Uccello's chalice

Abstract

A handdrawing made 550 years ago served as the basis for the computer-aided geometrical drawing, which forms the cover picture of this new journal. The 34 × 24 cm 2 drawing, to be seen today in the Gabinetto dei disegni of the florentine Uffizi, shows a chalic-like receptacle in perspective, using a thin and dense network of straight lines. This is currently a popular method for depicting sculptured surfaces using a computer. The original drawing was made by a florentine painter, Paolo Uccello, who belonged to the first generation of Early Renaissance artists. In a self-portrait he proclaimed to be himself one of the founders of the new art, together with the painter Giotto, the sculptor Donatello, the architect Brunelleschi and Antonio Manetti, a mathematician, with whom Uccello as his biographer Vasari relates often met and discussed the geometry of the Euclid. Brunelleschi, well-known above all as the constructor of the cathedral dome, had already demonstrated, using two painted panels, the laws of perspective drawing tO the florentine artists, and Uccello belonged to his initial group of followers. In his enthusiasm for the new doctrine, he ventured so far as to paint a battle-field scene, in which the corpses of the fallen and the scattered weapons on the ground were arranged into a perspectively accurate pavement pattern. In his search for the intr icate [Vasari 1550] he turned his attention to a special problem, namely the rendering of round objects in linear perspective. His drawing of a sphere in form of a polyhedron with 72 surfaces, whereby each individual surface possessed in addition a diamond peak (four-sided pyramid), became famous. His favourite demonstration-piece was a ringformed solid, the so-called Mazzocchio, part of a popular headgear created originally in Burgundy, which was worn on the head like a wreath and was draped with cloth. The core comprised a frame made from wood or wire and it would appear conceivable that Uccello's lattice structure was inspired by it. Polyhedral, perspectively foreshortened mazzocchi appear in many of his paintings as a form of trade-mark; the most striking example being in a giant-sized portrayal of the Great Flood, in which a woman in the foreground is wearing her mazzocchio around her neck quasi like a life-belt. The huge chalice is a direct product of Uccello's studies of the mazzocchio. Even the enricing effect derived from the superimposed diamond facets was modelled on it. As with the mazzocchi, the basic figure is a 32-sided polygon, repeated with varying diameters in at least 58 planes. The subsidiary lines of the perspective construction, scratched in the paper (not visible on the photo), show that the mapping of every one of these polygons was achieved by the planeand front-view method, according to the costruzione legittima, which at first had been described by Alberti and then graphically represented by Piero della Francesca, but which doubtless date back to Brunelleschi. As the mazzocchi, Uccello imaginated h is chalice as a transparent one, representing also the rear view; thus his drawing appears much richer and much more complex than that of the computer. A few details he seems to have drawn free-hand, such as a torus at the base of the chalice, not entirely translated into the polyhedral scheme.