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

Keystone — where it appears

The trapezoid a rectangle becomes when a projector or a camera is not square-on to the surface it works with. It is a homography of the intended picture and nothing more, so the result is still a correct picture of a transformed scene, and one four-point correction removes it exactly.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

the seatcentre of curvatureR = 1000 mm · seat at 650 mm51.4 px off a homography

The screen is a picture surface too

A curved television is one of the six named picture surfaces sitting in a living room, and from its own axis it delivers azimuth in proportion to the picture, exactly. What it is shown is a rectilinear picture from a sofa, and the difference is not a matter of degree — a flat screen from any seat shows a homography of the intended picture, so it is a correct picture of a transformed scene, and a curved one shows a map that is not a homography from any seat at all.

screen · curvedscreen corrected from the picture — 0e+0° between the verticalscorrect from 20 cm, at 160 mm wideagrees with a level camera at the same eye to 3e-13 px

Straightening does not move the eye

Correct a photograph's converging verticals and what comes out agrees with a level camera at the same point — one the correction was never shown — to 3e-13 px, with the verticals parallel to 0e+0°. The cross-ratio of four points along a ground line reads 1.3333 before and after, so the corrected picture measures exactly what the original measured, from exactly where the original was taken and nowhere else.

construction · keystone

Named alongside it

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

HomographyArea scalecentre of projectionCross ratioCylindrical projectionDemonstrationDevelopableDisplayFocal lengthPicture planePicture surfacePrincipal point

All concepts