Visual Plane
every picture states the point it is correct from
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The thread: Taught, and never measured

The standard constructions are drawn here exactly as they are taught, and then asked what solid or what spacing they depict. Some answers are fine. The point is that the method itself supplies no way to find out, so nobody drawing knows which case they are in.
horizon3 vanishing points at a finite distance2564 px · 8129 px · 531 px Constructing a view

One, two and three point are one construction

The names count how many vanishing points sit at a finite place in the picture, and the count is a fact about how the object is turned and the camera is aimed. Nothing about the method changes between them, and a vanishing point does not appear — it arrives from infinity.

 horizoncorner angles90.000° — forced by the methoddepicted side ratio0.7195lens this drawing implies60° acrossdrawn exactly as the method prescribesthe free step is where the far edges go Drawn confidently

The cube that is a box

The two-point cube every book teaches has a step it supplies no construction for. Place the two far edges symmetrically and the drawing depicts a cube for free; place them eight points apart — a difference invisible on the page — and it depicts a box 1.4 times shallower than it is wide.

 24VPcorrect from 26 cm, at 160 mm wide34° across Constructing a view

The measuring point, and the step the method leaves out

Laying out equal depths correctly needs a second vanishing point that most treatments never introduce — the one belonging to the diagonals. With it the construction lands on the projected divisions to eighty femtopixels. Without it, depth is placed by judgement and the drawing depicts something nobody chose.

 54 px69 px84° across27% wider at the edge Where to stand

Wide angle is not distortion

A wide lens stretches shapes at the edge of the frame by exactly 1/cos θ — 3% at 28° across, 41% at 90°. Every bit of that is what a correct rectilinear projection must do, and every bit of it disappears if the picture is viewed from the point it was made for. Nobody views it from there.

 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 The other systems

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.

 horizonshadows meet at x = -58, off the frameon the horizon, as it must be Light and mirrors

Where shadows vanish

The shadows of parallel posts under the sun meet at a point, and that point must lie on the horizon. Under a lamp they meet at the lamp's foot instead. Both are checkable in any photograph, and a picture whose shadows fail the check was not lit by anything.

 horizonequal stepshalve thetaper byworst error, in metres of depthequal steps to the horizon11.72 mhalve the remaining gap225.13 mtaper by eye347.80 mcorrect from 26 cm, at 160 mm wide34° across Drawn confidently

Dividing depth by eye

Three methods for spacing a receding row, all of them taught, all of them wrong. Read back as distances, the best misplaces a post by 3.5 metres in a row that is supposed to be spaced 1.4. And the obvious way of checking them gives one of the three a perfect score.

 horizon = eye level, 1.62 m91.01%correct from 26 cm, at 160 mm widespread 0 Constructing a view

The horizon is at eye level — if the picture plane is vertical

The horizon cuts every standing figure at the same fraction of its height however far away it is, which is the most immediately usable fact in the subject. It holds when the camera is level, and a twelve-degree tilt is enough to spread the fractions by more than a percentage point.

 centre of the ellipseimage of the centrecorrect from 22 cm, at 160 mm wideoffset 21.1 px What survives

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.

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