Concept

Dimetric — where it appears

An axonometric projection in which two of the three axis scales are equal and the third is not. Asking for a ratio fixes everything: 1 : 1 : ½ forces scales of 2√2⁄3 and √2⁄3 and forces both drawn angles, so a dimetric system has no freedom left once its ratio is named.

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

Also named here as trimetric — the same set of essays touches all of them, so they are one junction rather than several.

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
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 · 0.0002.0000military · planometric 1.000 · 1.000 · 1.0003.0000isometric'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 ORTHOGRAPHIC projection of anything. A later rung shows what the departure is a measurement of.

parallel · Axonometric
isometricdimetrictrimetricelevationx scalez scalea curve, not a squarethe third scale is not free

The dimetric the set square draws

An orthographic direction has two parameters and produces three axis scales, so the achievable triples are a surface rather than a list. The drawing office's dimetric — one axis at 1 in 8, the other at 7 in 8 — has the right three scales exactly and the wrong two angles, and the picture it makes is an oblique projection of a cube rather than an orthographic one.

parallel · Axonometric

Named alongside it

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

AxonometricForeshorteningIsometricTrimetricOrthographicConditioningdegrees of freedomDrawing systemOblique projectionOrthographic projectionPicture planeStraightedge construction

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