Visual Plane
every picture states the point it is correct from
The collection

Every essay — page 6

Page 6 of 6, continuing through the fields in the same order.

What survives Constructing a view Where to stand Surfaces that are not flat The other systems Light and mirrors Measuring from one picture Through water and glass The real instrument The second eye What a pair is for Many pictures at once The eye that moves Systems that kept the measure What each system gave up What a machine computes The rectangle behind the lens The second projection Drawn confidently

Where to stand

A perspective picture is correct from exactly one point in the room. Every figure here computes where that point is, which turns the oldest complaint about wide-angle photographs into arithmetic.

eyefaint: the row it imitates · solid: the row that is builtbuilt row21.0 pxthe deep row28.4 pxdisparity across the row, two eyes 63 mm apartfar column cut to 0.300the eyes read 74.1%, not 22.2%

A set cut for one eye

Build a colonnade four metres deep and cut every column so that its picture is the picture of one eighteen metres deep. The taper is forced rather than chosen — height and width both scale as the real depth over the intended one — and the match from the design eye is exact to sixteen decimal places. What gives it away is the second eye, and not by the ratio anybody would predict.

13 figures

Drawn confidently

The constructions taught in every book on the subject, measured. Some are fine. The point is that nobody knows which until the drawing is asked what solid it depicts.

horizoncorner angles90.000° — forced by the methoddepicted side ratio0.7195lens this drawing implies60° acrossdrawn exactly as the method prescribesthe free step is where the far edges go

The cube that is a box

The two-point cube every book teaches has a step it supplies no construction for. Place the two far edges symmetrically and the drawing depicts a cube for free; place them eight points apart — a difference invisible on the page — and it depicts a box 1.4 times shallower than it is wide.

10 figures horizonequal stepshalve thetaper byworst error, in metres of depthequal steps to the horizon11.72 mhalve the remaining gap225.13 mtaper by eye347.80 mcorrect from 26 cm, at 160 mm wide34° across

Dividing depth by eye

Three methods for spacing a receding row, all of them taught, all of them wrong. Read back as distances, the best misplaces a post by 3.5 metres in a row that is supposed to be spaced 1.4. And the obvious way of checking them gives one of the three a perfect score.

12 figures drawn: 1.309 : 1subtended at the station point: 1.000000000 : 1the faint circle is the mean radius, for comparisonthe drawn centre sits 3.42 px from the axis's own mark

The sixty-degree cone of vision

Every book says keep the subject inside a 60° cone. Measured, the marginal stretch the rule is nominally about is exactly zero from the station point — 1.000000000000 to 1, over 720 sampled points. The rule is a statement about the reader, and books do not obey it.

10 figures