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

Crossratio — the series

2 essays on one idea, from the one that introduces it to the one that assumes the rest.
  1. horizonABCDon the groundin the picturelength AB1.00011.3930ratio AB:CD0.56670.6837cross-ratio1.31681.3168correct from 26 cm, at 160 mm wide34° across

    What a projection destroys

    A projection loses length, angle, area and the ratio in which a point divides a segment. Exactly one quantity comes through untouched, and almost everything that can be checked about a picture is checked with it — including, as it turns out, some things it cannot check at all.

    part 1 · foundations
  2. -3-2-1010123how many measurements are averaged, log₁₀the error in the recovered height, log₁₀ mmthe spread — -0.52the bias — flat, and microns1 px on the clicked topspread 0.177 mm at m = 1024, bias 20.0 µm

    The bias out of reach

    A single-view height recovered from the cross-ratio has an error with two terms. The spread of an average of m readings falls as one over the root of m, by a fitted exponent of −0.52 over three decades. The bias does not fall at all — and it is eight microns, against a single-shot spread of six millimetres, so the two cross at 535,000 measurements. There is a floor here and no experiment anybody will run can see it.

    part 2 · foundations

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