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

Size-distance — where it appears

The relation that makes a thing's drawn size fall as one over its distance, which is what lets a reader read depth from size. Removing it is a decision a great many drawing systems make deliberately, and a picture without it has no horizon findable from its figures.

Named by 4 essays across 3 fields — each of them below, with the objects they name alongside it.

horizonisometric — the same drawing, movedperspective — a different drawingcorrect from 23 cm, at 160 mm wideparallel: 4e-14 px · perspective: 87.2%

Nothing moves when the object does

Slide a box 3.2 m across the world and its parallel drawing is the same drawing translated 131.5 px — every edge the same length to 4e-14 px. The perspective drawing of the same move changes its edge lengths by 87.2%. One family's pictures depend on where a thing is; the other's do not, and almost everything the two families disagree about follows from that.

parallel · Translation correct from 15 cm, at 160 mm widefive figures · 100% rank

Size that means rank

In a great many pictures the drawn height records importance rather than distance. That is a decision rather than a mistake, and it can be caught with a straightedge by carrying one figure's height across the room by the taught construction and see where it lands. A tenth of rank in the picture already misses the drawn head by 21 px, the miss is exactly linear in how much rank is there, and the whole test needs two references and no arithmetic.

conventions · Diminution 25102050131030how far away the object really is, in metreshow far away it appears, in metresa flat mirrortwo metres of radiusboth axes logarithmic · the eye 0.8 m from the glassceiling 1.30 m

Closer than they appear, by a factor with a number in it

A wing mirror of one metre radius held eighty centimetres from the eye reports 1.30 metres for an object at sixty-four, because the image of anything distant sits half a radius behind the glass. The size such an object subtends reads as a distance 2.60 times the true one, and the factor is exactly one plus twice the eye's distance over the radius — so the warning is a number, and it is larger for the mirror that is further away.

mirrors · Curvedmirror horizoncorrect from 16 cm, at 160 mm wideeye at 1.20 m · 57% in the last tenth

Higher on the page, and where that stops being true

A pinhole's image height above the horizon falls monotonically with depth over the whole 2–400 m range sampled here, and 57% of that whole range lands in the ground's last drawn tenth — the accumulation the oldest depth convention is quietly built from. Above eye level the ordering inverts, and at eye level exactly, five different depths draw one height, a spread of 0.0e+0 px.

conventions · Diminution

Named alongside it

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

DiminutionForeshorteningGround planeHorizonAffine mapAngular sizeAstigmatismCentre of curvaturecentre of projectionDepth compressionDepth cueDetection

All concepts