- Let
and
be the vanishing points of two
lines in the image. If
is the angle between the two
scene lines, we have
- If is known the above equation gives a quadratic constraint on the entries of .
- If it is known that the scene lines are orthogonal (
),
then we have a linear constraint
- The vanishing point
of the normal direction to a plane
is obtained from the plane vanishing line as
- Writing the above as removes the homogeneous scaling factor and results in three homogeneous equations linear in the entries of .
- Given a sufficient number of such constraints can be computed and follows.
- The following can be verified by direct computation:
- If ( no skew) then .
- If, in addition, then

- Suppose it is known that the camera has zero skew and that the pixels are square (or the aspect ratio is known) the and can be computed from an orthogonal triad of directions.