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

Aspective — where it appears

A way of drawing an object from the views that identify each of its parts best, joined at the seams rather than projected from one station. Egyptian figures are the standard case — shoulders from the front, head in profile — and no single camera produces the result.

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

head0.668profile — the outline that names a faceeye0.669frontal — an eye in profile is a wedgeshoulders0.669frontal — the width that says two armslegs0.668profile — a stride is a side viewpond0.326plan — a rectangle of water is a rectangle1.000 — what its own aspect keepsshare of each part that reaches the picture, from the best single direction|d · n| for each part3.000 of 5, swept and in closed form

Assembled from several views

An Egyptian relief takes each part of a figure from the direction that identifies it — head in profile, eye and shoulders frontal, a pond in plan. What that buys is exactly measurable: any single viewing direction keeps at most √k of k perpendicular aspects, so the best compromise view retains 58% of each.

conventions · Aspective the plan, with its four walls rotated outward about their base linesthe planwalls rotated about their own base lines16 assemblies

The pond with its trees laid flat

An Egyptian garden pond is drawn in plan with its trees rotated outward about the bank they stand on. A rotation is an isometry, so every length in that drawing is exactly the length it is in the garden — zero error, not a small one. What is spent is the angle between any two faces, which reads 180° across every hinge and is 90° in the garden, and the four walls admit sixteen assemblies, so a reader supplies four bits to fold it back up.

conventions · Aspective a single angle, 60°, for every partfits to 6.7e-13 px

No solid casts an aspective figure

Fitting the best single rigid view to an aspective figure — head and legs in profile, eye and shoulders turned square — misses its own marks by 2.6% of the drawn height, and no yaw does better than 3.0% in a full sweep. A genuine single-view drawing of the same body fits to 7.6e-13 pixels, and the five rotations recovered from the marks alone match the convention's own list to 0.0e+0°.

conventions · Aspective

Named alongside it

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

IdentifiabilityOrthographicdegrees of freedomDemonstrationIsometryArea scaleCanon of proportionDevelopable surfaceDevelopmentDihedral angleDrawing conventionDrawing system

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