23.1.3 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:

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