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

Cone — where it appears

The set of rays through the eye over a curve in the picture, whose sections by planes are the world curves that could have drawn it. Its sections are what a single picture leaves possible, and choosing among them is what a second constraint from outside the picture does.

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

eye, on the axisa cone 29 cm across and 22 cm highthe design lies from 0.17 m to 0.47 m out

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.

mirrors · Conemirror 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.

DevelopableAnamorphosisArc lengthArea scaleCentral collineationcentre of projectionConformalCylinderGaussian curvatureHomographyInvertibilityIsometry

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