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

Sampling grid — where it appears

The array of samples a picture is stored on, whose density per unit solid angle is the reciprocal of the surface's area scale.

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

one pixel is an areacentrescornersprincipal point moves0.707 pxfocal length changes by4.5e-13 pxan edge-versus-centre viewport1.303 pxa half-pixel convention is a principal-point error; an off-by-one viewport is a focal-length error8 vertices, all shifted by the same 0.7071 pxspread across marks 0.0e+0 px

A pixel is not a point

Where the sample sits inside a pixel is a convention, and getting it wrong shifts every mark by half a pixel in each axis. This site can say what that costs, because it recovers cameras from pictures — the answer is a principal point exactly 0.707 px from the truth with the focal length untouched, and the other half-pixel mistake does precisely the reverse.

pipeline · viewport leftfrontrightbackupdownacross the left/front seam: 1.80°, with each side straight to 7e-16corner area ×5.196anisotropy √3 = 1.7321 there

Six flat pictures of everything

There is one way to photograph the whole sphere and keep every straight line straight, and it is to stop using one surface. Six flat pictures at ninety degrees cover everything, each of them a perfect pinhole, and the price is paid entirely at the seams — where a straight line does not bend but kinks, by an angle that reaches 45 degrees and is exactly zero for the lines lying in the seam's own plane.

curved · cubemap

Named alongside it

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

DemonstrationAnisotropyArea scaleBeltramiCamera calibrationCamera matrixCube mapfield of viewFocal lengthGnomonicIsometricPanorama

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