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

Orthographic limit — where it appears

What a perspective picture becomes as the eye recedes, with diminution falling to nothing and parallels staying parallel. The departure from it falls as one over the eye's distance, so a picture is a thousand times nearer to parallel at a kilometre than at a metre and never actually parallel.

Named by 6 essays across 4 fields — each of them below, with the objects they name alongside it.

halfway along the drawn linethe actual midpointcorrect from 26 cm, at 160 mm wide7 px apart

The eye taken to infinity

A parallel projection is a photograph from infinitely far away with the lens lengthened to match. That is not an analogy — it is the limit, it can be watched happening, and it explains why a long lens flattens a scene and why an isometric drawing has no viewing distance to state.

parallel · Limit a centretrue measurediminutionbounded depthstraight linesperspectivehandscrollisometricdimetrictrimetriccavaliercabinetelevationmilitaryfilled means the system keeps itmeasured from each system's own projectionno row is filled in both of the first two

Each system answers its own question

A comparison in which every system wins its own column proves nothing if the columns were chosen after the systems. The test that makes it a result is whether any system wins something it was not designed for — and two of them do.

choices · Exclusion the eyenear 0.90 mfar 4.20 mfocal 740 pxprincipal 345, 210

Four numbers and a window

A projection matrix is built from six numbers and one of them is not a number at all. Four sides carry the focal length and the principal point; the near and far planes move nothing a reader can see; and the bottom row, (0, 0, 1, 0), is the only place the depth divides — set it to (0, 0, 0, 1) and the same machine draws a parallel projection.

pipeline · Frustum an edge, read with the best single ruler for the pictureperspective39.5% outhandscroll39.2% outisometric0% outdimetric16.7% outtrimetric15.9% outcavalier0% outcabinet16.7% outelevation33.3% outmilitary0% out400 boxes, square3 of 9 exact

A yes in the table is a price

The comparison table says isometric, cavalier, the elevation and the plan oblique all keep measure. Priced on four hundred boxes, with each picture handed its own best ruler, the four charge 0%, 0%, 33.3% and 0% for an edge — and a pinhole charges 39.5%, only 6.2 points more than the elevation it is filed against. Turn the boxes and three of the four yeses cost something; only the plan oblique's stays free.

choices · Exclusion what was drawnthe solid it depicts — reading 1 of 2xyzlooked at 0.00° off the normalcube edge 1.0000 of the drawn unitresidual 1e-16

The drawing does not say which corner is nearer

The Necker cube is filed under optical illusion, as though the flipping were something the eye does. It is not: a parallel drawing of a cube is a drawing of exactly two cubes, mirror images of each other, and they project to the identical picture to the last bit. Perspective rules the second one out at a rate exactly inverse in the eye's distance, and never entirely.

parallel · Reversal 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.

DemonstrationParallel projectionDrawing systemProjective limitAxis scaledegrees of freedomDepth compressionOrthographicArea scaleAspectiveCamera matrixClip space

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