Anamorph — the series
-
Anamorphosis is only a viewpoint
A smear on a wall that resolves into a skull when the viewer stands in one particular place off to the side. It is not a trick added to perspective — it is perspective, with the centre of projection put somewhere nobody would naturally stand, and it is the clearest demonstration there is that every picture has such a point.
-
An anamorph at true size, on paper
An anamorph is the shadow of the intended picture, cast from the reader’s own eye. Every claim about a figure on a screen is quoted against an assumed display width, because nobody can know how wide a screen shows it; this one is not, because it ships a sheet in millimetres and states where to put an eye.
-
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.
-
The anamorph that crosses a corner
Cast one design onto a floor and the wall at the end of it, from one eye. Each plane gets a collineation of its own; the two agree on the line where the planes meet, exactly, because a point of that line is a point of both. What they do not agree about is scale — the design runs 7.8 times its own size along the floor and 2.0 times up the wall, and the jump at the join is a factor of 3.9.
-
A stair does not use all its faces
A corner anamorph is two homologies and a flight of nine steps is eighteen, which is arithmetic and is the least of it. What a flight has that a corner does not is that which faces exist and which faces can be painted are different questions. From the top of a descending flight not one riser is reachable at any eye height, so half the planes are unpaintable by construction — and from the bottom of an ascending one, 58 per cent of the picture lands on risers that are 36 per cent of the surface.
-
What an eye can paint
A flight of steps has eighteen faces and no eye reaches more than fifteen. Pointed at a cluster of blocks, a seating rake and a corridor with a doorway in it, the same measurement finds 8 of 21, 7 of 13 and 6 of 7 — and the plane, which offers its whole self to every eye, is the control that makes the law a law rather than a fact about stairs.
-
Facing the reader is not being reachable
A face turns toward the eye or it does not, and that is a dot product any reader can compute. Whether the eye’s rays actually land on it is a different question with a different answer — on a seating rake, three faces of ten that face the reader receive nothing, and they are 27 per cent of the facing area. On a corner the same test loses nothing at all, which is what makes the gap occlusion rather than arithmetic.
-
One flight, two pictures
From the top of a descending flight every riser faces away, so the design lands entirely on treads. From the foot of the same flight the risers take 68 per cent of the design at a median stretch of 1.4, and the treads take the rest at a median of 2.6. Give each reader the faces the other cannot use and one staircase carries two pictures, with no face asked to hold both.