Stereodisplay — the series
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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.
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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.
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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.
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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.
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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°.
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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.
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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.