Local axonometry and promising effects Automatic translate

As has been repeatedly emphasized, axonometry is quite appropriate when depicting a separate relatively small object. If the antique or medieval artist had the task of conveying a sufficiently large space, then, having only the axonometric method of image, he was forced to use it in order to correctly show the appearance of each individual object, each in its own local axonometry. At the same time, no prospective coordination of these local axonometries was carried out: in particular, each of them could use its own direction of design, its own angle. However, although each subject was portrayed from a particular point of view, often completely inconsistent with others, sometimes there were peculiar promising effects, the nature of which will become clear from the examples below.

The main principle of axonometry, as already mentioned, is the observance of parallelism when portraying structures parallel in objective space. What can follow him lead to, is illustrated in fig. It shows the eruption of a fragment of the 11th century Byzantine miniature. "David between Wisdom and Prophecy." As can be seen from the above diagram, the Byzantine artist basically followed a moderate reverse perspective, completely explained by natural visual perception (left and right foot). However, observing the parallelism of the borders of neighboring foots parallel in the objective space has led to the fact that the middle foot is shown in an exaggerated strong direct perspective, i.e., it is prospectively erroneous. This example suggests that, using his right to distortion (their inevitability was commented on in previous chapters), the artist considered that the parallelism of close edges is more important than the uniformity of the images of the bottoms themselves. As a result, an image of an eclectic nature arose (in the sense of refusing to follow any one version of the perceptual perspective system when transmitting the appearance of objects), and axonometry was manifested in the image not of the foot itself, but of the spaces between them.

Significantly more significant are the promising effects of the use of local axonometrics when representing different areas of space or different objects from different points of view. We begin the description of emerging promising effects with ancient art - with images of interiors in Pompeii paintings.

Being in the interior, a person immediately becomes convinced that he is not able to see him simultaneously equally clearly in all directions. Usually he sees the part of the space on which his gaze is directed, axonometric - the reasons for this have already been discussed. Therefore, transferring his gaze, looking around and going around the interior, a person will perceive it as a set of local axonometries. The artist, trying to convey his visual perception as undistorted as the sum of local axonometrics, immediately becomes convinced that this is often impossible to do — local axonometrics come in screaming contradiction with each other. Therefore, there will also be a need (as discussed in previous chapters) for introducing distortions into the image, as well as masking the inevitable distortions to those where possible.

Central to the image of the interior is the task of conveying the appearance of angles at which two walls and a ceiling or floor meet. As soon as a solution is found, the further presents no particular difficulties: the boundaries of the walls can be conveyed in straight lines. The corners of the interior are most expressive if you portray the left corners as they are visible from the right side of the interior, and the right corners - as they are visible from its left side. If you do just that, then the geometric basis of the image can be represented by diagrams. The left side of the figure shows four mental parallelepipeds that graphically represent the types of axonometry most natural for the transmission of each of the four angles. Each axonometry corresponds to its point and direction of view, and the bold lines show the edges forming the axonometry structure of the corresponding angle. On the right side of the figure is a diagram of the interior of how it will turn out when using the four axonometric structures shown on the left.

The axonometric structures in question are valid not only for depicting the boundaries of walls, floors and ceilings, but also for conveying design features that limit the interior of planes (columns, coffered ceilings, boards or floor slabs). From the right diagram of fig. it is clear that no difficulties arise when portraying the columns, since the images of the vertical structures on the lower and upper axonometries coincide (relatively speaking, the lower and upper parts of the columns are closed). When transmitting the appearance of horizontal planes (floor and ceiling), an extremely undesirable situation may arise. In the diagram, this is shown on the example of the ceiling. It is obvious that the upper and lower boundaries of the walls in natural space are parallel, but in the diagram they have lost this quality: all four straight lines bounding the walls above and below have different directions. In this example, the ceiling is shown to have a pronounced linear structure parallel to the walls (it can be boards, beams, coffered ceilings, etc.). The image is promisingly reasonable in the left and right upper corners of the interior, these linear structures are shown parallel to the upper boundaries of the walls, but an absurd triangle appears in the center of the ceiling. The left and right sides of this triangle should have been shown parallel (after all, in nature they are parallel!), Which, of course, is geometrically unthinkable. The way out of this situation is to refuse to show linear structures (in the diagram this is illustrated by the image of the floor) or to mask an undesirable triangle in one way or another.

