Construction of geometric bodies in perspective in stages. The shape of simple geometric bodies

First stage. Determining the size of the ball, the fulcrum and the plane on which it is located.


Second phase. Refinement of the diameter of the circle of the ball, determination of the boundaries of light, midtones and own shadow, reflex and falling shadow.


Third stage. The transfer of volume with strokes superimposed in the shape of a ball. It is necessary to pay attention to the smoothness of tonal transitions on a spherical surface.


166. Turning a circle into a ball


See how easy it is to turn a circle into a ball using various hatching techniques or just thickening the outline on one side.

Words are not as powerful as a few hours of practice in drawing the indicated objects. You can try to depict some simple things and geometric bodies.

When choosing objects, take an egg or a solid ball as sphere-like models, a cardboard box can be a cube. Pyramids, cones and prisms are also easy to make from cardboard. But don't limit yourself to just white models, try to depict light and dark, matte and shiny objects.

Light, shadow and penumbra play essential role on the shape of the object. The artist, drawing a live model or still life, often experiments with light sources.

Use them consciously to best convey the features of the shape and texture of objects, try to illuminate them with different sides.




167. Paper tape


The contrast of light against dark or dark against a light background is greater the closer the light source is. Objects that are fully lit from all sides appear flat.

See how differently the shape is perceived depending on the change in the direction of the light source.




168. Still life in different lighting


Consider pictures 169 a, b. Smooth shading of one tone does not convey the three-dimensional shape of objects. Applying strokes to the shape of objects, taking into account light and shadow, turns flat silhouettes into three-dimensional things.




169. Still life: a - planar tonal solution, b - volumetric tonal solution


still life with geometric shapes- we know how to draw geometric shapes separately from this page, we also learned how to use the eye and perspective skills to build volumes of shapes. Good. And now we will take two or three figures with you, place it on the object plane and make a drawing. Most likely, when you made layouts of geometric shapes, you got them in different sizes, different. For a still life with geometric objects, we will need figures, preferably different in size, so that in the composition they do not have the same volumes, masses. So more interesting and harmonious.

I take a ball, a cone and a cube. The cone is a little the same size as the ball, but it is directed upwards, and if the ball is a static figure, then the cone is dynamic, it is he who sets the format for me - the still life in the sheet will be placed vertically. Well, the third I'll take the cube. It will be smaller than the other two figures, which will give variety in the "assortment".

Look at the photo on the right. Here is my still life. My object plane and figures are white, and for this, we will consciously assume that the wall will also be white. We will do this so that additional tones in the drawing do not interfere with us. Now we will not copy, but first of all analyze and transfer what we already know in the sheet. And by this moment we should already know the basic laws of drawing. And knowing the basic rules and laws in the drawing, after the construction stage, you can often not resort to the help of nature, since it can give you a lot of reasons to divert your attention from the main thing - we consolidate knowledge.

Also in this fragment of the picture you can see how the shadows will behave. The most active is the drop shadow from the cube. All shadows that will be removed into space will lose their activity, BUT! will still be shadows. Don't forget about it. Now let's look at the whole job:

Here is a still life you can get.

Let's analyze a little more. See which side the lighting is on? It's not hard to tell from a cube. Its side face is illuminated the most. This means that the light source is located more on the side than on top. That is why the object plane will already initially have a darker tone than the wall in the background. The only area is the lightest on the object plane - closest to us, in front of the cube. There is even a reflection from the white illuminated plane of the cube. But still, the tonality will be stronger than on this side of the cube. And the overall tone of the object plane will be darker than the tone of the wall. This is how you can "play" with stroke and tone, creating space in the sheet.

By the way, there are reflections both on the shadow side of the cube and on the ball; they reflect from the object plane. See? But this only adds to the liveliness and realism in the drawing, and as before, the shadow remains a shadow - the reflex should not have a tonality equal to the tonality of the illuminated surface. When you look at this area in nature for a long time, it may often seem so to you, but in fact you just need to give your eyes a rest, and then look at the whole picture, scattering your eyes and analyzing everything in general.

Now the area closest to us is a break in the object plane, it receives enough light so that it does not make it the darkest, but perhaps we would need to select the area under it (under the table) as the darkest. But we will not do this, since the main action we do not take place under the table. I think that it is enough how actively the fracture of the object plane is shown and how much is allocated in the sheet of the place of the shadow located under it. Importance we handed over to this section and that's enough here. And also notice how the stroke falls in this place: also, obeying the general system, the stroke burns the already created mood of the composition with the horizontal direction of the lines. And even though our tablet is turned vertically, the figures are also located supporting the vertical, but such a character of the stroke does not spoil our verticality in any way, on the contrary, it balances and gives order and static. Everything is balanced, harmonious and perfectly coexists with each other.

This is how we arrange the space in the sheet. Work hard, you'll be fine. A good beautiful still life with geometric figures is worth a little work on its creation. This is how we gradually learn how to learn how to draw in order to draw anything later.

Any geometric body consists of a shell, i.e., an outer surface, and some material that fills it (Fig. 42). Each geometric body has its own shape, which differs in composition, structure and size.

The composition of the shape of a geometric body is a list of compartments of the surfaces that make it up (Table 4). So, the shape of a rectangular parallelepiped consists of six compartments, surfaces (faces): two of them are the bases of the parallelepiped, and the remaining four compartments form a closed convex broken surface, called the side surface.

Fig 42. Geometric body: 1 - shell; 2 - compartments of surfaces forming the body shell

Form structure geometric body - a characteristic of the form, which shows the relationship and location of the compartments of surfaces relative to each other (see Fig. 44).

These characteristics are interrelated and to the greatest extent determine the shape of a geometric body and any other object.

By shape, simple geometric bodies are divided into polyhedra and bodies of revolution.

Plane is a special case of a surface.

Polyhedra - geometric bodies, the shell of which is formed by compartments of planes (Fig. 43, a).

Facets - compartments of planes that make up the surface (shell) of the polyhedron; edges - line segments along which faces intersect; vertices are the ends of edges.

Solids of revolution - geometric bodies (Fig. 43, b), the shell of which is a surface of revolution (for example, a ball) or consists of a section of the surface of revolution and one (two) section of planes (for example, a cone, a cylinder, etc.).


Rice. 43. Polyhedra (a) and bodies of revolution (b): 1 - shell of a geometric body;
2 - compartments of planes; 3 - compartments of surfaces of revolution

4. Composition of simple geometric bodies







The structure of the form affects the appearance of the geometric body. Let's consider this using the example of straight and inclined cylinders (Fig. 44), the base compartments of which are located differently relative to each other.


Rice. 44. Structural differences in the shape of cylinders


Rice. 45. Changes in the shape of cylinders




Rice. 46. ​​Quadrangular pyramids of various shapes

Comparing the images of the cylinders in Figure 45, we can conclude that a change in the position of one of the bases leads to a change in the shape of the geometric body.

Changing the height, width, length, base diameter, axial inclination angle, the position of the bases relative to each other significantly affects the shape of geometric bodies. For example, consider quadrangular pyramids of various shapes (Fig. 46).


Rice. 47. Geometric bodies