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

Edge stretch — where it appears

The enlargement of a shape near the edge of a wide flat picture, exactly the reciprocal cosine of its angle off axis. It is correct from the station point and visible from anywhere else, which is why a wide-angle photograph looks wrong to a reader standing too far back from it.

Named by 6 essays across 3 fields — each of them below, with the objects they name alongside it.

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.

viewing · Widefield 051050100150field of view the picture was rendered at — degreeshow many times the depicted depth is stretchedthe screen subtends 49.3°100° → depth ×2.6027-inch monitor at 650 mmsubtends 49.3°

A wide field on a small screen

A picture rendered at a hundred degrees and shown on a screen that subtends forty-nine is being read from two and a half times its own station distance, so the depicted space is two and a half times too deep. The stretch at the edges everybody complains about is correct; the complaint is really that nobody is sitting where it would be invisible.

screen · Screenfov 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.

viewing · Surface 11.201.401.6001234how far along the sofa the seat is (m)largest pixel over smallest, across the picturecurvedflat, same widthcurved television against a flat panel of the same widththe curved worst case is at 1.5 m, not at the end

The evenness a curve buys

A curved screen is sold on evenness, and evenness turns out to be three quantities that disagree. On pixel pitch the curve wins from every seat; on the angle the glass is turned through it wins until three and a half metres along the sofa; on the plain distance from eye to glass — the reading the argument is usually made in — it gives up before half a metre.

screen · Screenfov correct from 8 cm, at 160 mm widestretch 1.358 · centres 4.28 px

The ball at the edge of the frame

A ball photographed near the edge of a wide picture is not drawn as a circle. It is an ellipse, longer along the radius from the centre of the picture than across it, and the centre of that ellipse is not the image of the centre of the ball. Both are properties of the flat sheet the picture is on, and an exact pinhole produces both.

foundations · Quadric 00.2500.5000.75010.2500.5000.75011.25the largest stretch a painter will accept, log₁₀share of the design that is inside ita flat floora cornera cluster of blocksa seating rakean ascending flighteye at 1.70 m, 2.4 m in front of the picturethe cap a painter will accept

The stretch decides the band

A design band chosen by geometry — the rays that meet the object — includes rays that graze along it, and a grazing ray lands two design points twenty times further apart than the design says. Cap the stretch at four and a bare floor keeps 55 per cent of its design, a corner 80, and the top of a descending flight all of it.

viewing · Anamorphmap

Named alongside it

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

field of viewPicture surfaceViewing distanceViewing positionAnamorphosisDemonstrationForeshorteningResolutionSampling gridSubtended angleAnisotropyArea scale

All concepts