Axonometry queen of promising systems: Image of the subject inland Automatic translate
A serious problem in various types of parallel perspective systems found in the visual arts was the image of the direction “in depth”. If you imagine a small cube, then its frontal face can be depicted easily - in the end, you can give it in its true size. As for the edge of the cube directed inward, it is obvious here that it should be shorter than the front edge. But how much? In technical drawing, this problem is solved simply: a conditional rule is introduced that allows us to uniquely determine this edge, without any claim that it is depicted correctly (corresponds to the natural visual perception). Artists of the past, and indeed contemporary artists, show this length of the rib going inland, not reckoning with any conditional rules, but based on their vision of the subject, and this is reasonable. But a natural question arises: what should this edge be from the point of view of the doctrine of perspective, if it is portrayed correctly, exactly in accordance with visual perception?
The question posed to this day had an answer with which all scholars associated with the theory of perspective in works of art agreed: the direction “inland” cannot be found rationally. It can only be determined conditionally. But this immediately excluded axonometry from the image methods, which were united by the concept of “scientific system of perspective”. This opinion is now generally accepted, and it can be found in all art history literature. After all, the scientific system should be determined on the basis of axioms; any conventions introduced as necessary are absolutely contraindicated to it. And this was also one of the reasons why the axonometric method of depiction was attributed to the craft, secondary, scientifically imperfect, those that were used when they still did not know the doctrine of perspective - that is, in the end, the thesis of "inability" reappeared.
If we take the position of a scientific perceptual system of perspective, then the situation changes in the most cardinal way. Axonometry has become a special case of the general scientific theory of perspective, valid for areas of space very close to the beholder, and it has become possible to apply the entire mathematical apparatus of this theory to it. It turned out that since the mathematical equations of the perceptual system of perspective for close space take on the form of equations of parallel perspective, the value of the segment directed “deep” can be found quite accurately without introducing any conventions for this purpose. Axonometry has become as rigorously scientific as the Renaissance perspective system, and even “more scientific,” since it takes into account the transformative activity of the brain. Therefore, ancient masters depicting close objects, relying on the axonometric method, acted flawlessly scientifically, which cannot be said about many modern artists (looking at their canvases, one can often find their adherence to dry Renaissance rules, deeply erroneous to convey the appearance of close objects). Words and expressions “inability”, “ignorance of the doctrine of perspective” so familiar to many writers on ancient and medieval fine art can now be attributed to artists of the New Age.
The axonometric method of depicting close objects is remarkable in another respect, which puts it in a special, exclusive position among all variants of the perceptual system of perspective (especially the Renaissance). Speaking earlier about the inevitable distortions of natural visual perception when trying to transfer it to the plane of the picture, we introduced the concepts of transmission errors of depth, scale and similarity and pointed out the possibility of a numerical description of the nature of these inevitable errors. If we evaluate the errors that occur with the axonometric method of the image, we find out a striking circumstance: in the correct (constructed in accordance with the theory of perceptual perspective) image, all these three errors are zero! It turned out that axonometry is the only unmistakable way of imaging, absolutely correctly conveying the appearance of close and small objects on the plane of the picture. If all other perspective systems are, as it was figuratively said, curved mirrors, then axonometry is an impeccable mirror! She, of course, the queen of all scientific promising ways of depiction. All other methods have flaws, inaccurately convey visual perception in the picture, only she, like the real queen, is devoid of flaws.
It is time to supplement the quite enthusiastic tone of the description of the unique qualities of axonometry with rigid prose of the consequences of its absolute perfection. Giving an impeccable image of small objects that are relatively close to a person, axonometry transferred the inevitable distortions to more distant plans, where they took on a literally catastrophic character. Absolute impeccability in the transmission of a loved one is not for nothing, it leads to disaster in the image of the distant - this is the true price of local impeccability! Here, one could give relevant examples of the growth of a “promising catastrophe” as the depth of the depicted space increases. We restrict ourselves, however, to one thing: axonometry does not know such a cardinal concept as the horizon! It is impossible to depict the horizon in a parallel perspective system: there should, for example, be the vanishing point of the edges of the cube from which the discussion of the properties of the axonometric image method began, but, having drawn these edges with parallel lines, we are not able to find their intersection point, vanishing point - it theoretically it is in infinity, that is, it is incalculable. All this leads to the fact that axonometry is only relevant when portraying close and small objects. In the transition to the transfer of deeper spaces, the version of the prospective system used should be changed.
It is time to illustrate general considerations about axonometry and its properties with an image constructed according to its rules. Take, for example, an engraving by a Japanese artist of the early 19th century, Hokusai, “A Girl Working on a Fuji Model”. Here, the whole space can be called close, and the use of axonometry in its image is quite justified. Attention is drawn to the artist’s desire to avoid the dryness of the drawing by weak rotations of the axonometric structures of the individual image elements relative to each other. This engraving provides an example of the exact following of a person’s natural visual perception. In addition, she convinces that the axonometry is able to convey not only the appearance of individual close objects, but also close, small and shallow spaces.
The advantages of the axonometric image method when transmitting close and shallow spaces, the reason for which is now completely clear, made even artists who were enthusiastic adherents of the newly created doctrine of the Renaissance perspective system use axonometry on their canvases. As an example, we give the painting of Andrea Mantegna "Dead Christ". Having paid tribute to the Renaissance system of perspective when depicting the bed on which the body of Christ lies, he depicted the body itself without any perspective reductions. This can be seen by comparing the width of Christ’s feet with the distance between his eyes. The absence of promising reductions is, as already mentioned, the main sign of axonometry. Here Mantegna demonstrates the primacy of the transmission of natural visual perception, which is associated with axonometry for nearby areas of space, and, it would seem, calmly violates all then accepted laws of perspective. In fact, he simply uses, as it is now clear, the most suitable variant of the scientific system of perspective, doing this, of course, intuitively.