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

Screen — where it appears

A display considered as a picture surface with a shape and a seat, rather than as a rectangle of pixels. It projects a second time — the picture that reaches an eye is the shown picture seen from somewhere — so a screen has a correct point of its own, distinct from the one the picture was made for.

Named by 7 essays across 2 fields — each of them below, with the objects they name alongside it.

025507505001e+31.5e+3how far along the sofa the viewer sits, in millimetreshow far a mark is from where it was drawn to be seen, in arcminutesthe matched picturean ordinary flat picturethey crosscurved television, along the sofacrossing at 400 mm

Matching buys one seat

Feeding a curved screen its own picture surface makes the picture exact at one point and worse everywhere else than the flat picture it replaced. Forty centimetres along the sofa the two cross, and past that the matched picture is the worse of the pair — because a flat picture is mediocre everywhere and a matched one is perfect at a point and falls away from it faster.

screen · Matched -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.

screen · Stereodisplay 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°.

screen · Stereodisplay the centre of curvature, 4.0 mthe sitting distance, 2.6 mno single viewpoint — the rays miss by nothing — this is a plan of a room319′ out where people sit

Drawn for the cylinder, shown on the cylinder

Four essays in this collection have named the arrangement where a picture's surface and a screen's surface are the same surface, and none has run it. It is exact — a tenth of a millionth of an arcminute — and the exactness is not the finding. Three separate things have to be true at once, and a curved television's own maker prints a sitting distance where the first of them is out by five degrees.

curved · Matched 01002000.80011.20the condition, as a fraction of what makes the picture exacthow far a mark is from where it was drawn to be seen, in arcminutesthe seatthe horizontal scalethe vertical lawcurved television, one condition at a timeall three linear

Three conditions, and three prices

A matched picture needs the seat, the horizontal scale and the vertical law all at once. Each is broken alone here with the other two held, and all three turn out to be linear in the mismatch — the unforgiving case, with no margin at all. The vertical law costs a third of an arcminute on a television and eighty-four on a dome, because it is the difference between an angle and its tangent and that difference is cubic in the picture's vertical field.

curved · Matched cylinderexactequirectangular0.18′equidistant fisheye0.73′equal-area fisheye0.82′stereographic0.99′flat plane1.79′curved television, from its matched seateach surface fitted to it

The surface a screen wants

Six picture surfaces laid on one screen and viewed from the seat its curvature names, each with its own extents fitted so the ranking is about shape rather than scale. Each screen's own surface is exactly right on it and nothing else is — and on a curved television the runner-up is a fifth of an arcminute behind, which nobody can see.

curved · Matched flat panel1.000×exact at its seatcurved television1.000×exact at its seatcurved monitor1.000×exact at its seatcinema screen1.000×exact at its seatdome1.180×exact at its seatthe stretch of laying the picture downbefore anybody sits

A picture that can be printed

Two screens are fed the surface that is exactly right for each, so nothing about the viewer is left in the answer. What remains is whether the picture can be made flat before it goes up — and a cylinder unrolls while a sphere does not, so the dome's picture is stretched by eighteen per cent between its middle and its rim before anybody sits down.

curved · Developable

Named alongside it

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

ArcminuteCentre of curvatureMatched surfacePicture surfaceAngular sizeCylindrical projectionEquirectangularHomographyBinocular disparityInterocular distanceToleranceAnisotropy

All concepts