Series

Stereodisplay — the series

7 essays on one idea, from the one that introduces it to the one that assumes the rest.
  1. 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.

    part 1 · screen
  2. vertical difference up to 30.8 px, drawn 8× overbaseline 63 mmconvergence 2.0 m

    Turning the cameras inwards

    A stereo pair made by rotating two cameras toward a common point puts the same world point at different heights in the two pictures — up to thirty pixels here, on a frame of four hundred. Two eyes level with each other see every point at the same height, so a pair with vertical difference is a pair of pictures of no scene at all.

    part 2 · screen
  3. -10100.5001the screen's radius, log₁₀ metresvertical difference between the eyes, log₁₀ arcminutesa stated fusion limit, 15′eyes 63 mm apart, at each screen's own sitting distanceunder the limit throughout

    What the two eyes are sent

    A reader's eyes are two seats sixty-three millimetres apart, so a curved screen delivers each of them a different map — and the part of the difference no homography absorbs is binocular evidence of the glass. Turned into a depth it comes back as the screen's own sag, 49 millimetres against 47 on a television, by a route that never saw the radius.

    part 3 · screen
  4. -2024-0.500-0.25000.2500.500where the viewer sits, as a fraction of the sitting distance (log₁₀)the two eyes' vertical disagreement, in arcminutes (log₁₀)15′ fusion limitthe raw differencewhat a common frame leavesthe sitting distancecurved monitor, against the chairlimit at 29 cm

    The distance at which the eyes part

    The two eyes' disagreement on a curved screen was measured at each screen's own sitting distance and reported as a null result. The sitting distance is a parameter and the chair moves — swept, the raw difference falls like the cube of it and the residual like the fourth power, and a viewer twenty-nine centimetres from a curved monitor crosses the fusion limit the null result was quoted against.

    part 4 · screen
  5. 0102030400102030roll of the head about its line of sight (degrees)vertical disparity at the eyes (arcminutes)15′ fusion limitinfinityten screens backtwo screens backhalf-way outon the glass: 0′ at every rollscreen 2.60 m away · eyes 63 mm

    A stereo picture is drawn for a level head

    Every stereo pair is drawn for two eyes level with each other — a point's two images share a row and differ only across it. Tilt the head 10° in front of a television and that difference turns partly vertical, 14.46 arcminutes for anything drawn at infinity, and the two sightlines to a point stop meeting. At a desk monitor the same fifteen-arcminute limit arrives at 2.58°.

    part 5 · screen
  6. ++++++−−−−−−++++++−−−−−−++++++−−−−−−++++++−−−−−−+++++−−−−−+++−−−−−−+++−−−−−+++++−−−−−−++++++−−−−−−++++++−−−−−−++++++−−−−−−++++++the displayed picture, 700 mm across; darker is larger, + and − the signcurved monitor, 63 mm drawn separation, head levelworst 31.8′

    A curved screen tilts a stereo pair both ways at once

    A stereo pair drawn for a flat screen and shown on a curved one gets a vertical disparity from the curve alone, with the head level — opposite in sign either side of the middle, and 31.8 arcminutes at the corners of a curved desk monitor for anything drawn at infinity. A rolled head adds its own, of one sign everywhere. The two add in one pair of corners and cancel in the other, so the curved screen is kinder than a flat one in two corners and harsher in the two that decide.

    part 6 · screen
  7. 02550750246810roll of the head about its line of sight (degrees)worst vertical disparity on the screen (arcminutes)15′ fusion limitflat-drawn pair, curved screenpair drawn for the curveflat pair, flat screencurved monitor · content at infinitylimit at 2.58° flat, 2.38° drawn for the curve

    Drawing for the curve removes the curve, not the nearness

    A stereo pair drawn for a flat screen and shown on a curved one sends a level head 31.8 arcminutes of vertical disparity before anyone tilts anything. Draw the pair for the curve and that vanishes exactly. What remains when the head rolls is the roll's own disparity, and on the curve it is 8.6 per cent worse than on a flat screen — not because of the curve's shape but because the arc brings its edges nearer the eyes, and a fixed separation seen from nearer is a larger angle.

    part 7 · screen

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