Stereoscopic reprojection

There are two view points (centers of projection of the respective left-/right eye image), seperated by a distance e e. One of the view points is positioned at the origin and the other at the point . To accomplish that, the volumetric data is tranformed in the following way:

• Place the origin of the viewing coordinate system at the middel of the line between the two view points at .
• Set the w-axis of the (u,v,w) viewing coordinate system to .

This is done by a rotation in the x-z-plane around the point .

The volumetric data has now the "view-transformed" coordinates .

Now the left-eye projection is simply a parallel projection based on the data position after the viewing transformation.
The right-eye projection involves

• a rotation of about the y-axis
• a translation of , to place the right view point to the origin
• a second rotation about the y-axis to place P Pback on the z-axis.

The view-transformed point projects onto and as follows:

• Left eye-image:

  

• Right eye-image:

  

  or (approximating and for small )