The thread: Fitted, not assumed — page 7
The lamp a low shadow cannot locate
Five posts, their shadows, and the line from each foot through its own shadow's tip meet at the lamp standing over them — at 52 degrees up that meet moves 0.11 m for half a pixel of marking error; at 11.5 degrees, 0.64 m. The two eigenvalues of the same pencil of lines part by a factor of 8849084 across the sweep, and half a pixel becomes more than a metre of lamp below 14.4 degrees.
Light and mirrorsA shadow edge read as a profile
A lamp, a stick and a camera recover a stepped object's profile to 4.9e-15 m rms when the marks are exact, and to 10.4 mm once they are read to two tenths of a pixel — the same linear law a fitted exponent of 1.001 confirms. What actually sets that number is the angle between the sweeping light plane and the camera's own ray — the amplification is least, 17.0 times a pixel, broadside at 6°, and grows without bound toward -36.1°, where the plane contains the camera's own eye and the recovery keeps none of its marks at all.
Drawn confidentlyA straightedge convicts the rule on five braccia
The constant-ratio rule for spacing a pavement's boards leaves one mark a correct construction does not: its tile corners bow off the diagonal. The worry was that a painter's hand would bury the bow in its own scatter. At a pixel of scatter it does not, on any pavement of five braccia or more. What limits the test is not the hand but the page: a pavement drawn to one width bows no more at twenty braccia than at eight, while the hand's wander keeps growing with every tile.
Drawn confidentlyThe rule's bow is read by its shape
A straightedge on a painted pavement's diagonal convicts the constant-ratio rule by the size of its corners' worst departure, and gives out once the painter's hand scatters by a third of the bow. The bow has more than a size. It is one smooth arc, to one side, fixed by the ratio, and a hand's scatter is neither. Fit that arc with one free amplitude and the rule is ranked above a construction 96 times in a hundred on five braccia at two pixels, where the straightedge managed 83 — and the reading holds to half the bow's size in scatter.