The thread: Fitted, not assumed — page 6
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.