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

Station-disagreement — where it appears

The gap between the camera positions two halves of one picture imply, measured on the picture rather than in the room. Two pinhole halves cannot disagree about a horizon at all, so a measurable gap is evidence that the halves were drawn by different depth rules.

Named by 4 essays across 2 fields — each of them below, with the objects they name alongside it.

recovered 1.60 m8–26 mrecovered 4.00 m26–70 mrecovered 11.00 m70–200 melevation recovered from each band's own marksnot read off a ledger

A landscape that changes its rule halfway up

A reader handed only the marks of a three-station landscape recovers each band's own camera height without being told any of them — 1.60 m, 4.00 m, 11.00 m, to 3.6e-15 m. What that same reader cannot recover across a join is a common ground: the next band's own marks read as a ground point 2.40 m away from the true one at the first seam, 7.00 m at the second.

scroll · Threedistances three eyes, flat ground1.6 m4 m11 mone eye, stepped groundground 9.4 mground 7.0 mground 0.0 mone eye, 11 m99 ground samplesagree to 6e-14 px

The stations are also a staircase

A level eye draws a ground point on a row that depends on the eye's height and the ground's only through their difference. So a landscape drawn from three stations at 1.6, 4 and 11 m over flat ground is, to 6 × 10⁻¹⁴ px across ninety-nine samples, the same picture as one eye at 11 m over ground stepped 9.4 m and 7.0 m above the far plain. The station heights a reader recovers are recovered on an assumption the marks neither supply nor test — and what would decide between the two readings is a cliff 103% of a band's own height, which is exactly where the convention lays its mist.

scroll · Threedistances the join, 26 mnear band: 21.8°far band: 45.0°215 px wide under either8 m roadturns 23.2°, keeps its width

A seam breaks direction, not size

An eight-metre road crossing the first join of a three-station landscape is drawn 215.4 px wide under either band's rule, identically, and a six-metre post 161.5 px tall under either — the eye's height cancels out of any size taken at one depth. What does not cancel is where those sizes sit. The road's edges are turned 23.2° from each other and the post's foot lands 64.6 px out of place, and a painter butting two bands can absorb the offset and can never absorb the turn.

scroll · Threedistances 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

Named alongside it

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

Free parameterStation pointElevationMoving viewpointPiecewise mapSeamDepth compressionTotal least-squaresDiminutionDrawing conventionHorizonPicture plane

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