Visual Plane
every picture states the point it is correct from
Concept

Disparity — where it appears

The horizontal difference between a point's positions in two pictures, which carries the depth as a reciprocal.

Named by 4 essays across 3 fields — each of them below, with the objects they name alongside it.

025507510010203040true depth (m)depth reported from the disparity, with a 1 px reading error5.86–7.33 m13.96–26.69 m23.76–126.49 mat 40 m: +86.5 m against −16.2 munbounded past 58.5 m

Depth is a reciprocal

Two eyes measure a shift in the picture, and depth is that shift divided into a constant. So a fixed error in what is read maps to an interval in what is reported that is not centred on the answer, and at forty metres runs sixteen metres nearer and eighty-six further.

depth · disparity 123-2-10baseline (m, log scale)range past which 1 px of disparity error is unbounded (m, log scale)65 mm → 58.5 mrange = fB/δ — 58.5 m at a 65 mm baseline900 px focal length, 1 px reading

The range a pair cannot see past

A stereo rig has a distance beyond which it cannot say "no further than", and the distance is fixed before anything is built. It is the focal length times the baseline divided by the reading precision, and for a human pair of eyes it is fifty-eight and a half metres.

depth · disparity 010203040-2502550disparity on the screen — millimetreswhere the point is depicted — metres from the eyesd = 63 mm — the eyes' separationon the glassscreen at 2.0 m · eyes 63 mm apartthe ceiling is the head, and it does not move when the screen does

Two pictures on one screen

A stereoscopic display puts a point where two sightlines cross, so the depicted depth is b·D/(b−d) and the disparity that reaches infinity is exactly the separation of the reader's eyes — 63 mm, at any screen distance whatever. The depth budget is set by the width of a head and by nothing about the scene.

screen · stereodisplay eyefaint: the row it imitates · solid: the row that is builtbuilt row21.0 pxthe deep row28.4 pxdisparity across the row, two eyes 63 mm apartfar column cut to 0.300the eyes read 74.1%, not 22.2%

A set cut for one eye

Build a colonnade four metres deep and cut every column so that its picture is the picture of one eighteen metres deep. The taper is forced rather than chosen — height and width both scale as the real depth over the intended one — and the match from the design eye is exact to sixteen decimal places. What gives it away is the second eye, and not by the ratio anybody would predict.

viewing · builtset

Named alongside it

The objects these essays reach for when they reach for this one.

BaselineDepth uncertaintyDemonstrationDepth cueFocal lengthinstrument limitrectified pairReference lengthStation pointTriangulationViewing distanceAnamorphosis

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