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Harmonic Perspective Tutorial

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This is a giant pinhole camera on the goal line of a playing field. The tall clown is the vertical leg of a right triangle. The other leg is a horizontal flashlight beam.
Just as SAS (side angle side) makes triangles congruent, AAA (angle angle angle) makes triangles similar. Similar means same shape and proportions but not necessarily the same size.
Using similar triangles it can be shown objects on the 20 meter plane project as half the height as objects on the 10 meter plane. Objects on the 70 meter plane will project as 1/7 the height, etc.
Many of my perspective drawings use the harmonic sequence: 1, 1/2, 1/3, 1/4, etc. These are portrayals of objects lieing on evenly spaced parallel planes being projected by a pinhole camera. The pinhole as well as the film plane lie in this family of planes.
My coloring book Geoscapes [link] uses harmonic perspective to portray various crystal lattices where the atoms lie on evenly spaced parallel planes.
Periodic tiles cloned and scaled by a factor of 1/n retain the same periodicity as their parent tile. (n is a counting number: 1, 2, 3, etc.) So these perspective drawings are periodic tiles, a fact that startled me when I first noticed it. A couple of examples of these periodic tiles/perspective drawings:
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2686x2234px 517.65 KB
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Comments1
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Ludjia's avatar
I don't understand how this is applied in practice.