We have just seen that, in going from Euclidean to
projective, a point in
becomes a set of points in
which are related to each other by means of a nonzero scaling factor.
Therefore,
a point
in
can be visualized as a ``line''
^{2}
in three-dimensional space passing through the origin and the point
(Technically speaking, the line does not include the origin).
This three-dimensional space is known as the *ray space* (among
other names) and is shown in Figure 3.
Similarly, a line
in
can be visualized as a
``plane''
passing through the origin and perpendicular to
.
The ideal line
is the horizontal *W*=0 ``plane'', and the ideal points are ``lines'' in
this ``plane.''