Threedistances — the series
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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.
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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.
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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.
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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.
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A shadow decides which landscape it is
One sun over a several-station landscape is one sun: every band images the light's direction and its shadows' at the same page point, and each reports the altitude as 22.000000°. A shadow is still dislocated at the join, and the reading that could not be settled by any ground point is settled by one — because a ray crossing the seam has a riser to descend that the flat reading does not give it, and the two tips land 5.94 m and 11.7 px apart.
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Where a seam is allowed to go
Putting a join further off cuts the offset it forces from 210 px to 24 and leaves the turn at 23.2° exactly, so emptiness is a painter's only defence. And emptiness is not counted in metres: one twelve-metre object blocks 6.3 per cent of a landscape's depth wherever it stands and between 1.0 and 35.6 per cent of the picture, so how much room a seam has is set by where the landscape is crowded rather than by how much.
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A seam that bends trades a turn for a gap
A join laid along a river bank instead of across one depth was supposed to go round what crosses it instead of avoiding it. It can, at a price: the far band can be lifted by one amount only, so a seam that wanders in depth opens a gap between the bands — 3 px buys the first join 1.2 m of wander, and going all the way round a twelve-metre object costs 15.8 px. Across a hundred landscapes, bending opens under 0.4 per cent of the picture that a straight seam did not already have.
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A band lifted by columns bends its lines
A curved seam in a several-station landscape opens a gap because the far band is one picture lifted by one amount. Lift it column by column instead and the seam closes exactly — and the gap goes into the band's lines. Shift each column and every road bends by twice the old gap, horizon and all. Draw each column from its own eye and a road bends by 8.1 px near the seam and 3.0 at the band's far edge, dying only as one over its depth; the horizon stays straight; and the next join inherits 37 per cent of the gap the first one lost.
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A painter's closing can be read from one band
A band of a several-station landscape closed along a curved seam carries the record of how. A station per column bends a road by one over its depth, a column-wise shift bends every road alike, and one lift bends none. Four roads read to a pixel name the closing nearly every time, down to a station curve of about six centimetres, and the reading survives every depth being misjudged by the same factor.