Perspective Drawing by Numbers

Extract

The use of matrices in connection with geometric transformations is now well established in the literature devoted to the teaching of “modern mathematics” in schools. A possible way of motivating an interest in projective transformations is to be found in the problem of constructing an accurate perspective drawing of an object as seen from a selected viewing point. One of the first artists to master the technique was Albrecht Dürer, and the woodcut by him (Figure 1) shows clearly the basic idea, that such a drawing is a projective transformation from “3D” space onto a plane. These transformations can be represented by 3 = 3 matrices. This note gives an elementary derivation of such a matrix representation, and shows how it may be used to construct perspective drawings.