Visual Plane
every picture states the point it is correct from
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The thread: Determined up to something — page 6

Every recovery on this site returns an answer with a qualifier attached. One picture gives ratios and no size. Two give shape and no size. Many give a scene and a camera track up to seven numbers no quantity of pictures supplies. The qualifier is not a shortcoming to apologise for; it is the exact statement of what the pictures contain, and here it is counted, walked along and shown to be free rather than merely small. Essays 121 to 125 of 125.
ABCDjoin and meet only — no length, no angle(A B; C D) = -1.000000000 What survives

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.

 lamp 11 lampwedge holds 10.50× the object Light and mirrors

How many shadows determine the object

One lamp's shadow says only that a convex section lies inside a wedge 10.5 times its own area; four already cut that down to 1.17 times, and 128 close a convex section's boundary to 0.10 mm everywhere. The identical sweep on a section with a bite taken out of it stalls at 70.3 mm, 675 times worse, because an outline is the boundary of the smallest convex body with that shadow and no direction ever sees inside a concavity.

 one lamp, one floor — the rays reach the same markscorrect from 19 cm, at 160 mm widethe true pair Light and mirrors

The lamp and the floor cannot both be recovered

Every member of a one-parameter family of lamp-and-floor pairs draws the identical photograph to a fraction of a thousandth of a pixel — one member swings the lamp 90 cm and tilts the floor 4.3° and the picture does not move at all. A tape measure or a post of known height each pin the true member uniquely, and so does a wall known in advance to be square to the floor, whose angle to the recovered floor peaks at exactly 90° at μ = 1.000 and nowhere else; a receiver merely known to be parallel drifts thirteen times more weakly.

 horizonthe post, and the post behind the eyecorrect from 14 cm, at 160 mm wideone mark to 6.4e-14 px · off-eye centre 51 px away What survives

The picture contains what is behind the camera

A pinhole maps a direction, and a line has one direction, so a point behind the eye lands on exactly the same mark as its reflection in front — here to 6.4e-14 pixels. The sign the division throws away is why cheirality is a fact supplied from outside the picture rather than measured in it.

 0.050.10.20.5125105101520braccia in the pavement, drawn to one page widthpixelsthe diagonal, by straightedgethe transversals, by fittingboth read on one pavement47× at eight braccia Drawn confidently

The rule is exact for a floor that lengthens

The constant-ratio rule for spacing receding boards is an exact perspective — to the last digit, on the panel's own horizon — of a floor whose boards grow by the inverse of the ratio, 0.74 braccia deep at the front and 1.31 at the back on an eight-braccio pavement. The orthogonals agree with that floor. What says the tiles were meant to be square is a diagonal, which bends 8.1 pixels off straight where the reader's fitting test finds a sixth of one.

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