Anamorphosis

Furthest from the fold, and the same idea underneath. An agamograph hides its second picture until you move; this hides its only picture until you put the mirror down. Both are selectors — this one is made of geometry rather than facets, and it is the oldest trick in the family by three centuries.

On the paper — flat, meaningless

In the cylinder — what you would actually see

Subject

Bold shapes with long edges. Fine detail lands where the warp stretches hardest and disintegrates.

empty

Choose image

The cylinder

Radius: 30 mm

Where you stand

Eye height: 300 mm above the paperEye distance: 250 mm from the axis

The drawing

Arc: 150°Outer radius: 140 mm

Arc you can actually see: 166°
Mirror height used: 100 mm
Paper needed: 280 mm square

Only 100 mm of cylinder is doing any work, and it is the bottom 100 mm. As a point on the mirror climbs toward eye height the reflected ray flattens out and the paper point runs away to infinity — which is exactly why anamorphs smear so violently at their outer edge, and why the template has to be bounded by choosing an outer radius rather than a mirror height.

Print at 100% on 280 mm square, stand a mirrored cylinder of radius 30 mm on the dashed circle, and put your eye 300 mm up and 250 mm back. A tin, a mirrored tube, or acetate wrapped round a jar all work.

The mapping

No approximation is needed. Put the cylinder's axis at the origin with the paper at z = 0 and the eye at (D, 0, E). The surface normal at any point is radial and horizontal, so the reflection is a plain one:

d     = P − eye                incident ray
d · n = R − D·cos φ            n = (cos φ, sin φ, 0)
r     = d − 2(d · n) n         reflected ray

paper point = P + r · z / (E − z)

Because the cylinder is straight up and down it behaves like a flat mirror vertically and a convex one horizontally, which is why the distortion is so lopsided: gentle around the circle, violent away from it.

Two limits worth knowing

The drawing runs away. In the eye's own plane the paper radius is R + z(D − R)/(E − z), which diverges as a point on the mirror climbs toward eye height. There is no natural outer edge, so the template is bounded by choosing how far the ink may run and solving backwards for the slice of mirror that reaches it.

You cannot see the whole cylinder. A surface point faces you only while R − D·cos φ < 0, so the visible half-angle is acos(R / D) — never a full 180°, and narrower the closer you stand. Drawing past it fails silently: the ink goes down, the template looks plausible, and the edges of the picture are simply absent from the mirror. This tool clamps rather than let that happen.

Where it sits

Every other tool here interlaces — it cuts images into strips and puts a selector in front of them. This one does not. There is a single image and no strips at all; the selector is a coordinate transform, and the thing that recovers it is a mirror rather than a fold, a lens, or a mask. It belongs to the family by intent rather than by method: an image that exists from one place and nowhere else.