Stereo Vision

Stereo vision is a feature of 3D-XplorMath that is missing from most mainline mathematical visualization programs, and that is a pity, since it adds greatly to the ease with which a user can develop a good feeling for a complex three-dimensional object. This is particularly true for the Space Curve and three dimensional ODE Categories. Assuming that you have stereo glasses (see below) experiment with the Torus Knot, as suggested here. For another good demonstration of the power of stereo viewing, select the ODE(3D)2ndOrder category, then select Magnetic Dipole from the Charged Particle submenu of the Main menu.

To use the stereo vision capabilities of the program, your color monitor should be set to display thousands or millions of colors (although 256 colors also work reasonaby well). In addition, the user must have a pair of red/green glasses. These are usually not "glasses" at all, but a paper frame with a red plastic film filter that fits over the left eye, and a green (or "blue"---really cyan) filter that fits over the right eye. See Obtaining Stereo Glasses below for directions on how to obtain these glasses.

The stereo images produced by 3D-XplorMath are known as "anaglyphs", and they are created as follows. First the program paints one perspective view of an object on the screen in green, as the object is seen from a first ViewPoint. Then it moves Viewpoint left by the distance EyeSeparation and paints a corresponding perspective image on the screen in red. (By the way, ViewDirection is kept fixed for the two views---it is a common error to choose a second viewing direction for the left eye view so that the two directions from the two eyes converge at the screen center.) The green lens filters out the red image, so the right eye sees only the first image, and similarly the left eye only sees only the second image. By some sort of magic that we do not pretend to understand, the human brain takes these two only slightly different images on the right and left retinas and somehow fuses them into what our visual cortex interprets as a view of the object with an extraordinarily realistic illusion of depth.

(By the way, the red/green or red/cyan glasses behave nearly the same. The green filter passes green and blue and filters out red, while the cyan filter passes only green and filters out both blue and red. Since there is no blue in either of the stereo images anyway, the effect of filtering them with a green or a cyan filter would be exactly the same if the filtering were perfect---which it is not.)

Obtaining Stereo Glasses

To use the stereo vision features of the program you will need a pair of red/green or red/blue glasses (see the above discussion of stereo vision). These are quite inexpensive, but not always easy to come by. If you need them in multiples of a hundred, you can purchase them from a company in Memphis Tennesee called American Paper Optics (Tel. 800 767 8427) for about \$50 per hundred delivered. Another source is Reel 3-D Enterprises, Inc., P.O. Box 2368, Culver City, CA 90231 (Tel. 800 837-2368 ). While I don't want to get into the business of retailing them, if you cannot find them any other way, send me a stamped and self-addressed envelope and cash, and I'll mail you two pair for five dollars or five pair for ten dollars. If you are from outside the United States, send me the equivalent in your local currency (and forget the stamp). Use the address:

Richard Palais
68 Lexington St.
Weston, MA 02493
USA