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

Recovery — the series

2 essays on one idea, from the one that introduces it to the one that assumes the rest.
  1. recovered principal pointused to drawrecoveredgapfocal length853.90853.904e-15principal x345.0345.02e-12angle44.0°44.0°—correct from 20 cm, at 160 mm wide44° across

    Recovering the camera from the picture it drew

    Draw a box from a known camera, forget the camera, and get it back from the twelve drawn edges alone. Agreement to one part in 10¹⁵ is a statement about the geometry, because the only thing that crossed between the two halves was a list of line segments.

    part 2 · foundations
  2. 00.2000.4000.6000.50011.502how many points were measured along each line, log₁₀how wrong the recovered focal length is (%)a pinhole — no floora lens, k₁ = -0.05the floor, 0.72%two vanishing points, three lines eachpinhole floor 3e-16 · lens floor 0.72%

    A floor with a referent

    Recover a focal length from two vanishing points and measure more points along each line. Through a pinhole the error falls from 0.34 per cent to 0.05 and the instrument finds no floor at all. Through a lens of k₁ = −0.05 it falls, turns, and rises to 0.70 per cent — because the noise the extra points removed had been partly masking the lens's bend. The floor is 0.72 per cent of the focal length, and doubling the distortion coefficient doubles it to 1.44. It is not noise and not conditioning; it is the model, priced.

    part 3 · foundations

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