- Points on a line in 3 space through a point and with direction can be written as . As varies from 0 to , varies from to the the point at infinity .
- Under a projective camera
the points project as
- The
**vanishing point**of the line, , is obtained as - Parallel planes in 3 space intersects
in a common
line, and the image of this line is the vanishing line of the plane.
Thus, we have

*The set of planes perpendicular to the direction in the camera's Euclidean frame have vanishing line .*