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

re-projection — where it appears

Recomputing a picture onto a different surface from the same eye, which is available for any picture surface and for no curved mirror. It is what makes a panorama stitchable and what makes a picture in a mirror ball unstitchable, and the difference is whether the rays met at a point.

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

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 111 mm outcorrect from 21 cm, at 160 mm wide1e-12 mm with the floor · 111 mm without

Undoing a picture made on a curve

Three rounds of work here have measured what a curved receiving surface costs going forward — 5.67 mm on a dish, 9.07 mm on a ridge, 529.4 mm on a vault. None of them asked whether the design can be got back. It can, exactly, and the price is stated precisely: you have to supply the surface. Told the floor, the recovery returns a design to 1.1e-12 mm; told nothing, and fitting the four marks every rectification tool fits, it is 111 mm out.

curved · Curvedrectify 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 scaleFisheyeAnamorphosisAngular resolutionArc lengthAzimuthcentre of projectionChartDevelopableElevationEquidistantEquirectangular

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