Stereoscopic Projection
By Ian Romanick
Email: idr@cs.pdx.edu
Stereoscopic projection is the technique of creating two different projecttion of the same scene such that one is viewed with the left eye, and the other is viewed with the right eye. This technology is far from new. It has been used for more that a century to create the illusion of 3D from two 2D pictures. It has been used in everything from children's toys to horror films. The question is often brought up in the many graphics programming related Usenet news groups, "How does it work?" I will make an attempt to answer this question in a way that will be both clear and useful.
Physics of the Eyes
Nearly every human being is equipped with two eyes. They are generally placed about 650 mm apart. Each eye, therefore, will have a slightly different view of its surroundings. The brain uses this difference to gauge distance. For example, figure 1 shows that an individual object is at a different location in each eye's field of vision. While it is not totally understood how the brain does it, it is known that the difference between the two images is used to gauge depth. It is also know that a stereo pair does more to give the impression of depth than color cueing and size cueing put together.
Mathematics of Projection
When a point is projected from 3D to 2D, it is essentially mapped from a truncated-pyramidal volume to a rectangular plane, as shown in figure 2a. The is done as though the camera points is at the crest of the pyramid. This is simple enough to do, and can be done using two multiplies, two adds, and two divides. To create a stereo display, a point needs to be projected twice: once for each eye. It the eyes are a distance X apart, then we can model them as being at a distance of X/2 on either side of the original camera point, as shown in figure 2b. For a given point to be correctly projected for a given eye, it must first be transformed to that eye's view space. Using simple geometry, it can be seen that this is done by moving the point towards the other eye by a distance of X/2. Figures 3a and 3b show the left and right eye images generated using this method.
Stereo Hardware
Due to the fact that, when using stereoscopic projection, each eye needs to see a different image, some sort of special display hardware is needed. Typical hardware ranges from the very cheep to the very very expensive. At the low-end, there is either red-green or red-blue filtering. This method involves covering one eye with a red filter and the other with either a green or a blue filter. On the screen, both images are displayed, but the image for the red-filter-eye is drawn in blue (or green), and the image for the blue-filter-eye is drawn in red. This way the lenses will prevent either eye from seeing the other eye's image. The method has a number of drawbacks, the most important one being that you can only use ``gray scale'' display. That is, you get one hue that can vary intensities.
Another method, that is a bit more expensive and can be dangerous, is the use of shutter glasses. Anyone who owned a Sega Master System in the 80's know what this device is. The general principal behind it is that one eye is covered while the other eye's image is displayed. The obvious advantages to this method are that all available colors of the display can be used and that each point doesn't need to be projected twice pre frame, as with the red-green filters. While this may seem to be a very good solution, it has its drawbacks. First of all, some sort of device needs to be available to sync the shutters with the video display. The SMS had one built in, but the Amiga does not, so some sort of adapter would need to be built. Typical PC adapters connect to the serial port. The other problem is that there is some risk involved in having small pieces of plastic spinning at 60Hz less than four centemeters from a persons eyes!
The other popular device is by far the most expensive, costing from $500US to $10,000US, and most complex to interface. This device is the head mounted display. HMD's generally contain two small LCD monitors, on which each eye's image is displayed. In this case some problems are solved, but others are introduced. The biggest problems, other than the prohibitive cost, are that the resolution and color capabilities of LCD's are very low. The display pitch of a typical LCD is so bad, that the user would be legally blind. The other problem is that, even the lightest HMD's, are very heavy to have on one's head for an extended period of time. The final issues are that two complete images need to be generated every frame and some sort of Zorro II or Zorro III card would be needed to interface a HMD to an Amiga.
How Sweet It Is
In spite of all its drawbacks, stereoscopic projection can new depth to nearly any 3D display. The example program shows how effective stereoscopic projection can be, even with just the red-green glasses method. When used with position tracking and a head mounted display, stereoscopic projection can be used to create a very realistic, very submersive, 3D environment.
In the file stereo.zip I have included a demonstration program that shows simple stereoscopic projection.
References
Aukstakalis S. and Blatner D. 1992. Silicon Mirage: The Art and Science of Virtual Reality, Peachpit Press, Inc., Berkeley, CA.
Foley, J. D. and A. van Dam, et. al. 1990. Computer Graphics Principles and Practice, Addicon-Wesley, Reading, MA.
