Invertibility — where it appears
Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.
The cone that reads the floor
A conical mirror standing on a design turns it into a picture, and the map it performs is exact, one-to-one, and not a projectivity — a homography fitted to four of the marks returns those four to 7e-13 mm and puts the rest 2480 mm away, on a design 369 mm wide. The reason is that the cone turns the annulus inside out: the middle of the picture comes from the far edge of the floor and the rim from the near one.
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.
Named alongside it
The objects these essays reach for when they reach for this one.
AnamorphosisDevelopableHomographyProjective mapRay tracingArc lengthCentral collineationcentre of projectionConeGaussian curvatureIsometryleast squares