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

Taught and unmeasured — where it appears

A rule of the drawing office or the studio that is repeated without a number attached, and that turns out to be exactly right about the situation it grew up in.

Named by 3 essays across 2 fields — each of them below, with the objects they name alongside it.

isometric0.57741 : 1.732dimetric0.88191 : 1.134cavalier1.0000a circlemilitary0.57741 : 1.732the xy plane's drawn ellipseratio of the ellipse's axes, sampled

A ruler on an isometric drawing

Isometric drawing has one scale — 0.8165 — and every account of it stops there. But that number is about three directions and a drawing has infinitely many, so a length measured off the paper and divided by 0.8165 comes back anywhere between √(1/2) and √(3/2) of the truth: 29.3% short to 22.5% long, with nothing in the picture to say which.

parallel · ruler 00.50011020304050distance from the camera to the wall (m)relative to the value at 1 mthe patch, growing as d²the light per unit area, falling as 1/d²their product — what the picture records2500× the footprint at the far endproduct flat to 2e-16

A wall does not get darker as it goes away

The inverse square law is about a point source. A surface is not a point source, and the picture of a wall is exactly as bright at twenty metres as at two — the patch one pixel covers grows as the square of the distance and the light per unit area falls as the square of the distance, and a picture records the product. Which is why aerial perspective has to be the air.

light · radiance true ellipse — axis ratio 0.5774four arcs — 5.72% short along the major axisthe four tangent points are exactworst departure 5.72% of the semi-major axis

The ellipse the drawing office draws

Every isometric ellipse template is cut to a construction of four circular arcs, and every account of it calls the result an ellipse. It is not one and cannot be: a circular arc has constant curvature and a conic's varies, so the two can agree at four points and nowhere between. The four-centre curve reaches 2√2/3 of the true semi-major axis — 5.72% short — and its minor axis is 3.53% too long.

parallel · isocircle

Named alongside it

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

ForeshorteningAnisotropyDemonstrationDrawing systemFour centre ellipseIsometricOrthographicConicDepth cueDiminutionfield of viewinstrument limit

All concepts