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

centre of projection — where it appears

3 essays name this object, across 3 fields. What follows is each of them, and the objects they name alongside it.
the picture, 160 mm wide22 cm40°the eyefocal length 948 px22 cm at 160 mm wide

The point you have to stand at

A perspective picture is a projection through a centre, and scaling that centre's distance to the width the picture is actually shown at gives a distance in centimetres. Shown 160 mm wide, a 40° picture is correct from 22 cm and a 90° one from 8 cm. Nobody stands there, and that single fact explains most of what gets called distortion.

viewing · station the water surfacethe pinholethe rays miss by 9.9 mmno single viewpoint — the rays miss by 9.9 mmdry control: 0e+0 m

A picture through water has no viewpoint

Continue the rays of a refracted picture into the water and fit them to a common point. They miss it by ten millimetres. The same fit with the water taken away misses by zero, which is what makes ten millimetres a measurement rather than a number.

refraction · nocentre the far field — where the stitch was fitted2.2 m — 3.2 px out24 m — 0.3 px outthe sky registers to 1e-13 pxthe foreground does not — up to 3.2 px

The eye is a place, not a point

Rotate a camera about the wrong point and the sky still stitches perfectly while the foreground slides. The misregistration falls as one over the distance, exactly — which is what says the fault is the pivot and not the lens.

lens · pupil

Named alongside it

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

Focal lengthResidualVanishing pointCausticCross ratioDistance pointEntrance pupilfield of viewHomographyleast squaresPanoramaParallax

All concepts