, when the cutting planes of the cube do not pass through the center of the sphere

    Section 11. Complex tie-ins.

    • Oblique section of a hexagonal prism
    • Inset of two hexagonal prisms
    • Oblique section of the pyramid
    • Inset pyramid and hexagonal prism
    • Inclined section of the cylinder
    • Cylinder and hexagonal prism insert
    • Pyramid and Cylinder Insert
    • Inclined section of a cone
    • Cone and hexagon insert
    • Inset Cone and Pyramid
    • Inclined section of the ball
    • Hexagonal prism and ball inset
  6. Composition of simple geometric bodies

    Section 12



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