Visual Plane
every picture states the point it is correct from
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The thread: The viewer is in the geometry

A perspective picture is a projection from a point, and that point is a fact about the picture — computable from its focal length and the width it is shown at. Every figure states the distance it is correct from, because leaving it out is what makes the subject feel like a matter of taste.
the picture, 160 mm wide22 cm40°the eyefocal length 948 px22 cm at 160 mm wide Where to stand

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.

 horizon — the image of the line at infinityvanishing point at x = 1464 — off the framecorrect from 26 cm, at 160 mm wide34° across What survives

Where parallel lines meet

They meet at a point that is not in the plane, and the horizon is the line made of all such points. Treating that as bookkeeping misses what it buys — a vanishing point becomes an ordinary point of the picture, findable from the drawn lines, checkable, and enterable into any calculation the others are.

 54 px69 px84° across27% wider at the edge Where to stand

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.

 horizon = eye level, 1.62 m91.01%correct from 26 cm, at 160 mm widespread 0 Constructing a view

The horizon is at eye level — if the picture plane is vertical

The horizon cuts every standing figure at the same fraction of its height however far away it is, which is the most immediately usable fact in the subject. It holds when the camera is level, and a twelve-degree tilt is enough to spread the fractions by more than a percentage point.

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

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.

 isometric — the limit2.5 m6 m20 m200 msame box, same drawn sizethe eye recedes The other systems

The eye taken to infinity

A parallel projection is a photograph from infinitely far away with the lens lengthened to match. That is not an analogy — it is the limit, it can be watched happening, and it explains why a long lens flattens a scene and why an isometric drawing has no viewing distance to state.

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

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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