Graphics Programs Reference
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drawings, Navajo rock drawings, and ancient Egyptian art shown in the figure are two-
dimensional. They are flat and do not attempt to create a sensation of depth.
Flatness is also a common feature of modern art. The abstract art and cartoons of
Figure 3.2 look flat and use the painter's algorithm to create the barest hints of depth.
(The painter's algorithm is simply the way painters work. The first objects painted may
be partly or fully covered and obscured by objects painted later.)
Figure 3.2: Modern Art (Color Version on Page 231).
Art, especially painting and drawing, went through a revolution during the Italian
renaissance in the late Middle Ages. An important part of this revolution was the
technique of perspective. Almost overnight it became possible to create the illusion of
a three-dimensional scene in a flat, two-dimensional picture. Section 3.2 surveys the
historical developments that led to an understanding of perspective, but Figure 3.3
illustrates the basic idea. Part (a) of the figure shows a small, flat plane defined by two
sets of parallel lines. In part (b), some lines are made to converge to a vanishing point ,
thereby creating the sensation of depth. Part (c) maintains this feeling even though the
vanishing point itself has been removed. Finally, part (d) illustrates how four copies of
this plane can be connected to form an object that appears to us as a cube, a box, or
a room, even though we know that it is only a collection of lines on a flat surface.
(a)
(b)
(c)
(d)
Figure 3.3: Converging Lines.
Figure 3.4 is another illustration of the same concept. It is easy to see that the
railway tracks of part (a) are wrong, while part (b) looks realistic.
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