The display of figures in the plane (definition)

The ability to display different shapes on the plane of the sheet, canvas and any other surface is quite a significant skill. And above all, it is important for people of art and science.
the Ability to display different shapes on the plane sheet, canvas and any other surface is quite a significant skill. And above all, it's important for all artists: painters, sculptors, graphics, designers (interior spaces of the premises and of the architectural environment), and for men of science: mathematicians, physicists, designers, inventors.
But also a man far removed from these areas, to learn how to perceive and display the surrounding world is also important. It helps a lot to understand more deeply the whole of its versatility. If there is no sufficient ideas about how to do it correctly, then you most likely will not be a successful project, picture, or drawing of any invention. That is, this skill is important for solving simple household tasks, and a global, universal significance.

a Little history

since ancient times people have tried to portray what he saw around him: other people, some primitive buildings of those times, amazingly beautiful world of plants and animals, majestic mountains, and just things, objects. That is the world in all its diversity and grandeur.
But then they still had no idea on how this can be done accurately and correctly to the display of different three-dimensional objects on the plane was really realistic, alive. Didn't have a proper knowledge and even more absent special skills, except, perhaps, the most basic.
Said in the earlier sources that the world's first picture consisted merely of one line, which ran along the shadows thrown by the sun on the wall. That is the very nature prompted, in what direction it should move in the search for the correct solution of this question.
And this question was raised by a man of that time still and here's the reason: he didn't want simply to admire the voluminous living silhouette of the original, so to speak, and tried to capture the feature on the plane. And he did this in order to be able thus either to decorate your home or sacred place for him, or bring a bundle with a picture and move it to any distance.

Geometrical drawing

And say what you will, but the years went by, centuries passed, and somehow with the development of civilization, people gradually learned to represent complex shapes in two-dimensional space, i.e. on the plane. But the exact size and proportions of displayed objects began to seem very rough.

But the question of how to properly display the figures on the plane and how they match the volume of the original objects once became very relevant. In some way in addressing this issue has helped a new science called geometry. Or rather, her section – descriptive geometry.
Here she is just exploring shapes and plane, straight point, as well as their relationship to each other - as in the three-dimensional and two-dimensional space.

conversion Techniques

an Important feature in the visual arts is displaying the shapes on the image plane. In fact, it's just capturing the three-dimensional spatial objects in two-dimensional. Namely complex to convert to simple, that is, an object that has length, width, height, need to transfer to the plane.
And descriptive geometry exercises such “transitions”, thanks to some methods. There are about six. Here are three main ones and most popular in the world:
  • perspective (when the object is removed in space);
  • orthographic projection (projection in parallel, where the rays perpendicular to the plane);
  • oblique projection (projection Parallels, where the rays tilted relative to the plane).
Quite clearly appears the object in the axonometric projection (which include orthogonal and oblique). But most clearly and truly it is projected, which is depicted in perspective. And that the above methods largely solve the question of how to display the pieces on the plane.


the prospect of the other image takes the place of honor. Because the human eye, like a camera lens, sees the surrounding space in a similar way. Things that are farther away from the observer, according to their size look smaller, and sometimes much less than when they are close.
for Example, take the image of a cube in space. If, in fact, all its edges are parallel to each other, when you look at this object in the distance, it may seem that the edges converge (or should converge) at one point. And, most interestingly, does not just have to come together at one point and have a single intersection point.

Thanks to the masters of the Renaissance: Albrecht dürer, Piero Della Francesca, Andrea Mantegna, Leon Batista Alberti, contemporary painting knows what a direct linear perspective, how to determine the height of the horizon and vanishing points.
And world famous genius Leonardo da Vinci first explained the concept of aerial perspective. This change of color tone of the subject changes its contrast characteristics (decreasing as the distance of the object).

Orthographic projection

Orthogonal is called concurrent engineering, which is directed to the line that is perpendicular to the plane. In its application the size of the object outlines remain unchanged. That is, the object is displayed without distortion.
Projected three-dimensional object, as it is decomposed into three views: side, front and top. And looking at it at the same time, you can get an idea what the object looks like in volume. The dimensions of the shape remain unchanged as in the three-dimensional image and two-dimensional.

Oblique projection

This projection is further subdivided into several subtypes, namely:
  • isometric projection;
  • dieticheskaya projection;
  • trimetric projection.
isometric distortion coefficients in all 3 axes (length, width, height). That is, the angles between the axes taken in pairs is 120 degrees. Have dimitrieski – the distortion at 2-m axes equal and the third differs. And in trimetric projection, all the coefficients of the distortion (that is, in all 3 axes).

Shape rotation

When you rotate a right triangle along the axis of any one of two sides of its third side (the hypotenuse) will describe a new shape called a cone. And if you rotate the rectangle (square) on one of its sides, we get a cylinder. During the rotation of the semi-circle will be a sphere.

it follows that the rotating plane along any axis, we get the so-called figure of revolution.

these shapes have an axis of rotation. The way they look in the plane, depends on their location relative to eye level. For example, the upper and lower sides of the cylinder, in fact, represent the community. And if you look at them in the plane they appear as ellipses.
But the challenge becomes even more complex if the map of spatial figures on a plane they have an inclined axis. It is important that the contours of bodies of revolution were equidistant from the axis of the latter.

a Bit about chiaroscuro

an Important role when displaying figures on a plane plays chiaroscuro. Because the volume of the imaging object is created not only by lines but also by the proper distribution of light and shadow on the sides. And then he looks quite bulky in the two-dimensional surface.

Therefore, the display of figures on a plane, determination of their size and features the right blend of lightness and dark spots, it is possible to carry out thanks to the above-mentioned methods. And, most importantly, it is really proven methods used by leading specialists of our time.