Homography — where it appears
Flattening a façade out of the photograph
Four corners of a rectangle whose proportions are known are enough to undo the projection of one plane. After that the plane can be measured with a ruler — lengths, angles, areas, all of it — in units of the rectangle's own width, and lengths the map was never given come back to fifteen digits.
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.
The plan hidden in the photograph
Rectifying the ground is the same operation as rectifying a wall, and it turns a photograph into a site plan. The horizon is not an input to it and comes out as a consequence — the plan's points at infinity land on it, at first order, which is the check that the plan is a plan and not a plausible warp.
Recovering the camera from the picture it drew
Draw a box from a known camera, forget the camera, and get it back from the twelve drawn edges alone. Agreement to one part in 10¹⁵ is a statement about the geometry, because the only thing that crossed between the two halves was a list of line segments.
A turn of the head is not a step sideways
The textbook says a short baseline makes reconstruction ill-conditioned. Measured, the algebra does not notice — a two-millimetre baseline recovers the courtyard to nine digits from exact marks. What fails is the ratio of baseline to reading error, and it fails without refusing.
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 on this site is quoted against an assumed display width because the site cannot know how wide its figures really are; this one is not, because it ships a sheet in millimetres and states where to put an eye.
A projection of a projection
Photograph a photograph and the composite map is a homography — four marks determine it and every other lands where they say, to 1e-13 px. Roll the print and the same four mispredict the rest by 30.5 px, which is why straightening a page of a thick book never quite works.
The eye is a place, not a point
Rotate a camera about the wrong point and the sky still stitches perfectly while the foreground slides. The misregistration falls as one over the distance, exactly — which is what says the fault is the pivot and not the lens.
Named alongside it
The objects these essays reach for when they reach for this one.
ResidualRectificationVanishing pointAnamorphosisEntrance pupilFocal lengthParallaxPicture planePrincipal pointsingle-view metrologyAspect ratioBaseline