by Riccardo Migliari, Marco Fasolo and Leonardo Baglioni
This contribution identifies the recurring problems in geometric restitution of architectural perspectives and proposes a working method. The inverse problem of perspective proposes the reconstruction of the fundamental elements in space. However, when the observer and spectator are not congruent, a question is raised: should we reinstate illusory space in realistic or surrealistic way? To answer this question, a new approach to restitution is suggested, which is organized into three moments: visual analysis, geometrical analysis and three-dimensional reconstruction, and critical interpretation.
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by Federico Fallavollita, Marta Salvatore
This paper aims to highlight the utility of the synthetic approach in solving geometry problems thanks to the contribution of new digital technologies. The synthetic approach, as is known, addresses geometry problems without recourse to analytical methods; especially for architects, the synthetic approach relies on drawing and models, 2D graphics yesterday, 3D digital graphics today. The digital revolution has brought significant changes to the study of geometry both in education, and in research. If, for a long time, the instruments were rulers and compasses, today the main tools are computers. Currently, we can draw directly into space with an accuracy never before achieved, and we can use, in geometric constructions, forms far more complex than those represented by ruler and compass. This has enhanced the heuristic capabilities of the synthetic approach. There is a vast repertoire of geometry problems belonging to the Monge school that, for several years now is no longer studied in engineering and architecture schools: however, in the light of new digital tools, it is still a precursor to new ideas for research. This contribution aims to show how this heritage can be updated and expanded through the digital synthetic method.
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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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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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