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

Canon of proportion — where it appears

A grid ruled on a wall with a figure set at a fixed number of squares, used as a measuring system inside the picture. It needs no horizon and no centre, so it supplies a scale a perspective picture cannot, and it supplies no depth, which a perspective picture does.

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

head0.668profile — the outline that names a faceeye0.669frontal — an eye in profile is a wedgeshoulders0.669frontal — the width that says two armslegs0.668profile — a stride is a side viewpond0.326plan — a rectangle of water is a rectangle1.000 — what its own aspect keepsshare of each part that reaches the picture, from the best single direction|d · n| for each part3.000 of 5, swept and in closed form

Assembled from several views

An Egyptian relief takes each part of a figure from the direction that identifies it — head in profile, eye and shoulders frontal, a pond in plan. What that buys is exactly measurable: any single viewing direction keeps at most √k of k perpendicular aspects, so the best compromise view retains 58% of each.

conventions · Aspective 0.2500.5000.75010204060copies made, each from the one beforea landmark, as a share of the heightthin: no grid · thick: eighteen squareshand 0.8%

A grid stops a copy drifting

A figure copied by hand from the last copy drifts as a random walk, by the square root of the copies. Copied on a ruled grid, with each landmark brought back to a line, it does not drift at all, because rounding throws the error away. That is how a correcting code works. It holds only below a sharp threshold on the hand, and the grid's size is the trade between how much it corrects and how much it can say.

conventions · Canon correct from 17 cm, at 160 mm wide21 squares tall · pitch 14.7 px

A grid on the wall is a scale without a projection

An Egyptian canon rules a wall into squares and counts a figure's height against the ruling — no horizon, no centre, and a length recovered to 1.4e-14% of error where the same reading taken off a pinhole misses by 58%. Applied instead to a pinhole picture, the furthest of six equal figures reads at 19% of its true height.

conventions · Canon

Named alongside it

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

Drawing systemCountingDrawing conventionTrue scaleArea scaleAspectivecentre of projectionDemonstrationForeshorteningIdentifiabilityinstrument limitIsometric

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