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

Fisheye — where it appears

5 essays name this object, across 2 fields. What follows is each of them, and the objects they name alongside it.
plane — bend 0.0%cylinder — bend 6.0%stereographic — bend 3.5%equidistant — bend 4.5%equal-area — bend 5.1%equirect. — bend 5.7%120° across in every panelsame scene, same angle, six surfaces

No picture surface keeps everything

A picture has to be cast onto something, and every candidate surface destroys something different. Six of them are measured here on the same three properties, and the corner of the plot where a surface pays nothing is empty — not because nobody has thought of one, but because a theorem says there is none.

curved · surface fitted conic: a circle to 1e-9stereographicdashed: the fit, not the samples

Stereographic keeps every angle, and only stereographic

One surface in the family preserves shape exactly — every right angle stays a right angle and both its arms are magnified equally, to the last bit the arithmetic has. It also sends every circle in the world to a circle in the picture, which the site's existing conic fit can be pointed at and asked to confirm without being told what it is looking at.

curved · conformal 02468020406080angle off the optical axis (degrees)area scale, relative to the centreplanecylinderstereographicequidistantequal-areaequirect.measured by differencing on the spherethe plane leaves the frame

Every fisheye is a different rule

The word "fisheye" names a shape of lens and not a projection. There are several, they disagree with each other by tens of per cent at the frame edge, and each is the right answer to a different question — one is a protractor, one is a counting instrument, one preserves shape. Which one a lens implements is a fact about that lens, and it is rarely printed on the barrel.

curved · fisheye 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 no picture at 300°the plane is unbounded at 180°plane — bend 0.0%cylinder — bend 6.0%stereographic — bend 3.5%equidistant — bend 4.5%equal-area — bend 5.1%equirect. — bend 5.7%300° across in every panelsame scene, same angle, six surfaces

What a 360-degree photograph actually is

The format every spherical camera writes preserves nothing — not straightness, not shape, not area — and it is the right choice anyway, for a reason that has nothing to do with looking at it. An equirectangular file is a lookup table of directions, and the picture only exists at the moment something re-projects a piece of it.

curved · panorama

Named alongside it

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

EquirectangularArea scaleAnisotropyConformalfield of viewFocal lengthPicture surfaceAzimuthBeltramiCanopy photographyCircle preservingConic fit

All concepts