Drawing techniques: the rules of perspective

Backstage View of the Kabuki Theatre in Osaka, Utagawa Kunisada (1786-1865)

The representation of space using single-viewpoint perspective is a convention that is very familiar today. It is easy to forget that at one time the mathematical rules of perspective were themselves a new device to help artists to create the illusion of three-dimensional space on a two-dimensional surface.

The Italian architect and sculptor Filippo Brunelleschi (1377-1446) is credited as being the first person to make a mathematical study of the laws underlying linear perspective, but the art theorist Leon Battista Alberti (1404-72) was the first to set them out in writing for the use of artists in his treatise on painting, De Pictura (1436). From the 15th century onwards, artists have learnt these rules as part of their training.

Japanese artists developed a different way of depicting space. This too was based on mathematical principles which were passed on by teachers to pupils.

A lesson in perspective showing a method of drawing towers from a point above them, About 1780.

David Hockney, 'Scrabble, Hollywood, 1 January 1983', C-type colour photographs. Museum no. PH.1-1983.

Tobias Verhaeght (1561-1631) A Mountainous Landscape Pen and ink on paper.

Tavoletta di Biccherna: The Camarlingo, Niccolo di Lorenzo della Gazaia, making a payment to three claimants, with his scrivener, Sienese School