Parallax Examples

The tables below illustrate three examples of collections of homologous points rendered by the three main stereo generation methods. Within each of the three collections, the MC point coordinates are identical. The viewing parameters are also (essentially) identical. (The only differences are the obvious: Method 1 has a common center, but Method 2 requires two centers; the eye point for Method 3 is the midpoint of the eyes used for Methods 1 and 2; the center of attention for Method 3 is the same as for Method 1.)

The black dots represent the original MC points. (They were projected with ordinary non-stereo viewing and projection matrices.) The red dots correspond to the stereo projection of the MC points for the left eye; the green dots are the same for the right eye.

Method 1 exhibits negative horizontal parallax Method 2 (always) exhibits negative horizontal parallax Method 3 exhibits negative horizontal parallax because the projection plane is behind the black points		Method 1 exhibits positive horizontal parallax Method 2 (always) exhibits negative horizontal parallax Method 3 exhibits negative horizontal parallax because the projection plane is behind the black points		Method 1 exhibits negative horizontal parallax Method 2 (always) exhibits negative horizontal parallax Method 3 exhibits positive horizontal parallax because the projection plane is in front of the black points
Method 1 Method 2 Method 3		Method 1 Method 2 Method 3		Method 1 Method 2 Method 3

Methods 2 and 3 are fairly easy to understand in terms of when they produce positive or negative parallax, and of course neither can produce vertical parallax. Method 1, on the other hand, is a little trickier. First, note that it is the only one that can ever produce vertical parallax. Second, points will exhibit negative horizontal parallax if, for example, the points are on the right edge of the left eye view pyramid. Similarly, they will exhibit positive horizontal parallax if, for example, they are on the right edge of the right eye pyramid. Analogous observations can be made with respect to the left edges of the two pyramids. It should also be clear that there will be no horizontal parallax for points that are on the right edge of both view pyramids.

Exercise: Draw the two pyramids and the two projection planes and try to characterize more completely the regions in which points will produce positive or negative (or no) horizontal parallax when using Method 1. Then do the same for positive, negative, or no vertical parallax.