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

Equal-area — where it appears

A picture surface giving every patch of sky an image whose area is proportional to its solid angle. It spends its marks evenly by construction, and at its singular direction it pays in shape rather than in area, which is the opposite of what a conformal surface does.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

plane — ×24.99 edge to centrecylinder — ×2.40 edge to centrestereographic — ×2.22 edge to centreequidistant — ×1.30 edge to centreequal-area — ×1.00 edge to centreequirect. — ×1.34 edge to centre36 cells of 377 square degrees, out to 70°equal-area ×1.00 · plane ×25.0

Where a surface spends its pixels

A picture surface is a budget before it is anything else, and the six named ones distribute the same marks over the same directions quite differently. The flat plane lays 25.0 times as many on a square degree at the edge of a 70° field as on one at the centre; the equal-area fisheye is flat to 8.3e-6 per cent.

curved · Resolution one direction — the pole — drawn as the whole of this edge8° cap at the pole: ×9.2the same cap, 20° off axis: ×0.646both caps hold 201 square degrees of sky×14 between them

A pole is a line

An equirectangular surface sends one direction to a whole edge, so an 8° cap of sky at the pole takes 4.50 per cent of the marks against a 0.49 per cent share of the world. The worst singularity is not the pole at all — the equidistant fisheye's antipode costs ×17.9 — and only the cube map, which never holds a sphere in one chart, is bounded.

curved · Singularity

Named alongside it

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

Area scaleEquidistantEquirectangularFisheyePicture surfaceSolid angleStereographicAngular resolutionAnisotropyConformalfield of view

All concepts