Thus, ‘The Disputation of St Stephen’ is typical of the classical Renaissance in retaining the parallels for the transverse lines when the vanishing point is shifted over to the one side of the picture. These transversals are captured in this instance by the horizontal supporting struts under the arches (and also the line of the bases of the nearest pillars). The horizontals would be parallel to the canvas if the vanishing point were centered, but should rotate back at the left side when the vanishing point is shifted to the right. The horizontals should then converge to an appropriate vanishing point at right, but this necessity was not evident to any of the Renaissance artists surveyed, as in the three further examples from the early Renaissance in Fig. 9.

Fig. 9. Three examples of paintings in one-point perspective with laterally shifted vanishing points. Left panel. ‘The Annunciation’ by Fra Angelico (1436-1443); central panel: ‘Presentation of the Virgin’ by Fra Carnevale (1467); right panel: ‘The Vision of St. Catherine’ by Titian (1503?).

The turquoise lines in Fig. 9 show the convergence of receding horizontals to a vanishing point at the edge of the picture in each case. The red lines show the horizontals physically at right angles to the first set. For accurate perspective viewed from the center of the canvas, this second set should converge to some point beyond the other side of the frame, but they clearly remain parallel. This forced one-point construction remained the perspective convention for about two centuries. It is perceptually very effective, probably because we are used to inferring the shapes of objects from the default that depicted angles are likely to be right angles. The default to right angles allows a robustness to distortion (to use Kubovy’s phrasing). Retention of the parallelism when the vanishing point is shifted corresponds to the depiction of rhomboidal rather than rectangular building plans (like the John Hancock Building in Boston, for example). The perspective would be accurate for this unusual kind of architecture, but it is most unlikely that the Renaissance artists were intending to depict such non-rectangular structures. It seems clear that they were depicting rectangular buildings and felt that the vanishing point could be safely shifted without evoking the sense of a distorted building. In fact, they had a rule that the vanishing point could be safely displaced as long as it did not go not beyond the boundary of the picture frame. This rule implies an awareness that extreme displacement incurred distortions, but that the distortions were hardly noticeable within some limited range.

Fig. ? An oblique view of a cube inscribed in an octahedron.

Fig. 10 The Laocoön group, a Greek sculpture from the Hellenistic period that had a great influence on Michelangelo’s heroic style.

By the beginning of the 16th century, it appears that artists felt straight-jacketed by the central perspective scheme, without realizing the flexibility that would have been allowed by full perspective with arbitrary vanishing points. A key moment in this evolution was when Michelangelo was taken by the Pope’s art advisor, Sangallo, to view sculptures that had just been dug up in the ruins of Titus’ palace. They immediately identified one of the sculptures as the Laocoön described by the historian Pliny (see Fig. 10). Michelangelo often spoke of the effect of the muscular power of this epic struggle on his artistic development, which acted in turn as a catalyst of the High Renaissance.