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

Catoptric anamorphosis — where it appears

An anamorph read in a curved mirror, where the light bends once between the marks and the eye and no homography relates the two. Checking one means running the light backwards from the mark to the eye, because no map between the design and the marks can be written in closed form.

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

the sheet, seen from abovemirrorthe eye, 2.4 radii upwhat stands up in the mirrorthe light path reverses to the eye to 1e-15scale varies 7.2× across the design

The cylindrical mirror unbends it

Put a mirrored cylinder in the middle of the sheet and the light path from the eye to the paper bends once. The map that results is not a homography and not a projection in the plane sense at all — it varies its scale by a factor of seven across the design, which is why the smear is unreadable and why the mirror can put it back.

viewing · Anamorph barrel vaulteye · 1.62 mon the floor1e-12 mmon the vault529.4 mmworst miss of the best homography, log scalevault radius 4.0 m7.7% of the extent, against 4e-14%

The ceiling that is not a plane

Paint the same design for the same eye onto a floor and onto a barrel vault, then fit the best possible homography to each set of marks. On the floor it misses by femtometres, because the map is a collineation and four marks determine every other. On the vault it misses by half a metre, and no choice of four marks helps — which is where every projective construction made for a floor stops applying.

viewing · Vaultanamorph

Named alongside it

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

Area scaleAnamorphosisAzimuthCatoptricCollineationCross-ratioCylindrical mirrorDemonstrationHomographyLight pathPicture surfacePlanar homology

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