To give clarity to these general arguments, in fig. given the eruption of a fragment of the Pompeii fresco. The left and right parts of numerous ceilings and cornices (except for the top one) are perfectly axonometrically transmitted, and the mismatch of the left and right axonometries is removed by a gap that is formed by the image of a sculpture (sometimes instead of gaps depict draperies - or any objects that help to hide from the viewer an absurd “collision” left and right parts of the picture). The task of mitigating the inevitable “collision” of the left and right structures when depicting the upper ceiling was solved in a slightly different way. Here the artist did not have the possibility of direct disguise (tearing, draping) and used a different trick. The geometric structure of the upper ceiling is shown not in parallel, but in slightly converging lines. This is interesting in two respects. Firstly, it is obvious that a weak transformation of the axonometry was carried out so that the central trapezoid became less noticeable, and the linear structure of the ceiling in each corner continued to seem composed of parallel lines. Secondly, it is obvious that the artist does not know the central (renaissance) perspective, otherwise, by increasing the convergence of the straight lines forming the structure of the upper ceiling, he could get rid of the geometric inconsistency of the resulting central trapezoid and its neighboring elements. This is another argument in defense of the opinion shared by many that in ancient times they did not know a central perspective.

It is interesting to note that the combined effect of local axonometries creates an integrated circuit image of the interior in the direct perspective. Thus, the use of several points of view while maintaining local axonometry as the basis of the image in certain parts of the picture leads to a peculiar perspective effect, to the appearance of a direct perspective for the picture as a whole.

The problem of matching local axonometries when depicting interiors faced not only ancient art. Let us cite here an example of the eruption of the Italian predella of the fourteenth century, which depicts a composition on the theme of "Meeting". The left and right parts of the ceiling were transferred in a system of local axonometrics, and the artist masked their mutual inconsistency by the fact that in the middle part of the ceiling he showed a kind of hexagonal recess placed strictly above the throne. This made the throne give an unusual shape, which is based on a hexagon. Such a composition could solve the problem only partially, and in order to visually justify the hexagonal recess in the ceiling, the capitals of the thinnest columns shown in the foreground carry some construction elements of strange designation, which, however, appear parallel to the corresponding sections of the boundaries of this recess. It goes without saying that the task facing the artist was solved only visually. If you try to move to objective space, it immediately becomes clear that the left and right parts of the ceiling are actually formed by parallel boards and therefore the recess above the throne can only be rectangular, and this cannot be transmitted in the system of local axonometry of the type shown. Consequently, the spatial formations depicted are geometrically absurd, but arranged in such a way that they are not only not perceived as absurd, but, on the contrary, give the picture an apparent geometric persuasiveness.

In the cases considered, promising effects were described that arise when referring to local axonometrics for the image of interiors (look from the inside). What happens if you need to show objects “outside”, provided that the left and right parts of the image are symmetrical and equally important? Then it may turn out to be natural to use two points of view, and the “gluing together” of the two shown axonometric cubes will give a box depicted in the strongest reverse perspective.

One should not think that such a “gluing together” illustrates only the abstract possibility of the appearance of a strong reverse perspective effect (which obviously has nothing to do with the natural perspective of the visual perspective). Consider two examples of images, where various circumstances prompt the artist to “glue” two local axonometry. In fig. given the iris of the icon "John the Theologian and Prokhor on the island of Patmos", which depicts the dictating John and the writing Prokhor. Each of them is written in its own axonometry: John - when viewed from the left, and Prokhor - when viewed from the right, each in his seat (not shown on the outline), but their feet are so close together that it is impossible to draw a separate foot for everyone. The icon painter combines these two foots, “glues” them together, and as a result, the foot, which has become a single one, is depicted in contradiction with the entire geometric structure of the icon. This, of course, is not a promising technique, but a promising effect arising from compositional motivations (due to the mobility of the point of view).

