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

What each system gave up

The whole comparison on one battery: does it have a centre, does it keep true measure, does size fall with distance, is its depth range bounded, does it keep straight lines straight. No system answers yes to the first two at once, and the field ends by turning the table on perspective and pricing what it gave up to get its station point.
they meet at y = 924, off the pagefar edge ÷ near edge = 1.32a one-point construction, swept through its splaythe point is below the near edge

The picture whose lines spread

In a Byzantine icon the sides of a table diverge with depth. The standard account says the vanishing point is behind the viewer. It is not — it sits below the near edge, in front of the eye, and it is the vanishing point of a direction running down and away.

 near edge 155 pxfar edge 196 pxrecovered: ratio 1.000000, corners 1e-14° from squarecorrect from 12 cm, at 160 mm wideplane tilted -45°

An inverse perspective is a leaning plane

Ask a divergent construction what solid it depicts and it answers: a rectangle, four right angles, near edge equal to far. What the splay encodes is not the shape but the plane's tilt — and a real square on a plane leaning toward the camera really does photograph with its far edge wider.

 a centretrue measurediminutionbounded depthstraight linesperspectivehandscrollisometricdimetrictrimetriccavaliercabinetelevationfilled means the system keeps itmeasured from each system's own projectionno row is filled in both of the first two

A centre and a measure are exclusive

Eight drawing systems, measured on five questions, with the pinhole as a row rather than the header. Exactly one has a centre of projection and it is exactly the one with no true measure — and loosening the measure test by a hair lets it in, which is what says the boundary is real.

 a centretrue measurediminutionbounded depthstraight linesperspectivehandscrollisometricdimetrictrimetriccavaliercabinetelevationfilled means the system keeps itmeasured from each system's own projectionno row is filled in both of the first two

Each system answers its own question

A comparison in which every system wins its own column proves nothing if the columns were chosen after the systems. The test that makes it a result is whether any system wins something it was not designed for — and two of them do.

 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.

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