The ability to correctly display different shapes on a plane sheet, canvas and any other surface is a fairly significant skill. And above all, it is important both for people of art: painters, sculptors, graphic artists, designers (interior spaces and architectural environment), and for people of science: mathematicians, physicists, designers, inventors.
But for a person far from these areas, learning to correctly perceive and display the world around him is also important. This helps to comprehend all its versatility much deeper. If you don’t have enough idea of how to do it competently, then you most likely will not succeed in a project, painting or drawing of any invention. That is, this skill is important both for solving simple, everyday tasks, and for those that have global, universal significance.
A bit of history
Since ancient times, people tried to depict what they saw around themselves: other people, some primitive buildings of those times, a surprisingly beautiful world of plants and animals, magnificent mountains, and just things, household items. That is, the world in all its diversity and greatness.
But then they still had no idea how this can be done accurately and competently, so that the display of different volumetric objects on a plane is really realistic, lively. The person did not have the corresponding knowledge, and all the more lacked special skills, apart from perhaps the most elementary.
It is said in earlier sources that the first picture in the world consisted of only one line that ran along the shadow of a person cast by the sun onto the wall. That is, nature itself suggested the direction in which to move in search of the correct solution to this issue.
And this question worried the man of that time for the following reason: he didn’t just want to admire the voluminous live silhouette, the original, so to speak, but sought to capture a spatial object on a plane. And he did this so that he could either decorate his home or a sacred place for him, or take a parcel with a drawing with him and transfer it to any distance.
Drawing geometry
And whatever you say, but years passed, centuries passed, and somehow, as civilization developed, people gradually learned to display complex figures in two-dimensional space, that is, on a plane. Only now the accuracy of the sizes and proportions of the depicted objects began to seem very approximate.
But the question of how correctly displaying the figure on the plane and how much they correspond to the volumetric initial objects has once become very relevant. In a way, a new science called geometry helped to solve this problem. More precisely, its section is descriptive geometry.
Here she is just studying shapes and planes, lines and points, as well as their relationship to each other - both in three-dimensional and in two-dimensional space.
Conversion methods
An important feature in the visual arts is the display of figures on the image plane. Indeed, in essence, this is the capture of three-dimensional spatial objects in two-dimensionality. Namely: the complex must be converted into simple, that is, an object that has a length, width, height, must be transferred to a plane.
And descriptive geometry makes such "transitions", thanks to some methods. In total there are about six. Here are the three main ones and the most popular around the world:
- perspective (when the depicted object is removed in space);
- orthogonal projection (projection in parallel, where the rays are perpendicular to the plane);
- oblique projection (projection in parallel, where the rays are tilted relative to the plane).
The depicted object appears quite clearly in axonometric projection (to which include orthogonal and oblique). But most clearly and truly it is designed when portrayed in perspective. And it is precisely the above methods that largely solve the question of how to make the display of figures on a plane.
Perspective
Perspective among other image methods takes the most honorable place. Because the human eye, like the camera lens, sees the surrounding space in a similar way. Things that are farther from the observer look smaller in size and sometimes much smaller than when they are close.
For example, take an image of a cube in space. If, in fact, all its edges are parallel to each other, then when you look at this object in the distance, it may seem that the edges converge (or should converge) at one point. And, what is most interesting, not just due to converge at one point, but have a single intersection point.
Thanks to the masters of the Renaissance: Albrecht Durer, Piero Della Francesca, Andrea Mantegna, Leon Batista Alberti, modern painting knows what a direct linear perspective is, how to determine the height of the horizon and vanishing points.
And the world famous genius - Leonardo da Vinci - first argued the concept of aerial perspective. This is a change in the color, tone of the object, changes in its contrast characteristics (decrease as the object moves farther).
Orthogonal projection
Orthogonal is a parallel design that is directed to a straight line that is perpendicular to a plane. In the process of its application, the dimensions of the contours of the object remain unchanged. That is, the object is displayed without distortion.
The designed three-dimensional object, as it were, is decomposed into three types: side, front and top. And looking at all this at the same time, you can add up the idea of how the object looks in volume. In this case, the dimensions of the figure remain unchanged both in a three-dimensional image and in a two-dimensional one.
Oblique projection
This projection is divided into several subspecies, namely:
- isometric view;
- dimetric projection;
- trimeric projection.
The isometric has distortion coefficients in all 3 axes (along the length, width, height). That is, the angles between the pairwise taken axes are 120 degrees. In dimetric, the distortions along the 2 axes are equal, and the third is different. And in the trimeric projection, all distortion coefficients (that is, along all 3 axes) are different.
Rotation figures
When a rectangular triangle rotates along the axis of one of the two legs, its third side (hypotenuse) will describe a new figure called a cone. And if you rotate a rectangle (square) on one of its sides, you get a cylinder. When the semicircle rotates, a sphere will come out.
It follows that by rotating the plane along some axis, we get the so-called rotation figures.
These figures have an axis of rotation. How they look in the plane depends on their placement relative to eye level. For example, the upper and lower sides of the cylinder are essentially circles. And if you look at them in the plane, they look like ellipses.
But the task becomes even more difficult if, when displaying spatial figures on a plane, they have an inclined axis. It is important that the contours of the bodies of revolution are equidistant from the axis of the latter.
A bit about chiaroscuro
An important role in displaying figures on a plane is played by chiaroscuro. Because the volume of the depicted object is created not only due to the lines, but also due to the correct distribution of light and shadow on its sides. And then it looks quite voluminous in the plane of a two-dimensional surface.
Thus, the display of figures on the plane, the determination of their sizes, the features of the correct blending of lightness and dark spots is quite possible to implement thanks to the above methods. And, most importantly, these are already truly proven in practice methods that are used by leading experts of our time.