Series

Spread — the series

3 essays on one idea, from the one that introduces it to the one that assumes the rest.
  1. 0.0020.00334567number of viewsworst camera-centre error (fraction of the track's mean radius, log scale)7 flat7 flat7 flat7 flat7 flat60° sweep, filled in12° per view, wideningfilled in: 1.1e-3 → 2.0e-3widened: 3.2e-3 → 1.8e-3

    Another picture of the same sweep

    Going from three views to seven across the same sixty degrees leaves the reconstruction exactly where it started, and at one point makes it worse. What a reconstruction is short of is angular spread, not photographs.

    part 1 · manyviews
  2. 89°in plan · the mark's size is the angle at the pointthe track covers 60°

    The spread a point gets

    A track of sixty degrees gives no point of the scene sixty degrees. The nearest receive 89 and the furthest 41, a factor of 2.2, and their errors run from 1.5 to 8.4 millimetres — following the angle at the point as its −1.68 power, with 94 per cent of the variation explained. The arc a track covers is one number for forty-four different situations and predicts none of them.

    part 2 · manyviews
  3. in plan · ellipses 25× actual sizewithin 8.4° of the mean sight

    Split the track and the needles turn

    A point triangulated from a track of cameras is not known equally well in every direction: its error is a needle, long along the direction its lines of sight barely constrain. That direction is not the mean line of sight but the lines of sight weighted by how near each camera is — and it can be turned. Two groups of cameras more than a right angle apart swing every needle across, and the same six pictures of a facade then measure its depth four times better.

    part 3 · manyviews

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