page_title: Stereoscopic depth rendition
section_title: Stereoscopic reconstruction
hierarchical_section_title: Stereoscopic depth rendition / Stereoscopic reconstruction
caption_attribution_description: English: A small cubical target ABD at a distance z from a stereodevice whose two components R and L are separated by a. For viewing purposes, the depth is represented by BC, the intercept in the target plane of the two lines of sight to the back surface of the cube. The depth/width ratio of the actual target is 1.00; that of the representation in the target plane is the ratio of the angles subtended by and depth (BC/z) and width (AB/z). Category: 3D
context_page_description: Stereoscopic depth rendition specifies how the depth of a three-dimensional object is encoded in a stereoscopic reconstruction. It needs attention to ensure a realistic depiction of the three-dimensionality of viewed scenes and is a specific instance of the more general task of 3D rendering of objects in two-dimensional displays.
context_section_description: The right and left eyes' panels in a stereoscopic reconstruction are created by projection from the principal points of the twin recording camera. The geometrical situation is most clearly understood by analyzing how the screens are generated when a small cubical element of side length dx = dy = dz is photographed from a distance z with a twin camera whose lenses are a distance a apart.
  In the left eye panel of the stereogram the distance AB is the representation of the front face of the cube, in the right eye panel, there is in addition BC, the representation of the cube's depth, i.e., the intercept on the screen of the rays from the  cameras’ principal points to the back of the cube. This interval computes to the first order to .  (To simplify the account, the right and left screens are taken to be superimposed, as they would be in a 3D display with LCD goggles.)  Hence the depth/width ratio of the cube’s view, as embodied in its representation on the viewing screen, is  r = a×dz/z×dx = a/z  since dx=dz  and depends solely on the distance of the target from the twin lenses and their separation and remains constant with scale or magnification changes. The depth/width ratio of the actual object, of course,  is 1.00.
  This stereogram with the cube, whose depth/width ratio had been captured with recording parameters ac and zc and embodied in the ratio BC/AB = rc=ac/zc, is now viewed by an observer with interocular separation aₒ at a distance zₒ. An overall scale change in BC/AB does not matter, but unless rₒ = rc, i.e., aₒ/zₒ = ac/zc. this no longer represents a cube but rather becomes, for this observer at this distance, a configuration for which
   R = rc/rₒ ...... (1)
  i.e., whose depth is R times that of a cube.
caption: Geometry of screen view of a small cube at a distance z captured by a twin camera with separation a. Right and left eye images are shown superimposed.
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