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

Threedistances — the series

4 essays on one idea, from the one that introduces it to the one that assumes the rest.
  1. 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.

    part 1 · scroll
  2. 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.

    part 2 · scroll
  3. 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.

    part 3 · scroll
  4. 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.

    part 4 · scroll

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