1. Intuitive Perspective
by Brian Curtis
© 2002, The McGraw-Hill Companies

2. A PowerPoint lecture series to accompany DRAWING FROM OBSERVATION

3. What we ‘know’ and what we ‘see’ are often at odds with one another
What we ‘know’ and what we ‘see’ are often at odds with one another. For example, we know that the rails on railroad tracks are parallel to one another and therefore never meet. It is important to acknowledge that there is conflict between our conceptual understanding (Euclid’s theorem that parallel lines never meet) and what is perceived (convergence of parallel tracks). We need to acknowledge this conflict because if we fail to anticipate and compensate for the influence of rational thinking on our sensory perceptions, we will consistently underestimate the apparent angle of convergence of receding parallel lines.

4. When depicted in a drawing, lines that are parallel to one another in the real world and are receding from the observer appear to converge at a single point. We are familiar with this convergence of “parallel” lines from the classic depiction of railroad tracks vanishing into a distant horizon.

5. “Alas, poor Euclid!”
Euclidian geometry tells us that parallel lines never meet.
However, when observing sets of parallel lines or edges we find that when they are moving away from the picture plane they appear to converge at a single point.
Euclid’s concept and our everyday percepts are in conflict with one another. What we know and what we perceive are very different.

6. The Mondrian Tool Assisted Perception
The straight-edged Mondrian Tool introduced in the previous chapter becomes, with a rotation of the wrist, a clock-angle tool that is capable of capturing a solid approximation of linear perspective (also called optical, scientific, or Renaissance perspective).
Assisted Perception

7. The Clock Angle Tool Assisted Perception
Holding the straight edge perpendicular to your line of sight and then rotating it till it is aligned with a receding edge reveals the apparent tilt of any edge to which it is applied. When the clock angle tool is applied in combination with intuitive gesture and Mondrian lines, you are able to produce surprisingly effective depictions of three dimensional spatial recession on a two dimensional drawing surface. Feel now, think later.
A clock angle tool works most effectively when used in combination with an imaginary, analog clock face understood to be floating perpendicularly to your line of sight
Assisted Perception

8. There is a natural tendency when using a clock angle tool to measure a receding edge to tilt it toward an object so that the orientation of the tool mimics the actual recession of the object’s edge. Keep the clock angle tool parallel to your picture plane.
Don’t go there!

9. To take full advantage of the clock angle tool, extend your arm fully toward the object and rotate your clock-angle tool until it is perfectly aligned with the receding edge you wish to analyze. Keep the straight-edge tool in the same plane as that of the imagined clock face, perpendicular to your line of sight. Aligned this way, the straight edge not only duplicates the angle of the receding edge, but also mimics the position of what would be the minute-hand on your imagined clock face. Once the tool is aligned with the receding edge, you can transfer the angle to your drawing in one of two ways.

10. You can lock your hand and arm at the correct angle, and turn your body slowly and carefully until the accurately angled straight edge comes to rest in the appropriate position on the drawing surface.
Angle Transfer #1

11. Or you can estimate where the tool is pointing on the imaginary clock face and then use this estimated clock position to re-establish the angle of the tilting edge in the drawing
Angle Transfer #2

12. You can use an imagined analog clock face on the drawing surface to duplicate the angle you observed in your visual field.

13. Parallel edges that recede in space appear to converge at a single point. This optical phenomenon (convergence of receding parallel edges) occurs because the apparent angle of each individual receding edge appears slightly different from that of any other receding edge with which it is physically parallel.

14. When the observer moves laterally in relation to a rectilinear object, the angles formed by its perpendicular edges appear to change. Between the photographs a and b the observer has moved a little to the right, and this has resulted in a more steeply receding line segment A moving approximately twice as far in the clockwise direction as line segment B.
Lateral movement

15. Definitions a u cute adj. (of an angle) less than 90°
ob u tuse adj. (of an angle) more than ° and less than 180°

16. The sum of all of the angles of a rectangle equals 360°
The sum of all of the angles of a rectangle equals 360°. The same is true of the trapezoid that represents a rectangle plane moving back into space. When viewing a rectangular plane that is receding in space, the right angles of that plane appear as either obtuse or acute angles (concept vs. percept). The lower the eye level, the more the obtuse angles expand toward 180° while the acute angles contract correspondingly. When your eye level moves further away from the top edges, both the obtuse and acute angles move toward a 90° angle. In this case the obtuse angles contract and the acute angles expand.

17. The bottom plane of a rectangular solid is by definition a duplicate of the top plane, but one that is, obviously, further away from the observer’s eye level. The change in the appearance of its 90° angles is identical to the change that occurs when there is vertical shift in the observer’s eye level. As you can see in this illustration, once again the apparent angles of the bottom plane shift in the direction of a 90° angle. Acute angles expand toward 90° and obtuse angles contract toward 90°.

18. Down is Out and Up is Back
This image illustrates that when a rectangular solid moves closer to the position of the observer, it appears lower on the vertical axis of the picture plane.
The angles expand and contract in a manner that is identical to the shift that we observed when we changed eye level or when there was a change in the vertical height of the plane.
Down is Out and Up is Back

19. The fact that an object’s overall height and its distance into the picture plane are both expressed in terms of changes in vertical positioning on the drawing surface can lead to instances of confusion and ambiguity while creating spatial illusions.

20. Picture Plane Revisited

22. Intuitive Perspective
This concludes the lecture
Intuitive Perspective