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

Harmonic — the series

2 essays on one idea, from the one that introduces it to the one that assumes the rest.
  1. the diagonals against a ruler, at 3.2 mthe diagonals — exactthe ruler — 22.7 px outcorrect from 23 cm, at 160 mm wideharmonic set -1.000000 · 8e-14 px

    The diagonals find the middle

    Three taught methods for spacing a receding row are all wrong, and the best of them misplaces a post by three and a half metres. There is a fourth, it needs no measurement and no vanishing point, and it is exact at every camera and every depth — because 'the diagonals of a rectangle cross at its centre' is a statement about which lines meet where, and that is the one kind of statement a projection cannot damage.

    part 2 · foundations
  2. ABCDjoin and meet only — no length, no angle(A B; C D) = -1.000000000

    The quadrilateral that finds the middle

    The harmonic conjugate is usually built from four points. Built instead from four lines — the dual construction, the same number of straightedge steps — it lands on the same fourth point to 1.2 × 10⁻¹⁵ of the range's own length, gives a cross-ratio of exactly −1, and refuses the midpoint, whose conjugate is at infinity.

    part 3 · foundations

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