Experimenting with Perspective. Particular Relationships between the Image and the Mind

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The geometric certainty of perspective presents the Renaissance artist with a choice: should the work create the illusion representing the concrete, sensible world, or, on the contrary, should it portray the transcendent, speculative, abstract world of thought? This dichotomy would substantially characterise the culture of representation in the West from the Renaissance on. Perspective drawing becomes both the perfect experiment and the tangible testimony of this choice. For this reason, the phenomenon of perspective demands a unique analysis that considers this duality, since the informational intent reflected in the system for its realisation is different.

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Textual Criticism of Drawings in Historical/Scientific Treatise on Representation: the Caput in De Prospectiva Pingendi

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by Leonardo Baglioni, Marco Fasolo, Matteo Flavio Mancini

The proposed article aims to provide a methodological contribution to reading historical/scientific treatise on representation. In philology, textual criticism is the critical analysis of literary texts aimed at a deep understanding of the text and the
author’s intentions. In historical/scientific treatises on representation, the work is composed of two “texts” of equal importance: one is literary, the other graphic. In these cases therefore, textual criticism should be applied to both “texts” at the same time. The case study chosen to investigate the potential of the research method is the first illustrated treatise dedicated to perspective: De Prospectiva Pingendi by Piero della Francesca. While this is a work aimed at painters, the theoretical principles and applications of perspective are also addressed, contributing to a definition of the scientific basis of descriptive geometry. The bibliography is very rich, including essays by C. Winterberg (1899), G. Nicco Fasola (1942), M. Kemp (1994), and K. Andersen (2007). However, it should be noted that graphics that could explain the reasoning behind Piero della Francesca’s drawing are not always included, especially in critical editions. Among the pages of the treatise, proposition 8 in book III holds particular importance for the proposed investigation. Here, Piero constructs the perspective of a human head (Figure 1), which is first positioned straight (frontal position), and then looks upwards (generic position).
This proposition represents a major step in that for the first and only time, the author addresses the theme of free forms. To read this proposition critically, it is necessary to refer to a hybrid digital model (polygonal mesh, subdivision surface,
and NURBS) developed by studying the codices housed in the Palatina Library in Parma and the Municipal Library in Bordeaux. Construction of the digital model allows us to understand both Piero’s refined spatial reasoning and its relative plane rendering (Figure 2) in an original reverse path that highlights the scientific nature of the entire treatise and the potential of digital representation as applied to the textual criticism of drawings.

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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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