The last task in making a painting look real is giving its two-dimensional image the illusion of depth. Long practical experience, supported more recently by formal investigations, demonstrates that only a part of this relies on optically accurate perspective projection. Indeed, in many paintings, the latter isn’t even significant.

Among the cues used to impart the sense of depth are:

1. occlusion/overlay/interposition/superposition, resulting in depth order
2. relative size, including foreshortening effects
3. height in the picture plane
4. texture and detail gradient
5. shading and shadow
6. aerial perspective, including reduction in contrast, reduction in chroma, colour shift towards ‘cooler’ i.e. more blue, colours, and blur
7. linear perspective and outline shape.

Away from the geometrical regularity of human constructions, 7 (linear perspective) is usually almost absent, as there are few or no straight lines seen as converging to a vanishing point. Even where it’s depicted incorrectly according to geometry, as in Giotto’s Exorcism of the Demons at Arezzo, painted well before Brunelleschi ‘discovered’ linear perspective in the early fifteenth century, the result may look a little wonky, but we still get a good impression of depth and space.

Travel out of town to areas where most landscape painting is done, particularly scenic hilly or mountainous areas, and there are almost no linear edges seen converging to vanishing points. Even when armed with a photograph and a good imagination, it’s difficult to perform any sort of geometrical construction to allow you to estimate the location of vanishing points. In open views, where distant objects may be many miles away rather than a few hundred yards/metres, 6 (aerial perspective) dominates.

Depth order is apparent in the earliest complex Western paintings, from the Aegean civilisations of before 1627 BC, although from time to time, when paintings contained more symbolic collections than representations of reality, all sense of spatial arrangement can become lost. Examples of violation of depth order are extremely unusual, but they can sometimes occur in reflected images.

Paul Cézanne violated depth order on more than one occasion when painting reflections. In his Bords de la Marne I (l’Île Machefer à Saint-Maur-des-Fossés) of 1888-94 (the Hermitage version), the original image of the house and its tower shows poplar trees distinctly behind it. However, if you study the depiction of the same objects in reflection, the trees move forward in depth order and appear in front of both the tower and the house.

Repoussoir is a popular pictorial device in which a foreground element frames the more distant elements to strengthen the effect of space and depth. The subtle use of repoussoir might extend to the trunk of a tree forming one edge, most commonly the left, of the painting, but in more extreme cases trees can frame the top and both vertical edges. For all the claims that Cézanne sought to flatten the image in many of his later works, he used repoussoir not infrequently, as seen in this example from his series of La Montagne Sainte-Victoire; his later Lac d’Annecy is another famous example.

Diminution of size of objects that are progressively deeper into the motif is apparent in many, but by no means all, situations. Where the objects are very familiar and have sufficient detail to give further indications of their depth, they can be strong cues to depth and space. Caillebotte’s men in skiffs, although there are only three of them, make his painting appear very deep.

Eugène Burnand’s magnificent painting of Bull in the Alps from 1884 combines novel depth-of-field effects with extreme aerial perspective. There are marked contrasts between the foreground and background in terms of chroma, hue and lightness, and Burnand has reinforced these with defocussing in a photographic manner. The crisp edges of the bull stand proud of the softer edges and forms in the mountains behind.

The most famous example of how not to paint perspective was produced by William Hogarth, in his engraving for JJ Kirby’s pamphlet on the subject. I have here marked up its most obvious violations of proper perspective, using the same numbers as in the list at the top of this article. Although he shows no examples of incorrect height in the picture plane (3), those of violated depth order (1) and incorrect relative size (2) are frequent and obvious errors. This emphasises their importance in the perception, and creation, of depth and space in drawings and paintings.