Another example is the icon of the New Testament Trinity. Here it is even more obvious that the sowing of Christ and the Host of Christ, shown in a strong reverse perspective, was obtained by “gluing” axonometric images. This can be easily verified by drawing attention to the fact that the lateral sides of the altar and the foot are shown strictly axonometrically. Here, the desire to show the hosts of Christ and Christ in exactly the same way manifested itself, without mutual overlapping or any other (albeit unintentional) violation of the dogmatic doctrine of the unity of the Trinity Persons. The “gluing together” of the seats into a single seat is also important for dogmatic reasons: it symbolizes the inseparability of the Persons.

The examples considered allow us to state that the mobility of the point of view (the difference in design directions) when using for each point of view its own local axonometry can lead to the appearance of both direct and reverse perspectives in the picture as a whole. It all depends on how these local axonometric images will be combined. As a rule, the direct perspective arises when looking at the transmitted space “from the inside” (for example, interiors), and the reverse when looking around the object of the image “from the outside” (in the examples cited, the foot and the altar). The appearance of the effects of the second type mainly in icon painting is due to the fact that the icon painter did not seek to depict interiors, focusing mainly on the depiction of saints and related objects, while the ancient artist often sought to convey an empty interior without people and objects, for example, decorative wall painting. Thus, the manifestation in one case of a tendency toward a straight line, and in another, towards a reverse perspective (while maintaining local axonometry) is connected with what was portrayed, because in this sense the total effect was determined.

In connection with the foregoing, it seems appropriate to discuss one point of view existing in art history, according to which a gradual transition to a promising (renaissance) way of representing space took place according to the following scheme: first an “unscientific” image of individual objects, then using an intermediate version of a perspective system, when instead of a renaissance vanishing points of parallel lines there is an vanishing axis, and finally, the final step is the Renaissance system An intermediate version of the per pektivy with vanishing axis seen, in particular, in the ancient method of transmitting interiors. If we return to the interior with the one shown in Fig. Pompeii frescoes and continue the lines that transmit ceilings and cornices, until the intersection of the symmetrical lines with each other, then the points of their intersection will fall on one vertical line. This vertical line is also considered the vanishing axis, which later, during the Renaissance, will turn into a vanishing point, while the points shown on the vanishing axis are drawn into one. E. Panofsky gave a very figurative name to the promising scheme with the axis of the descent - “fish bone” [Lexikon, 1975].

The assumption that the perspective scheme with the vanishing axis is the first step towards a renaissance perspective system does not, however, withstand serious criticism. It is enough to look at the middle part of the figure to make sure that with the same success it can be argued that the promising fish-bone scheme is the basis of the reverse perspective, and therefore cannot lead to a renaissance system. Strictly speaking, geometric schemes with a vanishing axis, which are visible both in the upper and in the middle part of the figure, have nothing to do with systems perspectives. The appearance of the vanishing axis is an elementary consequence of the fact that both the Pompeii fresco and the icon of the “New Testament Trinity” are arranged according to the principle of mirror symmetry. Here on the left is a group of line segments, on the right is its mirror image, and in the middle is the vertical axis of the descent.

These examples indicate that no intermediate perspective scheme ever existed, although its presence would certainly adorn the history of fine art. In fact, the development of methods for transmitting visual perception of space on the plane of the picture most likely happened like this: first - the image of individual objects with support to the completely natural methods of the “queen of promising systems”, axonometry, and then, when it was necessary to transmit more extensive areas of spaces on the plane of the picture - reuse of already developed and of proven methods - a method of treatment of local perspective (by the way, does not necessarily require a mirror symmetrical compositions). The next step, which opens up fundamentally new ways, was already impossible within the framework of axonometric ideology.

The emergence of the theory of perspective in the Renaissance and the development of practical methods for its application made it possible, as is known, to move from the image of an object, and later - a collection of objects, to the transfer of space as a whole. This was an outstanding achievement of a revolutionary nature, and we must be immensely grateful to those who carried out this revolutionary revolution.