Concept

Drawing convention — where it appears

An agreement about what a picture records and what it leaves to its reader, held between a maker and an audience rather than imposed by geometry. Each one keeps some properties of a scene and spends others, and the trade is measured here rather than ranked against a photograph.

Named by 8 essays across 3 fields — each of them below, with the objects they name alongside it.

8–26 meye at 1.6 m26–70 meye at 4.0 m70–200 meye at 11.0 mthree stations, buttedfar band ×6.9

Three distances in one landscape

A landscape assembled from a low station for the near ground, a level one for the middle and a high one for the far gives its furthest band 6.9 times the picture one camera would allow it — because the image of a fixed depth interval falls as one over depth squared, and its own station gives that back. What it costs is a jump in the rate at which depth runs, 2.50 at the first join and 2.75 at the second, and three views from one height leave no seam at all.

scroll · Threedistances
1234correct from 15 cm, at 160 mm widefour moments · 8.5e-14 px

The same person, twice on one panel

A panel showing one figure at four moments is geometrically the least strange thing in this field — one camera, one floor, and every pair of copies meeting the horizon to 8.5 × 10⁻¹⁴ px. What the picture withholds is the order, and four copies admit twenty-four readings, and a reading convention supplies 4.6 bits from outside the marks. Enlarge one figure by six per cent and the horizon test that passed the panel catches it at 36 px.

conventions · Narrative
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
band 1band 2band 3every figure the same height, by constructionno horizon

A picture in bands

A register picture stacks its scene in horizontal bands, each with its own ground line and every figure drawn at one height. The feet line and the heads line of any pair are then parallel to the arithmetic floor — 0° against 15.4° in a photograph of the same figures — so the picture has no horizon anywhere in it, and what a reader recovers is an ordering with no metre attached.

conventions · Register
the plan, with its four walls rotated outward about their base linesthe planwalls rotated about their own base lines16 assemblies

The pond with its trees laid flat

An Egyptian garden pond is drawn in plan with its trees rotated outward about the bank they stand on. A rotation is an isometry, so every length in that drawing is exactly the length it is in the garden — zero error, not a small one. What is spent is the angle between any two faces, which reads 180° across every hinge and is 90° in the garden, and the four walls admit sixteen assemblies, so a reader supplies four bits to fold it back up.

conventions · Aspective
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
rule A — ordinaryrule B — blendedmix = 0.0207.80 px

Two stations in one picture

A parallel floor under a perspective room found one map absorbing two centres into one sheet. Split a two-rule picture down the middle instead and each half hands back its own horizon — 7.80 px apart at a rule-mix of 0.02 — and no eye's position has anything to do with the gap, because an ordinary pinhole picture's recovered horizon does not depend on where the eye stood at all.

conventions · Mixedcentre
no single viewpoint — the rays miss by no distance at all — the rays are parallel3e-14 px of movement

Nothing moves along the direction

A part slid four metres toward the reader along the direction an isometric drawing projects along keeps its drawn place to a ten-thousandth of a pixel, and the same slide seen from a station point moves it forty-four. An exploded drawing is not an approximation that works because the parts do not move far — it is an identity, and it is why cutaways are drawn in parallel systems.

parallel · Noeye

Named alongside it

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

HorizonIdentifiabilitydegrees of freedomDiminutionForeshorteningFree parameterVanishing pointcentre of projectionGround planeOrthographicParallel projectionStation point

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