Perspective The Rise of Renaissance Perspective Page 4

Fig. 8. Reconstruction of the plan of Raphaels School of Athens. The reconstruction assumes that the floor tiling (red) is based on a square motif, as shown. Locations of the pillar, the table and the globes are indicated. The archway in the far distance is, omitted in the interests of scale.

Despite the accuracy of the paintings geometry, it is evident that it was not designed with its final location in mind. As a fresco painted into the plaster of the wall, it must have been intended for this particular location in the central of the three Stanze at the Vatican. However, the reconstruction of Fig. 8 reveals that the center of projection falls at a distance of 9 m away from the painting, whereas as the room is only 8 m in length. The natural distance at which to locate the center of projection would be at eye height at the center of the room, 4 m in front of the painting. (The only way to avoid this implication is to assume that the floor tiles were based on a rectangular motif with a 2:1 width/depth ratio). Instead, Raphael locates the center of projection behind the far wall, a point that is inaccessible both in distance and in height. In this, he follows the majority of the Quattrocento frescoists, who rarely sited their perspective constructions so as to be conveniently viewed from the true center of projection. It was only with the advent of the seventeenth century that the great ceiling artists Pozzo, Veronese and Tiepolo began to really pay attention to the viewers location for their masterworks.

What is the perceptual effect of this displaced viewing position? It is very obvious in Fig. 4 that, even from the furthest viewing distance within the room, the floor appears to be sloping upward, although the ceiling vaults do not seem noticeably distorted. Typical observers do not, when questioned on the appearance of the floor, exhibit the robustness to viewing position proposed by Kubovy (1986) in relation to the elevated center of projection of Leonardos Last Supper in Milan. They see the floor as noticeably distorted, suggesting that the human visual system is highly sensitive to certain types of perspective distortion (despite a lifetime of inappropriate viewing conditions for art, printed and video media).

On the other hand, consideration of the alternative suggests that Raphael may have adopted this construction intentionally, because it is the only way to design a view of the scene so that the floor and its inhabitants are visible into the distance. Since the bottom of the frame is above the spectators eye height, a literal construction would not allow any of the floor to be visible. The scene would have to be painted with the viewers looking up at the edge of a stage and able to view only the philosophers near the front from a low viewpoint. Perhaps Raphael was aiming to evoke a robustness of viewing position to a point where the distortion was hardly noticeable, allowing the deep view into the distance and the natural layout of the buildings arcades. On this interpretation, the shallow angle of the lower floor construction would then be a compromise intended to lead the eye into the scene without the floor seeming too steep. By spreading the oblique projection points more widely, the foreground flooring may be seen as better approximating the level that it would have realistically had.

It is of interest to reconstruct the three-dimensional geometry of the architecture of Platos Academy from the information given in the painting, something that has never been previously published. An outline attempt at this reconstruction is developed in Fig. 9 (in orthographic perspective). Most of the features of Raphaels design may readily be captured, but the interwoven hexagonal and diamond-shaped coffers in the barrel vault proved too daunting for this task. Presumably Raphael used a perspective base grid and a beam compass in the plaster to lay out the geometry of this pattern, but it would seem to challenge the geometry of his time even to define the hexagonal geometry, let alone to project it in perspective on a curved vault. The skeptical reader may wish to spend a little time developing this construction with the tools and understanding of 21st century mathematics in order to appreciate Raphaels achievement. Perhaps it was this that Bramante is depicted as laboring so hard on analyzing at the lower right of the scene!

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