Visual Plane
every picture states the point it is correct from
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The thread: Projected twice

A photograph is a projection onto a sensor and then a projection from a screen into a room, and the second one has a correct point exactly as the first does. Every essay before this quoted its viewing distance against an assumed figure width; here the assumption is replaced by a chain — focal length, sensor width, display width — and the two projections are compared. Almost nobody is standing where the picture says to, and what that does is already measured.
full frame · 39.6°APS-C · 26.6°Micro Four Thirds · 19.6°1 inch · 15.0°phone (1/1.7″) · 8.7°one 50 mm lens · the angle is a property of the rectangle behind itMicro Four Thirds: 2.00× diagonal, 2.08× wide, 1.85× tall50 mm across five formats39.6° down to 8.7° The rectangle behind the lens

A focal length is not an angle

Fifty millimetres means nothing until a rectangle is named behind it. The same lens is 39.6° across full frame, 26.6° across APS-C and 8.7° across a phone sensor — and the distance the resulting print is correct from depends on the ratio of the two, so two cameras matched on angle agree exactly whatever their formats.

 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 second projection

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° The second projection

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 The second projection

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 second projection

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.

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