glOrtho describes a transformation that produces a parallel projection. The current matrix (see glMatrixMode) is multiplied by this matrix and the result replaces the current matrix, as if glMultMatrix were called with the following matrix as its argument:
left ( matrix { ccol { {2 over {"right" - "left"}} above 0 above 0 above 0 } ccol { 0 above {2 over {"top" - "bottom"}} above 0 above 0 } ccol { 0 above 0 above {-2 over {"far_val" - "near_val"}} above 0 } ccol { {t sub x}~ above {t sub y}~ above {t sub z}~ above 1~ } } right )
where t sub x ~=~ -^{{"right" ~+~ "left"} over {"right" ~-~ "left"}} t sub y ~=~ -^{{"top" ~+~ "bottom"} over {"top" ~-~ "bottom"}} t sub z ~=~ -^{{"far_val" ~+~ "near_val"} over {"far_val" ~-~ "near_val"}}
Typically, the matrix mode is GL_PROJECTION, and ( left, bottom, -near_val) and (right, top, -near_val) specify the points on the near clipping plane that are mapped to the lower left and upper right corners of the window, respectively, assuming that the eye is located at (0, 0, 0). - far_val specifies the location of the far clipping plane. Both near_val and far_val can be either positive or negative.
Use glPushMatrix and glPopMatrix to save and restore the current matrix stack.