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

Station — the series

5 essays on one idea, from the one that introduces it to the one that assumes the rest.
  1. 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.

    part 2 · viewing
  2. the piazza, in planthe Baptistery, 25.6 m53 m27.2°the cathedral doorthe panel, and the eye it needsthe Baptistery fills 100%the eye is 60 cm back — off this sheet290 mm panel · 27.2° of Baptisterycorrect from 60 cm · 27° across

    Brunelleschi drilled a hole in his panel

    The first perspective demonstration in the European record came with its viewing point enforced — a hole through the back of the panel, a mirror held out in front, and one place to stand. That distance is computable from the panel's size and the angle the Baptistery subtends, and the answer lands squarely on the arrangement the account describes.

    part 3 · construction
  3. 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.

    part 3 · viewing
  4. 50 mm on full frame · 39.6° acrossphone3.71×94 mm correctlaptop1.28×431 mm correct27-inch monitor0.78×829 mm correcttelevision1.52×1.7 m correctcinema0.84×16.7 m correct×1 — standing at the station pointhow many times further away the reader is than the picture's own station pointworst is the phone at 3.71×

    The screen sets the distance

    Every viewing distance quoted for a picture on a page is conditional on an assumed figure width. Replace the assumption with an actual chain — focal length, sensor width, display width — and the same 50 mm frame is correct from 9 cm on a phone, 83 cm on a monitor and 16.7 m in a cinema. Nobody is standing at any of them.

    part 4 · screen
  5. 0.6× the page48 mm×8.3 at 4000.8× the page64 mm×6.3 at 4001.0× the page80 mm×5.0 at 4001.4× the page112 mm×3.6 at 4002.0× the page160 mm×2.5 at 4003.0× the page240 mm×1.7 at 4004.5× the page360 mm×1.1 at 4007.0× the page560 mm×0.7 at 400distance the picture is correct from, shown 160 mm widea rule about the paperwhich is a rule about the reader

    Both vanishing points on the paper

    Putting the two vanishing points on the sheet is presented as a composition rule. It is a statement about the reader: with the two points one page-width apart the picture is a 90° view, correct from 80 mm, and a reader holding it at arm's length is shown a room five times as deep as the one drawn. The layout that is honest at arm's length puts both points four and a half pages off the sheet.

    part 5 · wrong

All series