Ground plane — where it appears
Named by 9 essays across 3 fields — each of them below, with the objects they name alongside it.
The forty-five degree shadow
Draw the shadow at forty-five degrees and make it as long as the object is tall. In the plan that is exactly a sun halfway up the sky. Applied on the paper it puts four posts under four different suns — altitudes from sixteen to twenty-nine degrees, azimuths thirty-two degrees apart, and shadows between one and three-quarters and three and a half times the height. No drawing angle brings them together.
Measured down from the waterline
Whatever stands so far above the water, draw its reflection the same distance below. Through a vertical picture plane that is not an approximation — it is the reflection, to the arithmetic floor. Tilt the camera twenty-two degrees and it is eleven pixels out. Draw a gull, which touches the water nowhere, and guessing its waterline point wrong by two metres of depth costs fifty.
Carrying a height across the room
A known height at one place on the floor, and the same height wanted at another: two lines settle it, and they settle it exactly, at every camera and every pair of positions. What the recipes never mention is that one of those two lines has to be drawn to a point that is usually not on the paper — 3,300 canvas widths away in the case drawn here — and that the repair is not to extend it further.
A picture with nothing straight in it
Every construction on this site is handed the horizon, and a photograph of a crowd, a hillside or a curved façade has no straight edge to give it. What such a picture does have is repetition — and three things of one height put the horizon exactly where the camera has it, from the picture alone. Two things do not, and three standing abreast do not either, and both refusals are the reader's ordinary situation.
The room the eye may stand in
An anamorph is correct from one point, and one point is not a thing a person can occupy. Fix a tolerance on the picture and the set of eye positions that meet it is a solid — for a design 1.8 m wide and a ten-millimetre tolerance it is 36 mm long, 14 mm across and 31 cubic centimetres altogether, a spindle pointing along the line of sight. Ten times the tolerance is a thousand times the room.
An anamorph has one eye
From the design point exactly — a camera's single eye — the floor marks give the design back to sixteen decimal places. A head carries two eyes 63 mm apart, and neither of them is the design point. The difference between the disparity the floor gives and the disparity an upright board would give runs to 47 arcminutes, against a stereoacuity of a few tens of arcseconds. This is why pavement paintings are photographed.
The design that outruns the floor
A pavement anamorph of a design forty per cent of eye height needs two metres of floor. Eighty per cent needs thirteen. Ninety-four per cent needs fifty, ninety-nine per cent needs three hundred and seventeen, and the sky needs an infinite one — because the ray through a design point level with the eye never comes down. Depth times the height still to go, divided by the height already reached, is the eye's own distance at every point of the family.
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.
The height a flat floor cannot give
The marks of a floor anamorph name the eye's position on the floor exactly and say nothing about how high it was — every candidate height explains them perfectly, to one part in a thousand trillion. That is a fact about planes rather than about anamorphs. Ripple the floor by six centimetres and the family collapses: the true height explains the marks exactly and the nearest wrong one, five centimetres away, leaves two millimetres on a design 1.8 metres wide.
Named alongside it
The objects these essays reach for when they reach for this one.
HomologyAnamorphosisHorizonVanishing pointPicture planeConditioningIncidenceCollineationForeshorteningGrazing incidencesingle-view metrologyStation point