Orthographic — where it appears
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.
A scroll is a camera that moves
A Chinese handscroll is not a picture with a wandering viewpoint or a picture with no viewpoint. It is the image of an eye that travels along a track and records one vertical line at a time, and that object has an exact geometry — orthographic along the roll, perspective across it.
What the removed roof buys
The Japanese convention of drawing an interior with its roof lifted off is usually explained as a way of seeing inside. What it actually buys is uniformity — every room reports the same share of its floor, to the last sample, where the eye that frames the same building reports three different numbers.
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.
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.
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.
A carpet and the people on it
A Persian miniature draws the ground as though from above and the figures standing on it as though from in front. The two views want optical axes exactly ninety degrees apart, and the plan view does not shorten a standing figure — it replaces its height with its distance from the point under the eye.
Assembled from several views
An Egyptian relief takes each part of a figure from the direction that identifies it — head in profile, eye and shoulders frontal, a pond in plan. What that buys is exactly measurable: any single viewing direction keeps at most √k of k perpendicular aspects, so the best compromise view retains 58% of each.
Named alongside it
The objects these essays reach for when they reach for this one.
ForeshorteningIsometricPicture planeParallel projectionStation pointAxonometricDemonstrationDrawing systemOblique projectionOcclusionArea scaleDimetric