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

Curvedrectify — the ladder

2 distinct arguments against one idea, from the one that introduces it to the one that assumes the rest.
  1. 111 mm outcorrect from 21 cm, at 160 mm wide1e-12 mm with the floor · 111 mm without

    Undoing a picture made on a curve

    Three rounds of work here have measured what a curved receiving surface costs going forward — 5.67 mm on a dish, 9.07 mm on a ridge, 529.4 mm on a vault. None of them asked whether the design can be got back. It can, exactly, and the price is stated precisely: you have to supply the surface. Told the floor, the recovery returns a design to 1.1e-12 mm; told nothing, and fitting the four marks every rectification tool fits, it is 111 mm out.

    rung 4 · curved
  2. 025507510010203040how wrong the assumed curvature is, as a % of the true oneworst error in the recovered design (mm)0.91% buys 1 mma a ridged floor, k = 0.0644.0 mm at 41% out

    How well the floor has to be known

    “Supply the surface” is an instruction with no number in it, and an instruction with no number is a wish. Here is the number: the error in the recovered design is very nearly proportional to the error in the assumed curvature — the constant varies by 1.4% across a twentyfold range — so about nine parts in a thousand of the curvature buys one millimetre on a design 1800 mm wide, and 40% out costs 43.5 mm.

    rung 5 · curved

All ladders