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

Viewing tolerance — where it appears

How far a picture's reader may move before the reconstruction departs measurably, which for an anamorph is zero along its ground line and linear in height above it. The error is linear in the displacement, so ten times the tolerance is ten times every dimension of the region and a thousand times its volume.

Named by 5 essays across 2 fields — each of them below, with the objects they name alongside it.

ground line — right from anywherefaint: intended · solid: seendeparture (mm) against height (m)01.38the error map is an elation, with the ground line as its axisno characteristic ratio — nothing off the axis is fixed250 mm sidewayszero on the axis, 212.5 mm at the top

Where the anamorph still works

A picture correct from one point raises an obvious question that nobody answers with a number — how far may the eye move. The answer here is exact rather than approximate: a wrong viewpoint composes the intended picture with a central collineation whose axis is the line the picture stands on, so the error is zero along that line and grows linearly upward, and a step sideways costs precisely as much as the same step upward.

viewing · Anamorphreach -1012-0.25000.2500.5000.750how many pixels of departure are allowed, log₁₀the volume of acceptable seats, log₁₀ cm³11×4 mm184×58 mmcurved monitor, the acceptable seats as a solidfitted exponent 2.978 against a cube law's 3

The seats a screen will accept

Collect the seats whose picture is within a pixel of the one intended and the result is a solid — half a cubic centimetre in front of a curved desk monitor, a litre in front of a curved television. Ten times the tolerance is a thousand times the room, which is the pavement anamorph's own law arriving on an object that has nothing else in common with it.

screen · Curvedscreen 0102030400123how wide the audience is (m)the worst seat, in pixels of departure14.1 px per metrea flat panel of the same sizecurved television, the best single pre-warpthe flat panel's line is the axis

One picture and three people

A curved screen can be pre-warped for one seat, and the search over which seat to choose returns the middle one to a quarter of a per cent — there is nothing to be clever about. What the correction buys the sofa as a whole is six per cent, and the worst seat grows at fourteen pixels for every metre of audience, with no width at which it is zero except one person.

screen · Curvedscreen 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 00.2500.5000.75012345how high the eye is (m)share of the object, and share of the design that landsof the object's surfaceof the design that landsa corridor with a doorway, 7 facesbest surface share 100% at 2.5 m

The eye that reaches the most

A higher eye buys the faces occlusion was hiding and loses design off the far end of the object, so "the best eye" is not a question with an answer until somebody says which of the two they are paying for. On three objects the answer is as high as possible; on a corridor with a doorway in it the two quantities cross and the best height is two and a bit metres.

viewing · Anamorphreach

Named alongside it

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

Free parameterAnamorphosisStation pointViewing positionConditioningDemonstrationForced perspectiveForeshorteningHomographyIdentifiabilityPicture surfaceResidual

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