#### Theory

Consider, to start, a vertical plane **a** perpendicular to the picture plane.

Since the picture plane is vertical and perpendicular to the reference plane, the trace **t**** _{a}** of this plane is perpendicular to trace t

_{p}**of the reference plane. Since the plane is perpendicular to the picture plane, its vanishing line**

_{1}**i’**

**passes through the principal point**

_{a}**O°**. The trace

**t**

**and the vanishing line**

_{a}**i’**

**are parallel.**

_{a}Similar considerations allow us to set up the perspective of any plane sloping to the reference plane. If these planes are perpendicular to the reference plane, the angle formed by the trace of the sloping plane and the trace of the reference plane is the *sloping angle* of the plane.

#### Practice

To set up the perspective of a vertical plane **a**, you draw, first of all, the trace **t**** _{a}** of the plane, and then the vanishing line

**i’**

**, passing through**

_{a}**O°**.

To set up the perspective of a sloping plane, you draw the trace **t**** _{b}** remembering that the angle (

**t**

_{b }**t**

_{p}**) is the sloping angle of the plane. Then, draw the vanishing line**

_{1}**i’**

**, parallel to the trace.**

_{a}#### Notes

The two lines **i’** and **t** `represent’ the plane **π**** _{1}**, according to geometry, but they do not describe it effectively. So it is always best to add some architectural element, like a wall, a roof, a ramp etc.