Perceptual methods of representing space and volume, which render them as seen at a particular time and from a fixed position and are characteristic of Chinese and most Western painting since the Renaissance, are in contrast to conceptual methods. Pictures drawn by young children and primitives (untrained artists), many paintings of cultures such as ancient Egypt (art and architecture, Egyptian) and Crete, India, Islam, and pre-Renaissance Europe, as well as the paintings of many modern artists, depict objects and surroundings independently of one another—as they are known to be, rather than as they are seen to be—and from the directions that best present their most characteristic features. Many Egyptian and Cretan paintings and drawings, for example, show the head and legs of a figure in profile, while the eye and torso are shown frontally (see photograph-->). This system produces not the illusion of depth but the sense that objects and their surroundings have been compressed within a shallow space behind the picture plane.

The early European artist used a perspective that was an individual interpretation of what he saw rather than a fixed mechanical method. At the beginning of the Italian Renaissance, early in the 15th century, the mathematical laws of perspective were discovered by the architect Filippo Brunelleschi (Brunelleschi, Filippo), who worked out some of the basic principles, including the concept of the vanishing point, which had been known to the Greeks and Romans but had been lost. These principles were applied in painting by Masaccio (as in his Trinity fresco in Santa Maria Novella, Florence; c. 1427), who within a short period brought about an entirely new approach in painting. A style was soon developed using configurations of architectural exteriors and interiors as the background for religious paintings, which thereby acquired the illusion of great spatial depth. In his seminal Della pittura (1436; On Painting), Leon Battista Alberti (Alberti, Leon Battista) codified, especially for painters, much of the practical work on the subject that had been carried out by earlier artists; he formulated, for example, the idea that “vision makes a triangle, and from this it is clear that a very distant quantity seems no larger than a point.”