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

Little planet — where it appears

A spherical panorama re-projected stereographically from the nadir, keeping every angle exactly and running its area scale over orders of magnitude. Its area scale runs over orders of magnitude across one picture, which is the clearest demonstration that conformal and undistorted are different words.

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

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 angle, worst over the sphere4.4e-8°anisotropy, worst1.000000023area scale, largest over smallest×255what a reader calls distortedthe third row, not the firstthe disc is 160° of the spheredrawn to 160° off axisthe first two rows are conformality

Conformal is not undistorted

The most distorted-looking picture in ordinary circulation is the little planet — a 360 photograph re-projected from below, with the ground curled into a ball. Its worst angular error over 160 degrees of the sphere is 4.4e-8 degrees, which is arithmetic noise. Every crossing in the original crosses at exactly the same angle in the result, and what has gone is area, over a factor of 255.

curved · Littleplanet

Named alongside it

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

AnisotropyCircle preservingConformalEquirectangularfield of viewStereographic projectionArea scaleConic fitDemonstrationEqual-area projectionFisheyeJacobian

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