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

Rabatment — where it appears

Folding a plane about the line it shares with another until the two lie flat together, which is how a perspective construction gets both planes into one drawing. It is the reason a construction sheet carries a plan and an elevation on the same page, and the reason a lateral section can be drawn beside the picture it produces.

Named by 5 essays across 2 fields — each of them below, with the objects they name alongside it.

floorpicture planeeye level — no mark above thiseye · 1.62 m up, 2.40 m backthe ground line, seen from abovethe mark runs to 3.00 ma point 1.62 m up casts no mark at all

A floor anamorph is three numbers

An anamorph is described everywhere as a picture stretched until only one viewpoint can read it, which says what it looks like and nothing about what it is. Cast one onto a floor and fit a map to the marks, and the map turns out to be a planar homology — a line of fixed points, one point off it, and a single ratio. Those three numbers are not a description of the eye. They are the eye.

viewing · Anamorphmap axis — the ground line, fixed pointwisecentreaxisthe ground linefixed pointwisecentre(0.150, 4.020)height + distanceratio-1.481481−distance / heightheight × aspect = 2.592, and neither aloneeye recovered to 4.8e-12 mmeye 1.62 m up, 2.40 m backthree numbers back to the eye: 2.2e-16 m

The marks name the place, not the height

Run the camera-recovery round trip on an anamorph — hand it the floor marks and ask for the eye back — and it returns the spot on the floor to eleven decimal places with nothing assumed at all. It does not return the height. What the marks fix is the product of the eye's height with the design's aspect ratio, and no amount of looking at the floor separates the two.

viewing · Anamorphrecovery correct from 16 cm, at 160 mm wide4 divisions per run · worst 5.7e-13 px

Three-point, laid out with a straightedge

Recovering a camera from a drawing is the familiar direction. The other direction — stand somewhere, measure a room, and lay the picture out — had never been taken in three-point, because the third axis needs a measuring point on a line nobody draws. With it, every corner lands where the camera puts it to three parts in ten million million of a pixel, and nothing anywhere is judged.

construction · Threepoint xupzthe plane of x and upthe groundthe plane of x and zthe orthocentrefocal 707.4 pxthree sides, three planes

A drawing has three horizons

The triangle three vanishing points form is not a scaffold. Each of its sides is the vanishing line of one of the three coordinate planes — the floor's horizon and two walls' — and its orthocentre is the centre of the picture. So the horizon a perspective drawing is built on is one side of a triangle, and it is special only because the ground is where things stand.

construction · Threepoint vanishing point 1vanishing point 2where the camera wasassumed centre 50% alongfocal 1129.9 px · 0.283 : 1

The arc every eye stands on

Four drawn corners known to be a rectangle fix the horizon of their plane and nothing else. The eye that drew them has to see the two vanishing points at a right angle, so it lies on the circle those points are a diameter of — and every point of that arc reconstructs a genuine rectangle, with right angles to five parts in ten million million of a degree, and a different proportion.

construction · Rectangle

Named alongside it

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

DemonstrationStation pointPrincipal pointVanishing pointAnamorphosisCamera tiltCharacteristic ratiodegrees of freedomFixed pointFocal lengthFree parameterGround line

All concepts