Perspective as a representation method

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by Riccardo Migliari, Jessica Romor, Marta Salvatore

Traditional teaching of perspective wants the perspective image to be generated with various procedures, which make use of the orthogonal projections of the object that is to be represented. It is nevertheless well-known that the perspective image also can be generated autonomously, that is to say, without resorting to the orthogonal projections, as part of a method known as ‘central projection’.
In many schools and in many textbooks these two paths, which both lead to the genesis of the perspective image, remain distinct, as if they were two different methods, if for no other reason than their vocation; the first, also called, improperly, ‘the architect’s method’, which only focuses on the achievement of the result: an image similar to the natural vision of the space; the second, conceptual, devoted to the study of the central projection in itself and its applications of projective nature: from the genesis of the quadrics to the homography.
In the Roman school, yet, as from the second half of the twentieth-century, it was attempted to bring together into one single method the two above-mentioned approaches to perspective, giving a happy ending to a history that for centuries has seen the perspective split between artists and mathematicians.
In this paper, after a short presentation of the characteristics of the ‘perspective as a representation method’, is highlighted the advantages of the aforesaid method in academic teaching. These are, precisely: first of all the possibility to see in the perspective the generalization of the representation methods, following on from the thought of Wilhelm Fiedler (1832-1912); then the possibility to easily add the concepts relating to infinity (points, straight-lines and the improper plane); and, the possibility to establish a relationship that is not general, but operational, between the graphical perspective and the digitally rendered perspective.

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Perspective: Theories and Experiments on the “Veduta vincolata” (Restricted Sight)

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by Riccardo Migliari and Jessica Romor

Erwin Panofsky’s work on ‘Perspective as symbolic form’, has had a powerful impact not only on the art critics and therefore on the artistic-historical literature, but also on the studies that deal with the theme of perspective from the scientific point of view. The reflections stated by Panofsky in the incipit of his essay, in fact, were considered in an uncritical and superficial way to say that the perspective describes an image of the space that it represents, similar to that of the human vision only if: the eye of whoever is looking is positioned exactly in the projection centre used to generate the perspective image; the same eye remains motionless and therefore with the direction of the gaze perpendicular to the picture. This condition of observation of the perspective is known to the Italian scholars as ‘vedutavincolata ‘. Recent studies have proved, theoretically and experimentally, that, on the contrary: the eye of whoever is looking at a perspective can move in an area around a projection centre without causing a collapse of the perspective illusion, or better, of the sense of visual depth evoked by the perspective; the eye of whoever is looking can freely move around, in every possible direction, without compromising the effects of the perspective. These studies are expounded in this paper, first of all describing the theories and the experimentations that have given the above mentioned results. Secondly, it describes the verifications carried out on important perspectives painted on walls and entire rooms, in which the conditions of one single projection centre are respected. It also describes other works, in which appropriate solutions permit to dilate the area of the vedutavincolata. Finally, in a quick re-reading of the first pages of Panofsky’s essay, this paper aims at an interpretation of it, which attempt to overcome the conflict between the advocates and the detractors of perspective as legitimate form.

16TH INTERNATIONAL CONFERENCE ON GEOMETRY AND GRAPHICS©2014 ISGG

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