OpenGL Z

Conversion Between OpenGL Depth-Buffer Z and Actual Screen-Space Depth Kenneth E. Hoff III (adapted from notes from Bill Mark)

OpenGL depth values are normalized values in [0,1] that represent the range between the near and far planes. The actual screen-space depth is the distance from the eye-plane through Z=0. The near and far planes are at Z=Zn and Z=Zf respectively. Basically, the center-of-projection - or eye - is at the origin and the viewing direction is down the positive Z axis.

 z = normalized OpenGL depth-buffer value 
     as returned by glReadPixels in [0,1]

 Z = actual Z value as distance from the plane 
     through the center-of-projection (Z=0)

Zn = distance from the eye-plane to the near plane (Z=Zn)

Zf = distance from the eye-plane to the far plane (Z=Zf

Given the screen-space depth Z and the distance to the near and far planes (Zn and Zf), we can compute the OpenGL normalized depth value as follows:

Screen-Space Z to OpenGL z:
z = (1/Zn - 1/Z) / (1/Zn - 1/Zf)

by solving for Z, we can determine the inverse conversion:

OpenGL z to Screen-Space Z:
Z = Zn*Zf / (Zf - z*(Zf-Zn))