C..1.3 Perspective z-Coordinate Transformations

The $z$ value in eye coordinates, $z_{eye}$, can be computed from the window coordinate $z$ value, $z_{window}$, using the near and far plane values, $near$ and $far$, from the glFrustum() command and the viewport near and far values, $far_{vp}$ and $near_{vp}$, from the glDepthRange() command using the equation:

$$z_{eye} = { { { { far \: near (far_{vp}-near_{vp})} \over far... ...)} \over { 2 (far-near) } } - {far_{vp}+near_{vp} \over 2 } } }$$

The $z$ window coordinate is computed from the eye coordinate $z$ using the equation:

$$z_{window} = { \left [ {{far+near} \over {far-near}} + {{2 \... ...}-near_{vp} \over 2 \right ] + {far_{vp}+near_{vp} \over 2 } }$$