Lesson 4 – Perspective of the reference plane π1

lesson_04

Theory
The observer is standing on the horizontal reference plane π1h measures the eye O height above this plane.
The reference plane π1 intersects the picture plane in the line t, which is named trace of π1.
Imagine a plane π1°, belonging to the point O and parallel to the plan π1,
This plane intersects the picture plane  in the horizon i’, which is named vanishing line of π1.
Since the planes π1 and π1° are parallel, the lines t and i’ are parallel too.
Since the picture plane is vertical, the horizon i’ passes through the principal point .

The line i’ is image of the line at infinity i, that the plane π1 has in common with all the planes parallel to it.
This is why we say that the vanishing line is the image of the laying of a plane and all the planes parallels to it.

If you want to explore this topic you can read: Perspective and infinity.

Practice
Measure the height of the eye  (h).
Draw two parallel lines (i’ and t).
Note that, if the picture plane is vertical, i’ belongs to .

Note
The two lines i’ and t `represent’ the plane π1, according to geometry, but do not describe it effectively. So it is always best to add a landscape allusion (e.g. the ground, the sky …).