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 3 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 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.

DemonstrationDrawing systemOrthographicAffine mapcentre of projectionConformalConicCross ratio testDevelopable surfaceDevelopmentFree parameterGaussian curvature

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