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

Great circle — where it appears

The intersection of the sphere of directions with a plane through its centre, which is the set of directions one straight world line occupies. Its drawn shape belongs to the picture surface: a straight line on a plane, a cosine on a cylinder, a circle on the stereographic.

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

plane — line, 5e-18cylinder — sinusoid, 6e-17stereographic — circle, 6e-16equidistant — circle, 9e-4equal-area — circle, 2e-3equirect. — sinusoid, 1e-4tilted 10°, sampled over 140° of azimuththe horizon swings ±10°

The horizon's shape belongs to the surface

The horizon is one great circle of directions whatever draws it, and at zero tilt all six named surfaces draw it straight. Tilt the camera and they separate — and the cylinder, not the equirectangular surface, is the one whose horizon is exactly a cosine, to 9e-16 against 8.3e-3.

curved · Horizonshape 42.0°27.3°13.5°13.5°27.3°42.0°leftfrontrightbackupdownmidpoint: 0°7 straight lines, at 60° to the seamworst 42.04° · midpoint 0°

The kink at a seam

A cube map is six flat pictures, so every great circle is drawn exactly straight inside a face — to 3e-15 of its chord — and breaks at the join. The break is a kink and not a bend, it is exactly zero at a seam's midpoint whatever the slant, and it is bounded by 2·atan(½) = 53.130° at the corner.

curved · Cubemap

Named alongside it

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

Equirectangularfield of viewPicture surfaceAnisotropyArea scaleChartCube mapEquidistantFisheyeGnomonicHorizonline at infinity

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