Illustrating Desargues’s Theorem

Triangles ABC and A'B'C' are perspective from the point O and perspective from the line o.

Desargues’s Theorem: If two triangles are perspective from a point, they are perspective from a line.

How to Make an A in Art

Draw the shadow to Make an A!

Observe the connection with Desargues’s theorem.

Now suppose that instead of a streetlight…

Watch how the shadow changes as you click back the point O is the moon. Watch how the shadow changes as you click back and forth between this slide and the previous one!

What’s the secret to drawing this new shadow?

Idealize: the earth as an infinite plane, the moon as a giant streetlight… thousands of miles high, and thousands of miles away!

Then proceed as before!

Some great tips for drawing shadows can be found in Perspective for Artists By Rex Vicat Cole Dover, New York, 1976