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

The other systems

Isometric, oblique, elevation. Not perspective done badly by people who had not worked it out yet, but a different answer to a different question — and the difference is measurable.
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 five 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 up to a quarter of the segment's length.

 elevation0.0000two equalcabinet0.5000two equalcavalier1.0000all three equaldimetric0.4714all three differentisometric0.8165all three equaltrimetric0.5479all three differentsmallest 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.

 isometric — the limit2.5 m6 m20 m200 msame box, same drawn sizethe eye recedes

The eye taken to infinity

A parallel projection is a photograph from infinitely far away with the lens lengthened to match. That is not an analogy — it is the limit, it can be watched happening, and it explains why a long lens flattens a scene and why an isometric drawing has no viewing distance to state.

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