Concept

Oblique projection — where it appears

3 essays name this object, across 2 fields. What follows is each of them, and the objects they name alongside it.
elevationx 1.000y 1.000z 0.000cavalierx 1.000y 1.000z 1.000cabinetx 1.000y 1.000z 0.500isometricx 0.816y 0.816z 0.816dimetricx 0.943y 0.943z 0.471axis scales measured from the drawingall 5 preserve midpoints

Parallel projection is not primitive perspective

Isometric and oblique drawing are not what people used before they worked perspective out. They are a different answer to a different question, and the difference is one measurable quantity — a parallel projection preserves the ratio in which a point divides a segment, and a perspective projection destroys it by 7% of the segment's drawn length at a comfortable depth, rising to 13% over the range the slider covers.

parallel · parallel
eye, 74° offgrey: the word before the projectionblack: the same word, projected

Anamorphosis is only a viewpoint

A smear on a wall that resolves into a skull when the viewer stands in one particular place off to the side. It is not a trick added to perspective — it is perspective, with the centre of projection put somewhere nobody would naturally stand, and it is the clearest demonstration there is that every picture has such a point.

viewing · anamorph
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.

AxonometricIsometricOrthographicAffine mapAnamorphosisCatoptricDimetricForeshorteningHomographyMidpointParallel projectionPicture plane

All concepts