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

Station point — where it appears

6 essays name this object, across 4 fields. What follows is each of them, and the objects they name alongside it.
the picture, 160 mm wide22 cm40°the eyefocal length 948 px22 cm at 160 mm wide

The point you have to stand at

A perspective picture is a projection through a centre, and scaling that centre's distance to the width the picture is actually shown at gives a distance in centimetres. Shown 160 mm wide, a 40° picture is correct from 22 cm and a 90° one from 8 cm. Nobody stands there, and that single fact explains most of what gets called distortion.

viewing · station 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

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.

wrong · cubebyeye 246VPcorrect from 26 cm, at 160 mm wide34° across

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.

construction · measuring 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.

parallel · limit drawn: 1.309 : 1subtended at the station point: 1.000000000 : 1the faint circle is the mean radius, for comparisonthe drawn centre sits 3.42 px from the axis's own mark

The sixty-degree cone of vision

Every book says keep the subject inside a 60° cone. Measured, the marginal stretch the rule is nominally about is exactly zero from the station point — 1.000000000000 to 1, over 720 sampled points. The rule is a statement about the reader, and books do not obey it.

wrong · cone the picture — identical at every viewing distanceplan: the true cube, and the solid depicteddepth × 2.12, width × 1.00correct from 18.8 cm at 160 mm wideread from 40 cm — depth × 2.12

Standing in the wrong place

A picture read from twice the distance it is correct from depicts a scene twice as deep — and not one mark on the paper moves. The error is invisible in the picture, which is why it survives everywhere.

viewing · station

Named alongside it

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

Viewing distanceFocal lengthVanishing pointPicture planefield of viewMeasuring pointBack projectioncentre of projectionCentric pointcone of visioncostruzione legittimaDepicted rectangle

All concepts