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

Stretch — where it appears

The factor by which a map lengthens a small step, which varies from place to place on every surface but a plane. Its variation with direction is the anisotropy, and its two extreme values are the semi-axes of the ellipse a small circle draws.

Named by 4 essays across 2 fields — each of them below, with the objects they name alongside it.

eye level — the ray never comes downeye · 1.65 m up12.8 m of floor at 80% of eye heightand the top of the design has no mark at all

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.

viewing · Anamorphmap wallthe intended picturethe joineyecontinuous across the cornerand 3.88× the scale on one side

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.

viewing · Anamorph no single viewpoint — the rays miss by no distance at all — the rays are parallel13 of 21 faces

A picture with no eye

The anamorph field measured which parts of an object one eye can paint, and every finding in it is about a point. A parallel projection has no such point, so the same questions have a different shape — and the two that change are the dimension of the answer and the map onto each face. The one that does not change is occlusion, which is routinely assumed away.

parallel · Noeye face 15.75×1.00× parallelface 21.41×1.00× parallelface 31.34×1.00× parallelface 41.13×1.00× parallelface 51.05×1.00× parallelface 61.03×1.00× parallelface 71.00×1.00× parallelface 81.00×1.00× parallelthe spread of scale within one faceparallel: 1.000000×

One face, one scale

A design carried from a point onto a flat face varies in scale by nearly six across that one face; the same design carried along a direction varies by 1.000000000. The stretch is reported here as the two singular values of the local map rather than as one directional difference, which is the honest form and which the previous round owed.

parallel · Noeye

Named alongside it

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

AnamorphosisAffine mapFaceted objectGrazing incidenceGround planeHomologyParallel projectionPicture planeAnisotropyArea scaleAsymptotecentre of projection

All concepts