Fig. 2.9 Cubes in perspective.

Proposition 2: When parallel lines are parallel to the picture plane, their images are parallel to each other; any line that is parallel to the picture plane projects to a line of the same orientation in the picture. When parallel lines are orthogonal to the picture plane, their images (or their extension) converge onto a point, called the principal vanishing point.

This proposition is illustrated by the cubes in Figure 2.9, which are drawn in one-point perspective. The edges of the square front faces are parallel to the picture plane, so the shape of their projections form squares in the picture. The sizes of their images diminish with the distance of the cubes from the center of projection. The square side faces of the cubes are bounded by orthogonals, so they all project to the principal vanishing point. The receding edges are all parallel to the ground plane, and therefore the vanishing point lies on a line called the horizon.

Even after the first accurate paintings in perspective were painted in the 1420s (such as Masaccio's Trinity, Figure 2.1), Italian artists were slow to apply the rules of one-point perspective. Many artists practiced what might be called local perspective in contrast with the thorough-going application of unified perspective. They used vanishing points for particular objects or floor-patterns, but they did not take care to have all the images of orthogonals in the scene converge onto the principal vanishing point. Local perspective was much more common than unified perspective before about 1450.

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