Lesson 5 – Perspective of a line perpendicular to the picture plane

lesson_05

Theory

  1. Consider a straight line r, belonging to the reference plane π1, and perpendicular to the picture plane.
  2. Set up a straight line , parallel to r, and passing through the centre of projection O (we call that condition of a line or a plane simply projecting; therefore, a projecting line is any line that passes through O, and so on).
  3. The line r meets the picture plane in Tr, called trace of the straight line. Since r belongs to the reference plane, Tr belongs to the trace t of the reference plane.
    The line meets the picture plane in I’r, called vanishing point of the straight line. Since r belongs to the reference plane, I’r belongs to the vanishing line i’ of the reference plane.

Notes
Since the straight line r is perpendicular to the picture plane, I’r coincides with the principal point .
In general, if a straight line belongs to a plane, the trace of the line belongs to the trace of the plane; the vanishing point of the line belongs to the vanishing line of the same plane.

Practice
To draw the perspective of a line perpendicular to the picture plane:

  1. Set up the trace Tr of the straight line r on the trace of the plane to which it belongs.
  2. Remember that the vanishing line of any straight line perpendicular to the picture plane coincides with the principal point .
  3. Then, draw the perspective r’ (Tr I’r).