APPARENT DEPTH in ANAGLYPHS
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Anaglyph prints produce a true three dimensional image, whose components occupy points in the space behind or in front of the print. The distance from these points to the surface of the print is called the apparent depth. The apparent depth d is a function of three variables. They are the deviation i of homologous points on the page, your interpupillary separation e, and your viewing distance v from the page:
One thing that makes the viewing of anaglyphs interesting is that the viewing distance v can be changed dynamically, and this changes the apparent depth of the image. The function works for calculating the depth of points in front of or behind the print surface. Points in front of the print have a negative deviation, and result in a negative value for d. For those readers longing back to the good old days of high school algebra, I provide the derivation of the function below. |
Positive Deviation Geometry This is the viewing geometry for points apparent behind the surface of the print.
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Negative Deviation Geometry This is the viewing geometry for points apparent in front of the surface of the print. Note that d and i will have a negative value.
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Derivation of Function
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Plot of Apparent Depth Function
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When using the function to determine depths in anaglyph prints, it is convenient to measure deviation i in millimeters, input e in millimeters, and v in centimeters. The depth result d will be in centimeters. The plot shows asymptotic limits for two variables. On the positive side d is pushed rapidly to infinity as i approaches the value of the interpupillary distance e (i.e. as the eye pointing approaches parallel). On the negative side, d approaches the limit of -v with infinite -i (i.e. negative d cannot go farther from the page than your eyes are located). |
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