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

Chart — where it appears

One picture surface's map from directions to marks, covering part or all of the sphere of directions. No chart covers the whole sphere without a singular direction, which is why a cube map uses six and every one-piece surface has a place it cannot hold.

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

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 02401020304050degrees off the optical axis, inside the reprojected framemarks the target wants, per mark the source laid downone mark for one mark×5.49 at the edge68% of the source unusedcorrect from 6.7 cm at 160 mm wide

Shot on one surface, shown on another

Two picture surfaces are two charts of the same pencil of rays, so a reprojection between them is a change of coordinates and loses no geometry at all — bit-exact at all 408 sampled directions. What it costs lies elsewhere — 70 per cent of the source has nowhere to go, and the target wants ×5.49 the marks at its edge.

curved · Composite

Named alongside it

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

Area scalefield of viewPicture surfaceAngular resolutionAnisotropycentre of projectionCube mapEquidistantEquirectangularFisheyeGnomonicGreat circle

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