Perspective Projection - Transformations and Projections in Computer Graphics - page 72

of reflection. Points “A” and “B” in the figure are seen by the viewer as if they are deep
in the mirror, and any group of parallel lines on a reflected object seems to converge in
themirrortoanewvanishingpoint.
Figure 3.10 shows a cube (in two-point perspective) reflected in a mirror. The two
real vanishing points are vp 1 and vp 2 . The cube seen in the mirror also has two virtual
vanishing points, vp 1 and vp 2 , and it is easy to see the symmetric relation between the
real and virtual points.

vp * vp 2 vp 1 vp 1

*

Figure 3.10: Real and Virtual Vanishing Points.

Note . This section discusses straight lines and their convergence, which is why the
examples here employ cubes and other objects with large, flat surfaces and straight
lines. However, curved objects with no straight, parallel lines can also be seen (and
drawn) in perspective, and techniques for achieving this are described in Section 3.3.
Vanishing points and converging lines are important in perspective, but perspective
has another important aspect. When an object is moved away from the viewer, it
appears smaller, but it also features less perspective. The amount of perspective seen
depends on the relation between the size of the viewed object and its distance from the
viewer. To see why this is so, we go back to the cube of Figure 3.5b, duplicated in
Figure 3.11a. Assuming that this cube is 10 cm on a side and that it is viewed from a
distance of 10 cm, its back face is 20 cm from the viewer, twice the distance of the front
face. The back face therefore seems to the viewer much smaller than the front face, and
the object is seen with a lot of perspective. If this cube is moved 90 cm away from the
viewer, its front face ends up at 100 cm and its back face at 110 cm from the viewer.
The difference between front and back is much smaller compared with the distance from
the viewer, causing the back face to appear just a shade smaller than the front, with
the result that the object appears to have much less perspective (Figure 3.11b).

Exercise 3.3: In addition to featuring less perspective, a distant object also looks
small. Can we bring such an object closer without increasing its perspective?