Field

Where to stand

A perspective picture is correct from exactly one point in the room. Every figure here computes where that point is, which turns the oldest complaint about wide-angle photographs into arithmetic.
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.

54 px69 px84° across27% wider at the edge

Wide angle is not distortion

A wide lens stretches shapes at the edge of the frame by exactly 1/cos θ — 3% at 28° across, 41% at 90°. Every bit of that is what a correct rectilinear projection must do, and every bit of it disappears if the picture is viewed from the point it was made for. Nobody views it from there.

eye, 74° offgrey: the word before the projectionblack: the same word, projected

Anamorphosis is only a viewpoint

A smear on a wall that resolves into a skull when the viewer stands in one particular place off to the side. It is not a trick added to perspective — it is perspective, with the centre of projection put somewhere nobody would naturally stand, and it is the clearest demonstration there is that every picture has such a point.

flat picture plane — straight lines stay straightcylindrical picture surface — even stretch, bowed linesone scene, two picture surfacesneither is the distorted one

When the picture surface is not flat

A flat picture plane keeps straight lines straight and stretches the edges without bound. A cylindrical one spreads the stretch evenly and bends every straight line that is not through the axis. Neither is the distorted one — they are answers to different questions, and the choice decides what a wide view can be.

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