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

Faceted object — where it appears

A solid modelled as a list of planar rectangles with a nearest-hit rule, which is enough to ask which parts of it a design can reach. The nearest hit is doing the work: whether a face turns toward a viewer and whether the viewer's rays arrive at it are different questions, and the gap between them is occlusion.

Named by 3 essays across 2 fields — each of them below, with the objects they name alongside it.

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 no single viewpoint — the rays miss by no distance at all — the rays are parallel4 pictures on 3 kinds of face

A flight that has ends

A real staircase has three families of faces and the rule proposed last round predicted three pictures. It supports four, because a picture is fixed by a direction and the flight's two sides point opposite ways — one kind of face that no single direction reaches both of. The rule counts words and the object counts orientations.

viewing · Anamorphreach 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.

AnamorphosisParallel projectionAffine mapcentre of projectionCoverageDesign planeOcclusionStretchAnisotropyArea scaleCountingDisjoint sets

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