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

True scale — where it appears

A drawn length that stands in a fixed ratio to the length it represents, so a single ruler reads it anywhere on the drawing. Only directions parallel to the picture plane have one under a parallel projection, and no direction has one under a projection through a point.

Named by 6 essays across 3 fields — each of them below, with the objects they name alongside it.

the sheet, 150 × 105 mmthe eye, 52 mm up and 80 mm backgrey: the word standing upright · black: the same word on the paper142 mm from the sheet's middle

An anamorph at true size, on paper

An anamorph is the shadow of the intended picture, cast from the reader’s own eye. Every claim about a figure on a screen is quoted against an assumed display width, because nobody can know how wide a screen shows it; this one is not, because it ships a sheet in millimetres and states where to put an eye.

viewing · Anamorph 0.2500.5000.75010204060copies made, each from the one beforea landmark, as a share of the heightthin: no grid · thick: eighteen squareshand 0.8%

A grid stops a copy drifting

A figure copied by hand from the last copy drifts as a random walk, by the square root of the copies. Copied on a ruled grid, with each landmark brought back to a line, it does not drift at all, because rounding throws the error away. That is how a correcting code works. It holds only below a sharp threshold on the hand, and the grid's size is the trade between how much it corrects and how much it can say.

conventions · Canon correct from 17 cm, at 160 mm wide21 squares tall · pitch 14.7 px

A grid on the wall is a scale without a projection

An Egyptian canon rules a wall into squares and counts a figure's height against the ruling — no horizon, no centre, and a length recovered to 1.4e-14% of error where the same reading taken off a pinhole misses by 58%. Applied instead to a pinhole picture, the furthest of six equal figures reads at 19% of its true height.

conventions · Canon a flat plate · best view0a bent plate · best view0.1224a dished plate · best view0.2298a bent plate · along its generators0patches wrapping 29°dished / bent = 1.878

No view draws a curved plate true

The auxiliary view is descriptive geometry's answer to a foreshortened plane — turn until the plane is parallel to the paper and it draws at true shape. A bent plate has no such direction and a dished one has none twice over: the best view of the first is out by 1 − cos w and the best of the second by 1 − cos²w, worse by exactly 1 + cos w, because its normals need two parameters rather than one.

parallel · Platepatch 00.2500.5000.7501-1-0.50000.5001across the plate, from one edge to the otherdrawn length of a unit of surfacealong the generatorsround the benda plate bent through 57°one ruler in one direction

The drawing and the development

A bent plate gets two flat pictures on the same sheet and each is exact in what the other loses. The parallel drawing keeps the generators at one scale and stretches the arc over a factor; the development keeps every length on the surface and keeps nothing of the shape in space. Neither is the plate and the pair of them is.

parallel · Platepatch one platethe otherthe hingedrawn at 94.3° · reads as 100.0° or 86.6°an orthographic drawing of a foldtwo readings, 13.4° apart

A drawn fold has a phantom

A Necker cube has two readings and so does a drawn fold, and the fold's second reading is not the supplement of the first. The drawing fixes each plate edge's component in the picture and leaves its component along the ray free up to a sign; a reflection identifies two of the four sign pairs, so there are exactly two plates — and a hundred-degree fold reads as eighty-seven as well.

parallel · Foldreversal

Named alongside it

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

Drawing systemDemonstrationOrthographicCanon of proportionCountingDevelopable surfaceDevelopmentDrawing conventionForeshorteningGaussian curvatureAnamorphosisArea scale

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