Perspective Drawing and Projective Geometry

  1. Place an x on the vanishing point in the picture below and draw a few of the lines converging at the vanishing point that are parallel in the real world represented by this picture.
  2. View the large drawing of the cube from the optimal viewing place and distance (by following the directions). Were you able to see the distortion disappear?

  3. Given a point (x,y,z) of a real-life object with z > 0, write out the mathematical formulas for the perspective drawing coordinates of x' and y'.

  4. Write out the corresponding Excel formulas for x' and y'.

  5. In your own words, explain how the method that we used to determine the optimal viewing distance of the box can be adapted to determine the optimal viewing distance of the painting below. Use detailed descriptions that refer to specific aspects of this painting and label the viewing distance:

  6. Extra Credit Due by Reading Day Find a real-life painting that was completed in one-point perspective and adapt the method to find the viewing distance of this painting. Write up a report on how you did this, giving specific details, and also on what you saw when you used the proper viewing distance for your painting.