Constructing Mathlets Quickly using LiveGraphics3D - Stereo Images

Jonathan Rogness and Martin Kraus

Stereo images are often used in other fields to give the viewer a sense of depth in a picture; chemists, for example, use stereo pictures to view a molecule in 3D, while geologists can use stereo versions of a relief map to view the topography of an area. Stereo pictures seem to be less common in mathematics, although web pages such as the KnotPlot Site (Scharein) and the Gallery of Famous Surfaces (3DXM) provide static stereo images of beautiful mathematical curves and surfaces. (As it happens, the latter site also uses LiveGraphics3D to display rotating versions of the surfaces.) If you would like to learn how to view these images, searching for "how to view stereo images" with any Internet search engine will lead you to a number of basic tutorials.

LiveGraphics3D can display any image in stereo mode with no extra development work on your part. As an example, we'll use the MAA's icosahedron logo. (To see the list of polygons used to create this image, you can use your web browser to view the source code of this page.) If you place the mouse in the applet below, you can use the 's' key to cycle through parallel stereo mode, cross-eyed stereo mode, and normal viewing mode. Press the Control key and click and drag horizontally to adjust the strength of the stereo effect.

None of LiveGraphics3D's features are affected when you use the stereo mode. You can still rotate and zoom in or out, and animations and parametrized graphics function normally. If you wish to have LiveGraphics3D start in stereo mode, you can include the following parameter in your HTML code:


The stereo distance  is appropriate for parallel stereo images; for cross-eyed viewing you should replace it with  . If you use the stereo mode, you might also wish to make your applet twice as wide as it is high, lest your stereo images get cramped.

Any discussion of stereo displays would be incomplete without mentioning the GeoWall system (, which has become very popular in the earth sciences. A GeoWall uses side-by-side stereo images, two computer projectors aimed at the same screen, and polarizing filters and glasses to create the illusion of a true three-dimensional display. Any mathlet created with LiveGraphics3D can be adapted for use with a GeoWall with virtually no additional effort: simply make your applet as wide as the entire GeoWall display (typically 2048 pixels), set the stereo distance to 0.05, and you have instantly created a "true" 3D applet.