staging.Frame

How THE EIGHTH KETYL is framed, at any screen shape.

A shot is authored here as a world box it has to hold — so many units tall, so many units wide — and the distance and the lens are solved for the screen as it is right now. Nothing in this module is a pixel and nothing in it is a number picked while looking at one viewport.

The game films at 1080x1440, so the vertical extent usually decides the shot: a wider screen holding the same vertical box simply gains margin at the sides. On a screen TALLER than 3:4 the horizontal extent takes over, and past DISTANCE_CAP the camera opens the lens rather than backing out through the glass wall of the still.

local Frame = require("staging.Frame")

local shot = Frame.play(ketylRadius)     -- dist, fov, orbitLimit, aspect, portrait
local R    = Frame.eyeRadius(r, shot.dist, 0)   -- where the eye stands, from the axis
local p    = Frame.ring(angle, y, 0.85)         -- a point just inside the glass

The gameplay box

PLAY_V	12.0	World units of height the playing shot holds — the plate you are on to the underside of the plate above.
PLAY_H	9.4	World units of width — the room the ketyl is read moving in, not the whole plate.
FOV_BASE / FOV_MAX	58° / 78°	The lens it prefers, and how wide it may open on a very tall screen.
AIM_RISE / EYE_RISE	2.3 / 3.3	The aim point above the plate floor, and the eye above that — a look down of about seventeen degrees.
EYE_MAX_RADIUS	COLUMN_RADIUS - 0.4	The eye never leaves the still.

Solving the orbit

Frame.play(r) returns orbitLimit, the angle the eye may be swung off "directly across the column" before its solved radius would reach the wall:

R(d) = r·cos d + sqrt(dist² − r²·sin² d)          ≤ Rmax
  ⟺  cos d ≤ (Rmax² − dist² + r²) / (2·Rmax·r)

Frame.eyeRadius(r, dist, delta) is that solve, clamped inside the still. The cinematics in staging.Beats place every one of their stations with it, so a beat filmed on a phone and the same beat on a television are the same shot.