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

necessary, not sufficient — where it appears

A test a correct construction must pass and an incorrect one may also pass, so that passing it settles nothing.

Named by 4 essays across 4 fields — each of them below, with the objects they name alongside it.

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.

wrong · deptheye clipped at the near planedivided without clippingdirection cosine -1.0000 — the far end is drawn 2142 px away20 grid segments, 2.4 m of them behind the eyea reversed line is not a large error, it is a different picture

What happens behind the eye

A point behind the camera has a perfectly plausible image. Dividing by a negative fourth coordinate flips both signs, so the point lands through the principal point on the far side of the frame, and a segment crossing the eye plane is drawn straight, inside the frame, and running in exactly the opposite direction — a direction cosine of −1.0000.

pipeline · clipping 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.

choices · exclusion pixels 2.00 : 1recovered focal length219.9 pxthe camera's actual one436.4 pxwhat the recovery returnsspread across three estimates 0.0e+0worst bundle residual 9.1e-13 pxboth are what a wrong picture would trippixel aspect 2.00 unmodelledfocal length 49.6% short, every diagnostic clean

The pixel that is not square

A camera with two focal lengths is a real thing — anamorphic cinema optics, non-square photosites, a stretched video format. Hand this site's own round trip a picture from one and it returns a focal length 49.6% out, a principal point far from the truth, three independent estimates agreeing to 1e-16, and bundle residuals at the noise floor. Every alarm the site has stays silent.

sensor · pixelaspect

Named alongside it

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

DemonstrationCamera matrixCross ratio testResidualAnisotropyAspect ratioAxis scaleCamera calibrationcentre of projectionClip spaceConformalDegeneracy

All concepts