Nevena RADOJEVIC
(Università di Firenze, Florence, Italy)
Keywords: 3d conchoid surface, Torus, Mirror, 3d mapping, Solid central projection
Abstract:
The subject of the research is the umbrella vault in the Pazzi Chapel in Santa Croce church in Florence. In some previous researches done by author, attempts were made to formulate new hypotheses on the form-finding processes that could have determined the shape of umbrella’s vault sail. The analyses were done by correlating detailed surveys and geometric analyses of the vault, comprising the curves, surfaces and the possible masonry texture with the hypothesized form. The hypothesized form of the inner sail is obtained by a three-dimensional transformation of a toric surface, with respect to the fixed point (dome’s oculus) and constant lenght (torus radius), like the Nicomede’s conchoid in 2d. The vault is made by the inner sail (the conchoid surface) and the outer sail that is not visible in this moment (the hypothesized toric surface). The results were verified by overlapping the hypothesized inner sail’s form and the laser scaner data, and only 3% of points were out of the 3 cm range. This very particular form, even though it explains the building process in a very satisfactory manner, is not amirabile by the visitors.
Actually, the the conchoid surface (that is a solid central projection of torus), could be perceived like a transformation of torus only under certain conditions. The first condition would be a sort of a three-dimensional mapping of inner sails, with the elements that represent the projection of the torus’s peculiar elements (circumferences for example) onto the conchoid surface. These irregular spatial curves, that represent the regular curves transformation, can be perceived as if they were circular if we look at them from the transformation center. So, the second condition would be the transportation of the observer’s view point in the center of oculus (not accessable point). The exhibition design (work in progress for the Opera of Santa Croce) involves the use of projectors for the 3d mapping of the sails and use of a plane mirrors system, that can move the observer’s view point as if he was in the cupola’s oculus.