Of all the changes that happened to painting during the Renaissance, the only one driven by science and maths was the adoption of linear perspective projection. Although classical geometric optics came remarkably close to its discovery, it was the Romans’ love of trompe l’oeil which could have provided the necessary motivation.
The Romans appeared content with the established cues to depth, notably
- occlusion/overlay/interposition/superposition, resulting in depth order,
- relative size, including foreshortening effects,
- height in the picture plane,
- texture and detail gradient,
- shading and shadow,
- aerial perspective, including reduction in contrast, reduction in chroma, colour shift towards ‘cooler’ i.e. more blue, colours, and blur.
No surviving work of visual art from Roman times comes close to demonstrating an understanding of modern perspective projection. We cannot know whether those who saw this fresco in the Villa of P. Fannius Synistor, in Boscoreale, Italy, would have recognised the incoherence of its perspective projection, though.
Before 265 BCE, Euclid established the geometrical and optical principles necessary to perform modern perspective projection, but amazingly neither he nor successors such as Hero or Ptolemy quite reached it. It also eluded the polymath Roger Bacon in the thirteenth century. During the fourteenth century, innovative artists like Ambrogio Lorenzetti drew ever closer, but never quite grasped the geometric principles of single-point projection.
Lorenzetti’s Presentation in the Temple (1342) uses a geometric pattern in the floor which appears to have been projected in accordance with principles which were unknown until Brunelleschi discovered them almost eighty years later. However, as is common in paintings made prior to about 1420, it has multiple vanishing points, as marked below.
The discovery of linear perspective projection is attributed to the Florentine architect Filippo Brunelleschi (1377-1446) in about 1420, although it may have been as early as 1414. Antonio Manetti, his biographer, wrote an account in which Brunelleschi constructed two paintings of churches in Florence according to geometrical optical principles, and made an arrangement using a small hole and a mirror so that a viewer could compare the 2D painted view with the observed view at the correct locations. Those who tried this out were apparently amazed at the similarities between the 2D and observed views.
It’s surprising that Brunelleschi should have made this discovery. Although he had been well educated in mathematics, and had been an innovative architect since about 1400, it’s plausible that he had the help of someone else with deeper insight into geometry, something which shouldn’t have been difficult in Florence at that time.
Soon after this discovery, in 1424-25, Masolino painted his Healing of the Cripple and the Resurrection of Tabitha in the Brancacci Chapel in Florence. He wasn’t one of those who shared Brunelleschi’s secret method of perspective projection, as shown in the perceptible incoherence of its multiple vanishing points.
Brunelleschi is thought to have worked with the brilliant young artist Masaccio in the oldest surviving demonstration of correct linear perspective projection, Masaccio’s Holy Trinity, which he completed when he was only 26. Within a few months, Masaccio was dead, but this painting lived on as the example to be studied by other artists.
As is shown in its lines of projection, Masaccio’s masterwork has only one vanishing point. It also left artists struggling to work out how to project common solids such as pyramids and cuboids for their own works. Within a decade, the first treatise providing a basic guide to linear perspective projection had been written by Leon Battista Alberti.
Alberti was born into a Florentine family who had been exiled in Genoa. His family was allowed to return to the city in 1428, when he was twenty-four. At some time after the completion of Masaccio’s stunning fresco, Alberti and Brunelleschi met and talked perspective. In 1431, Alberti travelled to Rome where he studied and presumably drew the ruins of the classical city, developing his own skills of perspective drawing. He then started work on his book Della pittura (On Painting), which he completed in 1435.
Dedicated to Brunelleschi, Alberti’s book distinguishes three components in painted images, those of form, composition and colour. His account of these includes a simplified description of perspective projection which enabled many artists to use it in practice.
One of Andrea Mantegna’s most stunning paintings is this Oculus on the ceiling of the Camera degli Sposi in Mantua’s Palazzo Ducale. Despite its domed appearance, this is actually a flat surface, with a view quite unlike anything most of its viewers had ever experienced. It’s a brilliant example of geometrically rigorous projection which impressed the Italian nobility of the day.
But Alberti’s account fell far short of being comprehensive, and two- and three-point projections remained too demanding. For those the more advanced and complete treatise by Piero della Francesca (c 1415-1492) was decisive. Another Florentine, Piero was not only one of the great masters of the Renaissance, but was also a renowned mathematician and geometer. From about 1500, while Alberti’s more extensive book on painting remained in wide use, it was Piero’s De Prospectiva Pingendi (On Perspective for Painting) and its successors which defined the science and art of perspective.
Just as Leonardo da Vinci and Filippo Brunelleschi were ‘Renaissance men’ with their seemingly endless range of specialties, so Piero della Francesca’s combination of maths, geometry and painting provided the basis for advances in visual art.
Linear perspective projection remained at the heart of painting for more than four centuries after Piero’s death, until the geometry of painting changed again with Cubism in the early twentieth century. Brunelleschi, Masaccio, Alberti and Piero della Francesca had brought art and science together.
References
Brunelleschi in Wikipedia
Andersen K (2007) The Geometry of an Art. The History of the Mathematical Theory of Perspective from Alberti to Monge, Springer. ISBN 978 0 387 25961 1.
Brener ME (2004) Vanishing Points. Three Dimensional Perspective in Art and History, MacFarland. ISBN 978 0 7864 1854 1.
Dunning WF (1991) Changing Images of Pictorial Space. A History of Spatial Illusion in Western Painting, Syracuse UP. ISBN 978 0 8156 2508 7.
Gombrich EH (1976) The Heritage of Apelles. Studies in the Art of the Renaissance, Phaidon Press, Oxford. ISBN 0 7148 1708 2.
Panofsky E, tr Wood CS (1997) Perspective as Symbolic Form, Zone Books. ISBN 978 0 9422 9953 3.
Sinisgalli R (2011) Leon Battista Alberti On Painting, A New Translation and Critical Edition, Cambridge UP. ISBN 978 1 107 00062 9.
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