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

Occlusion — where it appears

4 essays name this object, across 2 fields. What follows is each of them, and the objects they name alongside it.
parallel, 52° above the ground56% · 56% · 56%one eye, 14.5 m away49% · 56% · 49%a square metre of floor varies 1.000× against 1.535×spread across rooms: 0 against 6.2 points

What the removed roof buys

The Japanese convention of drawing an interior with its roof lifted off is usually explained as a way of seeing inside. What it actually buys is uniformity — every room reports the same share of its floor, to the last sample, where the eye that frames the same building reports three different numbers.

conventions · fukinuki a camera looking downthe carpet is true, the people are nota camera looking levelthe people are true, the carpet is notthe two views a miniature is assembled from90° apart, exactly

A carpet and the people on it

A Persian miniature draws the ground as though from above and the figures standing on it as though from in front. The two views want optical axes exactly ninety degrees apart, and the plan view does not shorten a standing figure — it replaces its height with its distance from the point under the eye.

conventions · twogrounds head0.668profile — the outline that names a faceeye0.669frontal — an eye in profile is a wedgeshoulders0.669frontal — the width that says two armslegs0.668profile — a stride is a side viewpond0.326plan — a rectangle of water is a rectangle1.000 — what its own aspect keepsshare of each part that reaches the picture, from the best single direction|d · n| for each part3.000 of 5, swept and in closed form

Assembled from several views

An Egyptian relief takes each part of a figure from the direction that identifies it — head in profile, eye and shoulders frontal, a pond in plan. What that buys is exactly measurable: any single viewing direction keeps at most √k of k perpendicular aspects, so the best compromise view retains 58% of each.

conventions · aspective the ratio along a receding line15.6%0% parallelthe depth range in the last tenth69.0%10% lineara square metre, near against far53.5% larger0% parallelthe floor of the far room6.2 points0 parallelwhat it costs, and what the other systems have insteadmeasured on this site's own machinerythe price of a station point

What perspective gave up

The field ends by turning its own battery on the system it has been comparing everything against. Four quantities a pinhole destroys that the other systems keep, each measured on this site's own machinery, and each the price of the one thing perspective has and they do not.

choices · exclusion

Named alongside it

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

DemonstrationDrawing systemArea scaleOrthographicStation pointForeshorteningAspectiveCamera tiltcentre of projectionDepth compressionfield of viewFukinuki yatai

All concepts