







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 onepoint 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 onepoint perspective.
Many artists practiced what might be called local perspective in
contrast with the thoroughgoing application of unified perspective.
They used vanishing points for particular objects or floorpatterns, 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.