multiverse . Art of vanishing points

Why we draw, doodle and paint is a hard question to answer, for the workings of the mind are not yet understood by humans. Yet the ‘how’ of painting remains an accessible question and, for those who create art, an exciting one. The ancient paintings at Bhimbetka, Altamira and Lascaux depict beasts and men, hunters and warriors, painted upon the undulating interiors of caves. Horses, bison and humans populate the walls and roofs of the caves — but their rendition does not replicate the real appearance of the subject. Bhimbetka drawings use morphings of geometric shapes, triangles for instance, to depict human and animal torsos to great effect.

Such figures reveal an innate human capacity for abstraction. Yet we also retain a fascination for accuracy. The sculptures adorning the temples of Belur and Halebidu in Karnataka as well as Laocoön and his Sons — from ancient Greece — are, despite their stylisations, a move towards realism. An extraordinary knowledge of the human form — proportions, postures and gestures — were idealised in keeping with the prevalent notions of aesthetics and then executed masterfully in stone. Realistic painters must depict a three-dimensional world on a flat two-dimensional piece of paper.

But how?

Some of these ideas were developed during the European Renaissance, a period of 300 years from 14th-century, when many practitioners routinely crossed the boundaries of individual disciplines in their work. They also approached the problem of three-dimensionalising painting with a determination, perhaps even obsession, not seen before. Let us consider one way, and they found many, of depicting the third dimension on a flat surface.

Consider the image (top left) of one of the wall murals at Ajanta, the earliest surviving examples of Indian painting dated between 2BC and 5AD. Now consider the painting from the Renaissance.

The School of Athens (top right) was a fresco painted in Italy by Raphael sometime in the early 16th-century, over a thousand years after the last works of Ajanta.

Study the paintings carefully and spot the differences and similarities in style. The ideas in these paintings can fill many books and bring scholars to impassioned debate. And they have.

Deep end: The stylisations of the postures and gestures in the Ajanta cave paintings and Rafael’s The School of Athens are different but the proportioning of individual figures is clearly the work of accomplished artists

Looking at individual figures we can gauge that much effort went into the proportions being ‘correct’. The stylisations of the postures and gestures are different but the proportioning of individual figures is clearly the work of accomplished artists. Raphael’s fresco achieves something else. It appears to recede into the distance, giving the illusion of three dimensions while being painted on two.

Let us do the following thought experiment. Imagine a sphere one metre in diameter placed just in front of you. Now imagine the same sphere placed 10m further from you. Will it look bigger or smaller? The Renaissance thinkers realised that as things moved further into the distance they not only looked smaller, but that the apparent shortening followed certain geometric laws.

They visualised the shortening due to distance of a cube thus. Observe the flow of lines going through corners of the square faces of the cube in the third figure. The square faces of the cube get smaller with distance but all the corners of the cube must fall exactly on the lines that go through the corners of the first square face and converge to a single point, the vanishing point, located on the horizon where the earth meets the sky. The simplest method of painting a ‘realistic’ three-dimensional perspective is to have all objects vanish into a single point — the so-called one-point perspective — on the horizon line. A telltale sign of this is that all horizontal lines — the beams in a building and the tiles on the floor — must converge to the vanishing point. But the vertical lines remain parallel to each other. Observe Raphael’s painting again and you will be able to see his use of the single vanishing point. Just this one technique has imbued the painting with a certain feeling of depth.

Talking point: A schematic drawing of the vanishing point

Other methods were developed which then inspired work in the sciences. An entire topic of mathematical exploration, called projective geometry, would stem from the study of perspective in art. These further developments are at the core of ‘realistic’ interactive video games today, wherein the computer calculates the precise geometry of the scene, shifting and distorting the view, based on the players’ position and line of sight in relation to the scene. The mathematics to enable these precise calculations are now known. They are essentially the algebraic counterparts of the graphical methods used by the artists of the Renaissance. The ability to perform these calculations quickly is at the core of computer graphics hardware such as the latest video cards. In fact one of the recent specialised additions into the graphics cards made by a leading vendor, NVIDIA, is the ability to do ray tracing using which we can calculate not only the geometry of shapes but also how light will bounce off them yielding the shading that gives the illusion of three-dimensionality on a flat computer screen. This is precisely the spirit of what the Renaissance masters did but without the benefit of computer hardware. To them we owe a certain debt and from their methods perhaps there is much to learn still.

(Multiverse is a new monthly column on manifestations that meld science with art.)

SANTANU CHAKRABORTY

Santanu Chakraborty is a Bengaluru-based engineer, scientist and photographer .

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