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

Arc length — where it appears

Distance measured along a curve rather than across it, and the coordinate a developable surface is unrolled into. It is what a developable surface is unrolled into, and it is the coordinate a scroll's own track is measured along.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

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.

curved · Curvedrectify the floor, in placeunrolled — 2.611 m of surfacea ridged floor, k = 0.062.6 m of plan is 2.611 m of floor

The floors that unroll

A ridged floor curves visibly and can be laid flat without stretching anything — 7.4e-9 of strain across the patch. A dished floor curves less and cannot be laid flat by any means whatever. The difference is one number, Gaussian curvature, and it is the number Gauss proved no bending can change: 0 for the ridge, 0.0144 per square metre for the dish, and no cleverness in the flattening touches it.

curved · Developable

Named alongside it

The objects these essays reach for when they reach for this one.

DevelopableGaussian curvatureIsometryPicture planeRectificationAnamorphosisArea scaleConeConformalCylinderHomographyInvertibility

All concepts