Constructive drawing of a still life of geometric bodies: Methods for constructing geometric bodies in space Automatic translate

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Methods for constructing geometric bodies in space

Cube

The cube is the very first and most important geometric figure that anyone who starts learning to draw faces. There is no better model for the development of spatial-spatial thinking. Cube drawing forms a vision of perspective, is the most important source of knowledge and drawing skills. The basis for future design decisions of the designer is almost always based on a cube or a combination of cubes.

The main thing in the drawing of the cube is to set three-dimensionality, build its base, taking into account the perspective reduction and angle. And then it’s easy to almost mechanically build all the faces, observing the proportions and perspective parallelism of the lines converging at a point on the horizon. Of course, in order to accomplish all this, the cube pattern should look like a structure or, in other words, a transparent frame. So, draw the cube frame.

Unfortunately, for some beginners, the cube is a kind of uninteresting, simple and useless drawing subject. Later, some of these “draftsmen” realize the volume of their own tragedy and will spend a tremendous amount of energy to re-learn to see the laws of perspective. And others will never see their own blindness. Because it all starts with a drawing of an ordinary cube.

Hexagonal prism

The hexagonal prism is a geometric body (on the one hand, the cross section of this shape looks like a quadrangle, and on the other hand, it is a hexagon, moreover, fits into a circle). It is very difficult to make a constructive drawing of this geometric primitive in space if you do not see a tetrahedral prism (“brick”) in its constructive basis, the construction of which is similar to the construction of a cube and which you already know how to draw.

Please note that, while performing the drawing of this geometric primitive, we are already trying to understand its design as the sum of simpler primitives, such as a tetrahedral prism and two trihedral prisms. The expression “if you don’t see” very accurately reflects the essence of the constructive drawing.

Perform a wireframe drawing of a “brick” (that is, a tetrahedral prism) in space, observing the proportional relations of height, width and depth. On the end surfaces of the "brick" draw diagonals. At the intersection of the diagonals, we get two points that will be in the center of the end surfaces and through which we can build a perpendicular section. It will pass through the figure of the tetrahedral prism.

We draw segments from the vertices of the tetrahedral prism, practically repeating the direction of the diagonals, until they intersect with the secant plane and get four more vertices of the hexagonal prism. Connect the vertices together using lines and get a constructive (wireframe) pattern of a hexagonal prism.

If the pattern is not entirely correct, look for the reason in the proportional relationship of the sides of the tetrahedral prism.

Ball

The ball is a geometric primitive. It is three-dimensional, has all sides of three-dimensional space, fits into a cube. The vertices of the ball inscribed in the cube are in the center of the surfaces of the sides of the cube (Fig. 10).

The simplest way to construct a ball constructively is as follows. Draw two centerlines, vertical and horizontal. From the center of intersection of the axial lines - according to the proportional relations of the ball with other geometric objects (if any) - set aside identical segments on the axial lines and draw a circle.

You will get a two-dimensional surface in the form of a circle, but it is not a ball, because it does not have a third dimension, that is, depth. To create volume, it is necessary to open the horizontal center line to the state of a square plane in perspective. The position of this plane in space will depend on your point of view on this subject. The circle should fit into the square: build a circle (section), which will be in the form of an ellipse, through four points. Thus, we got a constructive drawing of a ball in space.

You can also expand the vertical center line to the state of the plane. Then the constructive drawing of the ball will inform us not only about how we perceive the geometric figure from above or below, but also about how we perceive it from the right or from the left. And, of course, there is another significant plus in this: we get two vertices of the ball. One vertex will indicate the highest point of the ball in space, and the other - at the fulcrum, if the ball is on a plane.

Cylinder

A cylinder is also a geometric primitive. The shape of the cylinder is formed by a rectangular section, rotated in space 360 ​​degrees around the axis. The axis function is performed by one of the sides of this rectangular section. If we consider the sectional shapes of the cylinder (and there are two of them), then one of them is a rectangle, and the other is a circle.

In order to build a cylinder located vertically, it is necessary to draw a vertical center line, put on the axial proportional segment equal to the height of the cylinder. Then, through the extreme points of the segment, draw two horizontal axial lines strictly perpendicular to the vertical. On the horizontal center lines, set aside proportional segments equal to the width of the cylinder so that the vertical center line divides these segments equally. Connect the extreme points of the horizontal segments to each other. Get a two-dimensional rectangular shape with aspect ratios similar to the sides of the cylinder.

Create a third dimension. Draw two ellipses (circle in perspective) through four points. The upper ellipse will be narrower than the lower ellipse, as it is in a larger perspective reduction.

The main problem in constructing a cylinder is not to create ellipses, but in their centerlines, because their construction - by inexperience - is not taken seriously. Violation in the construction of the vertical center line leads to asymmetry and instability of the cylinder shape. Violation of the construction of the horizontal center line leads to the inability to draw a regular ellipse. But everything is simple: the vertical center line of the figure corresponds to the vertical side of the sheet of the figure, the same can be said about the horizontal center lines.

Of particular difficulty in the constructive construction is the shape of the cylinder lying on the side surface. The round section of the cylinder fits into a square (which can be relatively easy to construct in space) at four points. This means that it is easier for us to first build in space a tetrahedral prism corresponding to the proportional ratios of the sides of the cylinder, and then fit the cylinder into it.

How to find the centerline equal to the width of the cylinder in this view? Having built a tetrahedral prism in space, find the median line in it, draw a line at right angles to the median line through the center of the side surface. On this line is a segment equal to the width of the cylinder in this angle. It turns out that the side surface of the cylinder is built on six points.

Why are we talking so much about building a cylinder? Because you will encounter him at every step, whether it will be a household item, drapery, a person’s head or a person’s figure. Despite the ever-increasing complexity of drawing tasks, you will have to abstract complex plastic forms to simple concepts, if you, of course, want to convey them in the drawing.

We continue the theme of a constructive drawing of a still life of geometric bodies. The first thing to build in a still life drawing after creating the sheet composition is the plane on which the still life objects are located. The success of the whole drawing depends on how you correctly draw the position of the plane in space. Traces of objects are created on the plane, and only after you make sure that they really lie on this plane, proceed to further construction, that is, erect the frame.

In most still lifes, some geometric objects are on the second level. This means that the cube is on the plane of the table, and there is a cone on it. Until you determine the position of the cube on the plane of the table, you cannot build a cone on the cube. A typical mistake is the plane overturned on us - still life objects cut into the plane of the table (and in senior courses - human figures), as if rolling down a hill. All further construction of still life objects is carried out using the methods described above.

The constructive construction gives a clear understanding of the volume of still life objects in space and is carried out using lines. Drawn objects look like transparent frames.