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Composition of cubes in space. Composition of geometric solids in the entrance exams to the Marhi

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

Closed and open composition

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

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

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


Golden ratio rule

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

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

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

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

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

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

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

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

Three thirds rule

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

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

Creativity & Hobbies

Learn the basics of architectural drawing

The cornerstone of architectural education is knowledge of the fundamentals of architectural drawing. Although I did not enroll in architecture this year, I have not given up the idea of ​​becoming an architect and will slowly but surely move towards my goal.

So, in front of me is the book "Drawing by Representation. From Geometry to Architecture." WITH today I will begin to study this book thoughtfully and diligently, practicing drawing every day. I commit to spending 1.5-2 hours a day drawing from the book (exceptions: unforeseen circumstances, days off, travel and situations when I cannot use the tools and textbook) and showing my work to the community. I won’t be in a big hurry, and I’ll set the deadlines approximately, with a large margin. Deadline is March 6 next year.

Goal Accomplishment Criteria

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

Personal resources

Time every day, paper, tools, book.

  1. Part 1. Initial exercises

    Section 1, Drawing Straight Lines

    • Drawing straight lines
    • Drawing parallel straight lines
    • Drawing straight lines "from point to point"
    • Dividing lines into equal segments
    • Dividing angles into equal parts
    • Linear pattern drawing

    Section 2. Drawing curved lines

    • Drawing of curved lines
    • Drawing curved lines using reference points
    • Drawing of an ornament based on a circle
    • Ellipse drawing
    • Drawing of ellipses

  2. Part 2. Perspective of a square and a circle

    • Perspective diagram
    • Drawing of 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 drawing of a cube
    • Drawing of nine cubes
    • Linear-constructive drawing of a composition of cubes according to the plan and facade in frontal and corner 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. Perspective of a cylinder, cone and sphere

    • Linear design 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 a 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 shapes
    • Tonal scale made using hatching technique
    • Shading of flat figures
    • Hatching using the "broad stroke" technique
    • Planar composition of polygons

    Section 9. Black and white drawing of simple geometric bodies

    • Cube tonal pattern
    • Tonal pattern of a tetrahedral prism
    • Pyramid tonal pattern
    • Cylinder tonal pattern
    • Tonal cone pattern
    • Tonal pattern of the ball
    • Step cone tonal pattern
    • Tonal pattern of illuminated surfaces
    • Tonal pattern of shadow surfaces
    • Tonal drawing of a composition of four cubes

  5. Part 5. Insets of geometric bodies

    Section 10. Simple sidebars

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

    Section 11. Complex tie-ins.

    • Oblique section of a hexagonal prism
    • Insertion of two hexagonal prisms
    • Oblique section of the pyramid
    • Inset of pyramid and hexagonal prism
    • Inclined section of the cylinder
    • Insertion of cylinder and hexagonal prism
    • Inset of pyramid and cylinder
    • Inclined section of the cone
    • Inset of cone and hexagon
    • Cone and pyramid inset
    • Inclined section of the ball
    • Insertion of hexagonal prism and ball

  6. Composition of simple geometric bodies

    Section 12. Composition of simple geometric bodies on entrance exams at Moscow Architectural Institute

DRAWING BY REPRESENTATION: COMPOSITION OF GEOMETRIC BODIES. STEP-BY-STEP GUIDE. REVIEW

Volumetric composition of geometric bodies. How to draw?

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

Composition of geometric shapes, drawing

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

How to draw a cube correctly?

Using the example of geometric bodies, it is easiest to master the basics of drawing: perspective, the formation of the volumetric-spatial structure of an object, the patterns of light and shadow. Studying the construction of geometric bodies does not give the opportunity to be distracted by small parts, which means it allows you to better understand the basics of drawing. The depiction of volumetric geometric primitives contributes to the competent depiction of more complex geometric shapes. To depict an observed object competently means to show the hidden structure of the object. But in order to achieve this, the existing tools, even from leading universities, are not enough. So, on the left side, there is a cube tested in a “standard” way, widespread in most art schools, schools and universities. However, if you check such a cube using the same descriptive geometry, imagining it in plan, it turns out that this is not a cube at all, but some geometric body, with a certain angle, and probably the position of the horizon line and vanishing points only resembles it.

Cubes. Left is wrong, right is right

It’s not enough to put a cube and ask someone to draw it. Most often, such a task leads to proportional and perspective errors, among which the most famous are: reverse perspective, partial substitution angular perspective frontal, that is, replacing a perspective image with an axonometric one. There is no doubt that these errors are caused by a misunderstanding of the laws of perspective. Knowing perspective helps not only to prevent serious mistakes at the very first stages of form construction, but also stimulates you to analyze your work.

Perspective. Cubes in space

Geometric bodies

It shows combined orthogonal projections of geometric bodies, namely: cube, sphere, tetrahedral prism, cylinder, hexagonal prism, cone and pyramid. The upper left part of the figure shows lateral projections of geometric bodies, and the lower part shows 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. Thus, from the figure it is clear that at the base all geometric bodies have one module (the side of a square), and the height of a cylinder, pyramid, cone, tetrahedral and hexagonal prisms is equal to 1.5 times the size of a cube.

Geometric bodies

Still life of geometric shapes - we go to the composition step by step

However, before moving on to the composition, you should complete a couple of still lifes consisting of geometric bodies. The exercise “Drawing a still life from geometric bodies using orthogonal projections” will be even more beneficial. The exercise is quite difficult, which should be taken with due seriousness. Let's say more: without understanding linear perspective, mastering still life using orthogonal projections will be even more difficult.

Still life of geometric bodies

Insets of geometric bodies

Insets of geometric bodies - what is this? mutual arrangement geometric bodies, when one body partially enters another - crashes. Studying the variations of insets will be useful for every draftsman, because it provokes the analysis of one form or another, architectural or living in equal measure. It is always more useful and effective to consider any depicted object from the position of geometric analysis. Sidebars can be roughly divided into simple and complex, but it should be noted that even the so-called “simple sidebars” require great responsibility in the approach to the exercise. That is, in order to make the insertion simple, you should decide in advance where you would like to place the embedded body. The most simple option This arrangement turns out to be 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 inserts is the construction of the inserted body from its internal part, that is, the insertion of the body, as well as its formation itself, begins with a section.

Section planes

Composition of geometric shapes, step-by-step exercise

There is a widespread belief that it is easier and faster to form a composition by placing bodies in space through the “chaotic” overlay of their silhouettes on top of each other. Perhaps this is what prompts many teachers to demand the presence of a plan and façade in assignments. This is how, at least, the exercise is already presented in the main Russian architectural universities.

Volumetric-spatial composition of geometric bodies considered in stages

Chiaroscuro

Chiaroscuro is the distribution of illumination observed on an object. It appears in the drawing through tone. Tone - visual medium, allowing you to convey natural relationships of light and shadows. Precisely relationships, since even such graphic materials, How 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 accuracy is not inherent in the drawing; Thus, in specialized universities and colleges, using a ruler in classes is strictly prohibited. An attempt to correct the drawing using a ruler leads to further more errors. Therefore, it is difficult to belittle the importance of practical experience - since only experience can train the eye, consolidate skills and strengthen artistic flair. At the same time, only through the sequential execution of images of geometric bodies, their mutual insertions, familiarity with prospective analysis, from an 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, be it household items or human figure and head, architectural structures and details or cityscapes.