Concept

Foreshortening — where it appears

3 essays name this object, across 2 fields. What follows is each of them, and the objects they name alongside it.
elevation0.0000two equal, orthographiccabinet0.5000two equal, obliquecavalier1.0000all three equal, obliquedimetric0.4714all three different, orthographicisometric0.8165all three equal, orthographic ←trimetric0.5479all three different, orthographicsmallest of the three axis scalesmeasured from each projection

What isometric actually means

The three axis scales are equal to each other. They are not equal to one. Every unit along every axis is drawn at 0.8165 of its true length, which is √(2/3), and a great deal of confusion about isometric drawing comes from the word promising something it does not deliver.

parallel · isometric
centre of the ellipseimage of the centrecorrect from 22 cm, at 160 mm wideoffset 21.1 px

The circle whose centre moves

The image of a circle is an ellipse, and the image of the circle's centre is not the centre of that ellipse. The gap is 3 or 4% of the ellipse's width in an ordinary view — large enough to see, small enough to be dismissed as a slip by anyone not expecting it, and the reason drawn wheels look wrong.

foundations · conic
2 — every orthographic projectionisometric · axonometric 0.816 · 0.816 · 0.8162.0000dimetric · axonometric 0.943 · 0.943 · 0.4712.0000trimetric · axonometric 0.876 · 0.966 · 0.5482.0000cavalier · oblique 1.000 · 1.000 · 1.0003.0000cabinet · oblique 1.000 · 1.000 · 0.5002.2500elevation · orthographic 1.000 · 1.000 · 0.0002.0000isometric's three equal scales are forced to √(2/3) = 0.816497not chosen — the identity leaves no other value

Which axis scales are possible

An orthographic projection's three foreshortening ratios always satisfy one identity — their squares sum to two. Isometric's famous 0.8165 is forced by it rather than chosen, and cavalier's 1, 1, 1 sums to three, which is the arithmetic saying cavalier is not the projection of anything.

parallel · axonometric

Named alongside it

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

AxonometricDimetricIsometricOrthographicPicture planeTrimetricConicEllipse fitHorizonline at infinityMidpointMinor axis

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