Abstract
The research represents principles of projective-geometric design of illusory spaces and proposes a study about the relief-perspective which featured the applications of science and art to interior decoration and architectural spaces during the sixteenth and the seventeenth century. The research has analyzed a selection of figurative and built illusory spaces, going to deepen the formation of the concepts of perception and illusion. During Renaissance was given emphasis to projective methods, of which were investigated the principles of geometric and optical ones in the proportions and in the visualization of architectural works, and the use of projective system accelerating or slowing the effects of the natural perspective to modify certain environmental aspects, external and internal, to the built volumes. The research also compares two major applications, the relief-perspectives of Francesco Borromini and Giovanni Maria da Bitonto and their partnership in the design of the perspectival tabernacle in Bologna and in the perspectival gallery for the Spada palace in Rome.
TopThe Invention Of Space (And Time) Through Its Representation
Before the perspective was intended as an application of the Euclidean geometry, it was used as an intuitive expression of signs, in the attempt to reproduce the retinal image of an observed object into the real world. Painters of the twelfth century, thanks to the particular cultural conditions of the time, started to compare the perspectival tools with a broader understanding of its geometric meaning; scholars believed that it was the fundamental tool to fix the connection with the optical theories of representation.
The cultural and scientific information imported from the medieval world is a contribution of Islam whose philosophers and scientists had translated into their language most of the scientific documents of antiquity. The manuscript of Ibn-al-Haitam (better known as Alhazen) (965-1038) about optics had notoriety in Western culture, having been translated from Arabic into Latin by the Polish monk Vitellione in the thirteenth century. The works of Euclid itself were translated into Latin, at the end of the twelfth century, by Abelard of Bath, not from the greek, but from Arabic. The treaties about perspective, written by the Bishop of Lincoln, Robert Grossteste (1175-1253) and that one of Canterbury, Roger Bacon (1270), found inspiration in the knowledge possessed by the Islamic culture.
In this era the strong connection between the perspective of philosophers, the perspectiva naturalis and the one of painters, the perspectiva artificialis or pingendi, both arising from the optics of traditional Euclidean geometry, started to be a universal concept.
Key Terms in this Chapter
Perspective Limit Plane: Or Perspective edge plane is the planar support of images (vanishing lines) corresponding to directions and arrangements of the true space represented in 3D perspective (also known as plane of vanishing lines). True plane of the representation place corresponding to the infinity plane of the illusory space or the virtual one (or as represented); It is the first edge plane in the homology linking two 3D not identical collinear spaces. In the case of 2D perspective it coincides with the collineation plane (trace plane) and also belongs to the picture plane.
Vanishing Point: Is the apex of the pyramid that is bounding the relief-perspective. It is a fundamental parameter, with the viewpoint and the trace plane, for the generation of the relief-perspective.
Solid Homology: Is the system of projective relations between an object of the real space and its solid perspective. In other words, it is the projective correspondence between two spaces (the real and the scenographic one) by means of a plane of collineation; the two spaces are delimited respectively by two limit planes.
Viewpoint: The position in which the observer is assumed to be to match the regular model with the solid perspective: no other position allows such overlap or corrispondence. It is also used as a constructive parameter of the solid perspective.
Trace Plane: Known also as collineation plane, is the plane, perpendicular to straight line passing for the point of view and the vanishing point, that is a fundamental parameter for the construction of the relief-perspective. All the elements belonging to the regular model that lye on this plane are not underpassing any perspectival deformation or scalar reduction because they are part both of the real space that of the scenographic one.
Anisotropy: In the projective correspondence, the two spaces, are considered infinitely extended and overlapping but the first, the objective one, is isotropic while the second, the scenographic one, is anisotropic. The distance between the trace plane (or collineation plane) and the vanishing plane is an important feature of the solid perspective because it defines its anisotropy, or the compression of the scenographic space in the range between the two planes and the expansion of the same outside those.
Vanishing Point Plane: In the relief-perspective, it is the first edge plane which collects projections of points of real space that are located at a distance immeasurable, that are the projections of so-called “points at infinity”.
Regular Model: The three-dimensional model that has not yet undergone the perspective deformation.
Quadratura: Architectural perspective, usually painted on a vault or as background wall painting, where the observer perceives the representation space as a mere extension of its own empirical space.
Illusory Space: Space evoked from the relief-perspective when the entities that belong to the picture plane don't undergo reductions or enlargements (change of scale).
Perspectival Deformation: Is the transformation that, through the parameters of the solid perspective - the view point, the vanishing point, the position of the eye of the observer, the projection plane (or vanishing plane), the trace plane- allows the process from the regular model to the relief-perspective (direct deformation) or from the solid perspective to the regular model (inverse deformation).
Solid Perspective, or Relief-Perspective: Is the three-dimensional model that has undergone the perspective deformation. It is also known as a scenographic perspective and includes a variety of techniques to create a constructively three-dimensional effect in which the accelerated perspectival convergence is evident if compared to that which would occur naturally through visual perception. It builds a material space as background and extension of a real space whose fictitious depth refers to an ideal architectural, urban or scenographic space.