glClipControl

glClipControl: man4/glClipControl.xml

glClipControl controls the clipping volume behavior and the clip coordinate to window coordinate transformation behavior. The view volume is defined by $$z_{min} \leq z_c \leq w_c$$ where $z_{min} = -w_c$ when depth is GL_NEGATIVE_ONE_TO_ONE, and $z_{min} = 0$ when depth is GL_ZERO_TO_ONE. The normalized device coordinate $y_d$ is given by $$y_d = { { f \times y_c } \over w_c }$$ where $f = 1$ when origin is GL_LOWER_LEFT, and $f = -1$ when origin is GL_UPPER_LEFT. The window coordinate $z_w$ is given by $$z_w = s \times z_d + b$$ where $s = { { f - n } \over 2 }$ and $b = { {n + f} \over 2 }$ when depth is GL_NEGATIVE_ONE_TO_ONE, and $s = f - n$ and $b = n$ when depth is GL_ZERO_TO_ONE. $n$ and $f$ are the near and far depth range values set with glDepthRange. Finally, the polygon area computation defined by gl_FrontFacing to determine if a polygon is front- or back-facing has its sign negated when origin is GL_UPPER_LEFT.

The default GL clip volume definition is for a origin of GL_LOWER_LEFT and a depth of GL_NEGATIVE_ONE_TO_ONE. An origin of GL_UPPER_LEFT and a depth of GL_ZERO_TO_ONE corresponds to Direct3D's clip volume definition. An origin of GL_UPPER_LEFT and a depth of GL_NEGATIVE_ONE_TO_ONE corresponds to the upper-left origin of the window coordinate system of Microsoft Windows and the X Window System. There is extensive discussion of the uses and further consequences of the different clip volume settings in the GL_ARB_clip_control extension specification in the OpenGL Registry at URL http://www.opengl.org/registry/.