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

Complete quadrangle — where it appears

Four points in general position and the six lines joining them, whose three diagonal points are what the straightedge construction of a harmonic conjugate uses.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

the diagonals against a ruler, at 3.2 mthe diagonals — exactthe ruler — 22.7 px outcorrect from 23 cm, at 160 mm wideharmonic set -1.000000000 · construction 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.

foundations · harmonic centre of the ellipseimage of the centrepole of the horizon — 1e-13 px awaycorrect from 22 cm, at 160 mm widepole 1e-13 px from the truth

The centre, got back out of the picture

The image of a circle's centre is not the centre of the image ellipse — this site measured the gap four phases ago and left the obvious question unanswered. It has an exact answer, it needs a straightedge and the horizon, and it is one sentence: the image of the centre is the pole of the vanishing line with respect to the image conic.

foundations · conic

Named alongside it

The objects these essays reach for when they reach for this one.

Harmonic conjugateProjective invariantProjective stratificationVanishing pointConicCross ratioDepth divisionHorizonInverse projectionline at infinityMeasuring pointMidpoint

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