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

Axis scale — where it appears

How much a parallel drawing shortens one of the object's three axes, which is the cosine of that axis's angle to the picture plane. The three are not free — the sum of their squares is two — so any two of them fix the drawing, and a ruler laid along one of them reads a true length divided by its own scale.

Named by 6 essays across 2 fields — each of them below, with the objects they name alongside it.

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 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 a centretrue measurediminutionbounded depthstraight linesperspectivehandscrollisometricdimetrictrimetriccavaliercabinetelevationmilitarycrossed-slitsfilled means the system keeps it10 rowsthe last is filled in neither of the first two

The tenth row has neither

A crossed-slits camera divides by depth in both page directions and its rays miss any common point by 0.354 m. Put on the comparison table it prices 38.8% on length, 69.9% on area and 58.2% on angle against a pinhole's 39.5%, 70.8% and 60.9%, and its midpoint drift is 15.6% — the pinhole's own figure. It keeps a true scale in no direction at all, and it bows a straight run of ground by 1.11 px, which no row with a centre does. Giving up the point buys nothing and costs a third thing besides.

choices · Exclusion 78.510.51421421051050∞78.510.51421421051050∞where the horizontal slit sits (m)where the vertical slit sits (m)8 with a centre, 17 with a measurenone with both

The exclusion is two conditions, not ten rows

Ten systems have been measured and none has both a centre and a true measure. Ten is not a proof. Swept across the whole two-slit family — eighty-one members, both parameters run out to infinity — a centre appears at exactly the eight members whose slits sit at one finite distance, a measure at exactly the seventeen with a slit at infinity, and at none of them both. The case the two conditions appear to leave open is closed by the rays themselves: one divide is a slit, and eight page points use 6.02 m of it.

choices · Exclusion orthographicaspect 1.0000cavalieraspect 1.4142a camera, 37° off axisaspect 1.2593correct from 7 cm, at 160 mm widecentres 4e-14 / 3e-13 / 2.17 px

The ball a drawing does not draw round

An orthographic drawing of a sphere is a circle wherever the sphere is, and its centre is the image of the sphere's centre, exactly. A cavalier oblique drawing of the same sphere is an ellipse of aspect exactly √2 — and the drawing office reaches for a circle template. One formula covers both and the camera as well, and only the camera moves the centre.

parallel · Parallelquadric 00.2500.5000.7501-1-0.50000.5001across the plate, from one edge to the otherdrawn length of a unit of surfacealong the generatorsround the benda plate bent through 57°one ruler in one direction

The drawing and the development

A bent plate gets two flat pictures on the same sheet and each is exact in what the other loses. The parallel drawing keeps the generators at one scale and stretches the arc over a factor; the development keeps every length on the surface and keeps nothing of the shape in space. Neither is the plate and the pair of them is.

parallel · Platepatch

Named alongside it

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

Drawing systemDemonstrationcentre of projectioninstrument limitParallel projectionDepth compressionnecessary, not sufficientOblique projectionOrthographicOrthographic limitPushbroomAffine map

All concepts