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This short essay gets to the heart of the debate that arose about the upper part of Table 151 of the Manière universelle, written by Abraham Bosse and Girard Desargues, to illustrate how the interpretation of the figure from a perspective point of view (see Jean Pierre Le Goff) not only is legitimate, but it can be also be extended as far as to acknowledge in the figure the complete representation of lines, planes and measurement operations. The Proposition fondamentale pour la pratique de la Perspective proves therefore to be the foundation of a general theory of perspective.

The discerning of the visible part of an object from its invisible part, with respect to the centre of projection, is one of the problems that must be addressed in the representation of any object. The dividing line between these two parts is what we now call the apparent contour. In the history of representation, the study of this theme must be found in the analogies with the condition of illumination of bodies: when the light source is at a finite distance, this can be compared with a proper projection centre, as is the case of perspective. The research for the apparent contour is an easily solved problem in the case of a multifaceted object, otherwise, in curved or free surfaces its identification is more complex. The present study intends to investigate the important contribution provided by Piero della Francesca's work in De Prospectiva Pingendi to scientific theorizing on the central projection of the apparent contour. In this treatise, Piero addresses the theme in three cases: in the anamorphosis of the sphere and the goblet and in the perspective of the human head.

The present essay investigates the potential of generative representation applied to the study of relief perspective architectures realized in Italy between the sixteenth and seventeenth centuries. In arts, and architecture in particular, relief perspective is a three-dimensional structure able to create the illusion of great depths in small spaces. A method of investigation applied to the case study of the Avila Chapel in Santa Maria in Trastevere in Rome (Antonio Gherardi 1678) is proposed. The research methodology can be extended to other cases and is based on the use of a Relief Perspective Camera, which can create both a linear perspective and a relief perspective. Experimenting mechanically and automatically the perspective transformations from the affine space to the illusory space and vice versa has allowed us to see the case study in a different light.

This research is aimed at the analysis, communication and dissemination of projective principles at the basis of perspective through the construction of digital parametric models and physical models made with rapid prototyping techniques. The interest in perspective derives from its transversal nature, because it permeates the representation of reality in all its communication forms. The experimentation describes the perspective in its general form, namely solid form, and in the particular cases that correspond to the plane perspective and to the real space. It involves the realization of the physical models starting from the virtual models, with which the observer can interact, observing perspective from inside and outside, thus revealing the reasons of its illusory power.

The development of different types of digital representations has shifted the designer’s attention from the morphological description of the object to the associative relationships of the parts that compose it. The integration between different models has therefore become a central and critical activity. It is precisely in the integrated and simultaneous reading of ideal models of digital form that the contribution to the knowledge and transmission of a cultural asset could be provided. The present essay proposes a critical analysis of the use of generative procedural models applied to the digital representation of cultural heritage to analyze the potential of procedural models for integration with qualitatively different models. The proposed case study is the Arch of Titus in Rome, characterized by a strong sculptural and architectural value. For this reason, it appeared to be a particularly significant case study for developing an experimental investigation about integrated digital modeling.

Augmented Reality (AR) represents a growing communication channel, responding to the need to expand reality with additional information, offering easy and engaging access to digital data. AR for architectural representation allows a simple interaction with 3D models, facilitating spatial understanding of complex volumes and topological relationships between parts, overcoming some limitations related to Virtual Reality. In the last decade different developments in the pipeline process have seen a significant advancement in technological and algorithmic aspects, paying less attention to 3D modeling generation. For this, the article explores the construction of basic geometries for 3D model’s generation, highlighting the relationship between geometry and topology, basic for a consistent normal distribution. Moreover, a critical evaluation about corrective paths of existing 3D models is presented, analysing a complex architectural case study, the virtual model of Villa del Verginese, an emblematic example for topological emerged problems. The final aim of the paper is to refocus attention on 3D model construction, suggesting some "good practices" useful for preventing, minimizing or correcting topological problems, extending the accessibility of AR to people engaged in architectural representation.

The unpublished treatise by Matteo Zaccolini, Teatin father, painter and teacher of perspective, was composed in Rome in the first quarter of the seventeenth century and is composed by four books. The fourth book, entitled “The delineation of the shadow produced by opaque rectilinear bodies above the flat surface”, is dedicated to the projection of the shadows in perspective representation and is the most interesting for the history of scientific representation as it collects a vast catalogue of examples in which prismatic bodies project shadows on variously oriented flat surfaces, cylinders, cones and spheres. The projection of shadows produced by extended and multiple light sources and the knowledge of conic curves as planar sections of quadratic surfaces is also addressed. The graphic equipment is rich and characterized by the double draft of each drawing: the first version, drafted only by the shape’s outline, shows all the construction lines; the second version, characterized by the chiaroscuro, hasn’t any construction lines. The in-depth critical analisys of the volume allowed to give Zaccolini back a significant role in the panorama of the history of the science of representation in reference to the study of shadows in the perspective projection.

This study focuses on an analysis of perceiving the infinite “solid images” derived from the projective transformations of space in a relief perspective, with particular reference to Renaissance theatre scenery. Today it is possible to simulate the projective transformations of the scenic space in a parametric environment, dynamically. This parameterization allows to analyze the effects of visual perception of the scene, through the dynamic control of its projective transformations. The main objective of this study is the exploration of the places of the projective transformation straddling reality and illusion, where the metamorphosis of the space triggers changeable processes of perception. changeable processes of perception.

https://doi.org/10.1007/978-3-319-13695-0 This paper deals with the problem of surveying Architectural Perspectives, generally painted in a 1:1 scale, which represent illusory spaces, enlarging the hosting real spaces. In particular, we intend to propose a method of survey, applicable to the case of painted surfaces in general; this method allows us to achieve high-resolution images with a large information content that gives us detailed information on the colours and on the painting construction signs, in addition to the metric data. For this purpose, we tested image-based integrated survey techniques, which aim, on the one hand, at the construction of three-dimensional virtual models through consolidated image-based modelling techniques, on the other at the construction of high resolution images that have metric valence.

Il contributo è incentrato sulle definizioni alla base della modellazione numerica, delle superfici di suddivisione e della parametrizzazione. L’approccio impiegato per la definizione del modello e delle sue caratteristiche topologiche trae spunto dall’algebra booleana per definire il concetto di Constructive Solid Geometry (CSG) e 2-manifold; caratteristiche entrambe necessarie affinché la rappresentazione sia inequivocabile (unambiguous) stabilendo una frontiera priva di lacune e di elementi non necessari (dangling faces, isolated cluster). La seconda parte del saggio classifica e definisce i principali metodi di costruzione di modelli numerici nel campo dell’architettura, del design e dei Beni Culturali (box modelling, spline cage, adding modelling).