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

Matched surface — where it appears

The arrangement in which a picture's own surface and the physical surface it is shown on are the same surface, viewed from the point that surface's geometry names. It is exact, and it needs the seat, the picture's angular scale and its vertical law all to be right at once.

Named by 5 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 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.

Picture surfaceScreenAngular sizeArcminuteCentre of curvatureCylindrical projectionEquirectangularHomographyAnisotropyArea scaleAudienceDevelopable surface

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