Depth and Perspective Exercises

From EscherMath

1. Discuss all the methods that Escher uses to indicate depth in Cubic Space Division.

2. Problem 2: Image:Vanishing-points-exercise.pdf

   Download and print the page for this problem. It consists of two separate pictures.

   1. Draw the two vanishing points and the horizon line for the top two cubes.
   2. Draw the two vanishing points, the horizon line, and the zenith for the bottom "buildings".
3. Draw a cube:
   1. Using one point perspective.
   2. Using two point perspective.
   3. In three-point perspective (two vanishing points on the horizon line and a zenith or nadir).
4. For these Escher works, describe the locations of all vanishing points, the horizon line, and any zenith or nadir:
   1. Tower of Babel
   2. Inside St. Peter's
   3. Other World (and by the way, see Magic of M.C. Escher pg. 18).
5. What does Up and Down have in common with House of Stairs?
6. Look at Relativity. Bruno Ernst writes^[1]:

   The sixteen little figures that appear in this print can be divided into three groups, each of which inhabits a world of its own....In order to distinguish these groups from each other let us give them names. There are the Uprighters--for instance, the figure to be seen walking up the stairs at the bottom of the picture; their heads point upward. Then come the Left-leaners, whose heads point leftward, and the Right-leaners, with their heads pointing to the right.

   There are three main stairways in the picture: across the top, in the lower left, and in the lower right.

   1. Which of the stairways can the Uprighters use?
   2. Which of the stairways can the Left-leaners use?
   3. Which of the stairways can the Right-leaners use?
7. Draw an impossible tribar.
8. What impossible figure is Waterfall based on?
9. Look at Cube With Magic Ribbons. Describe how depth cues in parts of the figure conflict with depth cues in other parts of the figure.
10. Look at Convex and Concave. How could you cut this picture into two perfectly normal pictures? Suppose the two trumpeters jumped out their windows. What would happen to each one?
11. Look at Belvedere. How could you cut this picture into two perfectly normal pictures?

[edit] Notes

1. ↑ Ernst, Bruno. The Magic Mirror of M.C. Escher. 1978. Page 47.

Instructor:Depth and Perspective Exercises Solutions