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

The second projection

A picture that has been made still has to be shown, and the display is a projection with a correct point of its own. Here the assumed figure width every earlier essay quoted is replaced by an actual chain — sensor, focal length, screen — and the answer is that almost nobody is standing where the picture says to.
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 this site has quoted was 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.

 051050100150field of view the picture was rendered at — degreeshow many times the depicted depth is stretchedthe screen subtends 49.3°100° → depth ×2.6027-inch monitor at 650 mmsubtends 49.3°

A wide field on a small screen

A picture rendered at a hundred degrees and shown on a screen that subtends forty-nine is being read from two and a half times its own station distance, so the depicted space is two and a half times too deep. The stretch at the edges everybody complains about is correct; the complaint is really that nobody is sitting where it would be invisible.

 010203040-2502550disparity on the screen — millimetreswhere the point is depicted — metres from the eyesd = 63 mm — the eyes' separationon the glassscreen at 2.0 m · eyes 63 mm apartthe ceiling is the head, and it does not move when the screen does

Two pictures on one screen

A stereoscopic display puts a point where two sightlines cross, so the depicted depth is b·D/(b−d) and the disparity that reaches infinity is exactly the separation of the reader's eyes — 63 mm, at any screen distance whatever. The depth budget is set by the width of a head and by nothing about the scene.

 k₁ = -0.28 · the round trip closes to 8.0e-13 pxpale: what the eye receives · dark: what the renderer drawsthe inner 86% of a 72° frame, where the inverse is exact

The render is distorted on purpose

A headset renders a bent picture so its lens can straighten it, which is the lens field's polynomial run backwards and the one place on this site where distortion is introduced deliberately. The round trip closes to a thousandth of a millionth of a pixel, and the price is that one rendered pixel becomes 0.646 delivered pixels at the edge of the field and one at the centre.

 15° of yaw, 6° of pitch, 1.50 throw ratio81.3% of the panel reaches the corrected rectangleouter: the thrown quadrilateral · inner: what correction can keep18.7% of the panel discarded

A projector is a camera run backwards

Turn a projector fifteen degrees from square and it throws a trapezium; keystone correction cannot add light outside it, so it shrinks the picture until it fits and discards a sixth of the panel. And the instrument itself comes back out of the picture it threw — 2880 panel pixels recovered against 2880, by the function the wrong field wrote for hand-drawn cubes.

All essays