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

Surface normal — where it appears

The direction a face points out of a solid, which decides whether a projection can reach its front at all. Two faces sharing a name can have opposite normals and then no single direction reaches both, so a count of the pictures an object supports is a count over normals rather than over names.

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

a flat plate · best view0a bent plate · best view0.1224a dished plate · best view0.2298a bent plate · along its generators0patches wrapping 29°dished / bent = 1.878

No view draws a curved plate true

The auxiliary view is descriptive geometry's answer to a foreshortened plane — turn until the plane is parallel to the paper and it draws at true shape. A bent plate has no such direction and a dished one has none twice over: the best view of the first is out by 1 − cos w and the best of the second by 1 − cos²w, worse by exactly 1 + cos w, because its normals need two parameters rather than one.

parallel · Platepatch 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

Named alongside it

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

AnamorphosisArea scaleAuxiliary viewcentre of projectionCountingCoverageDemonstrationDesign planeDevelopable surfaceDevelopmentDisjoint setsDrawing system

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