Concept

Rectification — where it appears

4 essays name this object, across 3 fields. What follows is each of them, and the objects they name alongside it.
the picturethe same plane, rectifieddoor — 0.5068 widths (true 0.5068)sill — 0.3026 widths (true 0.3026)diagonal — 1.1766 widths (true 1.1766)worst error 4e-16 relativethe probes were not used to build the map

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.

metrology · rectify
eye, 74° offgrey: the word before the projectionblack: the same word, projected

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.

viewing · anamorph
the picturethe same plane, rectifiedacross — 0.6000 widths (true 0.6000)along — 0.7667 widths (true 0.7667)diagonal — 1.2023 widths (true 1.2023)worst error 1e-15 relativethe probes were not used to build the map

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.

metrology · rectify
an anchorcorrect from 19 cm, at 160 mm wideflat 1e-13 px · rolled 30.5 px

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.

foundations · composition

Named alongside it

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

HomographyVanishing pointResidualAnamorphosisAspect ratioCatoptricCompositionControl pointsCorrespondenceCross ratioFacadeGround plane rectification

All concepts