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

Azimuth — where it appears

A bearing measured around the horizon, which is the coordinate a rotating camera spends evenly and a flat picture does not. A cylindrical or spherical surface spends it evenly and a flat picture does not, which is why a panorama can run all the way round and a rectilinear picture cannot reach half a turn.

Named by 4 essays across 3 fields — each of them below, with the objects they name alongside it.

fitted conic: 1.467 from being a circlecylinderthe samples, fitted

The cylinder, and the price of going all the way round

A cylindrical picture can hold three hundred and sixty degrees, keeps every vertical vertical, and bows every horizontal. Its cost is a stretch of sec φ in elevation, which is also the equirectangular surface's cost exactly — two surfaces that are always described as different and are identical in the one respect anybody notices.

curved · Cylinder 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 the sheet, seen from abovemirrorthe eye, 2.4 radii upwhat stands up in the mirrorthe light path reverses to the eye to 1e-15scale varies 7.2× across the design

The cylindrical mirror unbends it

Put a mirrored cylinder in the middle of the sheet and the light path from the eye to the paper bends once. The map that results is not a homography and not a projection in the plane sense at all — it varies its scale by a factor of seven across the design, which is why the smear is unreadable and why the mirror can put it back.

viewing · Anamorph correct from 19 cm, at 160 mm wide46° across

The forty-five degree shadow

Draw the shadow at forty-five degrees and make it as long as the object is tall. In the plan that is exactly a sun halfway up the sky. Applied on the paper it puts four posts under four different suns — altitudes from sixteen to twenty-nine degrees, azimuths thirty-two degrees apart, and shadows between one and three-quarters and three and a half times the height. No drawing angle brings them together.

wrong · Shadowvp

Named alongside it

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

Area scaleElevationEquirectangularAltitudeAnisotropyCatoptricCatoptric anamorphosisConicCylindrical mirrorCylindrical projectionfield of viewFisheye

All concepts