Concept

Stitching — where it appears

Joining several photographs into one wider picture by registering them on what they share. It assumes every frame came from the same point, which is false whenever the camera turned about anything but its entrance pupil, and the residual is a parallax rather than a calibration error.

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

the pivottangent circle, 30.0 mmno single viewpoint — the rays miss by 24.98 mm6 frames · pivot 60 mm off

The pivot that is not the eye

A camera bolted to a tripod turns about the screw under its baseplate, and the light crosses somewhere else. Every ray of the panorama that results passes the pivot by e sin γ — the offset times the sine of how far off its own frame's axis the ray points — so the picture has a radius where a projection would have a point.

curved · pivot
0204060204060frames in the panoramadistance from the pivot (mm)π/β = 9.5across the seamup the framepivot 60 mm · frame 38° tallfloor 19.53 mm

The parallax you cannot shoot away

A stitched panorama's parallax has two halves and they do not behave alike. The one across the seam falls as the sine of half a frame spacing, so more frames buy it off; the one up the frame is the sine of half the frame's own height, and no quantity of shooting touches it. They cross at π over β, which has no pivot error in it at all.

curved · pivot
-500500.5001distance to the thing being stitched (log₁₀ metres)what the stitch leaves behind (px)2.86 m80 mm baselinezero at one depth each

A rig is right on one surface

Several cameras looking outward have several centres, and no warp registers all of a scene. The residual is a disparity, so the depth the stitch is computed for has an exact optimum — the harmonic midpoint of the depth range, not the middle of it — and the arithmetic middle costs a factor of 2 z_far over the sum, which tends to two.

curved · stitchdepth

Named alongside it

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

centre of projectionDemonstrationPanoramaParallaxPicture surfaceEntrance pupilBaselineCausticCylindrical projectionDepth from disparityDisparityfield of view

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