Perspective Projection - Transformations and Projections in Computer Graphics - page 73

Front

Front

Back

Back

(b)

(a)

Figure 3.11: (a) More and (b) Less Perspective.

3.2 History of Perspective

In art, the term “perspective” refers to a technique for depicting a three-dimensional
scene on a two-dimensional flat surface. The result is similar, but not identical, to the
way we perceive three-dimensional objects and scenes in space. Our eyes are separated
by a few centimeters and therefore see slightly different views of the same scene. The
brain combines these views in a complex way to generate the sensation of depth. When
we move, turn, or raise or lower our head, the image we see changes continuously. A
painting or drawing in perspective, on the other hand, is based on a fixed viewpoint
and is equivalent to looking at the scene through a peephole with one eye.
The principles of perspective were known to the ancients. Many Greek vase paint-
ings indicate a grasp of the principles of perspective. Roman wall paintings show lines
converging to vanishing points, and the Roman architect Vitruvius describes perspec-
tive in his writings [Vitruvius 06]. In the Middle Ages, especially in the 13th and 14th
centuries, several artists in Italy, France, and Holland (and perhaps also in the East)
independently discovered (or rediscovered) some of the principles of perspective, espe-
cially the concept of lines converging to a vanishing point. However, none came up
with a complete and consistent theory of perspective. Such a theory had to wait until
the second decade of the 15th century, when it was developed first experimentally by
Filippo Brunelleschi and later in more detail by Leon Battista Alberti. (Some experts
also credit the painter Paolo Uccello with major contributions to the understanding of
perspective.)

[Uccello] would remain the long night in his study to work out the vanishing
points of his perspective, and when summoned to his bed by his wife replied
in the celebrated words: “How fair a thing is this perspective.” Being
endowed by nature with a sophisticated and subtle disposition, he took
pleasure in nothing save in investigating di cult and impossible questions
of perspective ... . When engaged in these matters, Paolo would remain
alone in his house almost like a hermit, with hardly any intercourse, for
weeks and months, not allowing himself to be seen ... . By using up his time
on these fancies he remained more poor than famous during his lifetime.
—Giorgio Vasari, The Lives of the Artists (1567)

The remainder of this section discusses the contributions made by three Renaissance
figures, Brunelleschi, Masaccio, and Alberti, to the understanding of perspective.