Plato’s Cave — gaze-wall geometry planner

SCENARIO

Physical setup

Tracker reference

Tracker reference describes eye detection limits—not gaze coverage across this wall.

01 Wall & distance

Eye → wall distance (m)

Wall width (m)

Wall height (m)

Columns

Rows

Screen fill · width (fraction of pitch · 0–1)

Screen fill · height (fraction of pitch · 0–1)

For example, 0.90 means 90% of each pitch. Smaller values leave physical gaps; gaps widen screen-edge margins while center pitch stays unchanged.

Preserves the current wall aspect ratio. This is not a maximum supported size.

02 Visitor & camera

Eye movement at the nominal eye plane

Horizontal ± (m)

Vertical ± (m)

Camera center from nominal eye · x / y / z

Lateral x (m)

Vertical y (m)

Depth z (m)

Camera depth stays fixed as wall distance changes. If it would cross the wall, it is clamped just in front and called out.

03 Viewing aperture

Model a centered opening

Eye → opening (m)

Opening width (m)

Opening height (m)

Flat centered planes only: no opening thickness, depth movement, lens occlusion, or off-center wall is modeled.

04 Desktop angular reference

Compare a rated desktop display

Reference aspect ratio

Rated diagonal · source (in)

Reference eye distance (m)

Aspect ratio and diagonal describe the desktop comparison, not the physical wall tiles. Centered-eye angular equivalence only; reference distance is independent of camera depth and is not wall coverage or a maximum-size rating.

05 Assumed gaze envelope

Show a hypothetical / measured envelope

Horizontal half-angle (°)

Vertical half-angle (°)

Illustrative user assumptions—not inferred from camera FOV, display size, or tracker model. No manufacturer-supported maximum uncalibrated wall size is published in these sources.

06 Angular error sensitivity

Show hypothetical error bands

Assumed error per axis (°)

Separable yaw/elevation sensitivity model. Vendor typical, ideal, or calibration-free accuracy is not a worst-case bound and implies no success probability.

GEOMETRY, NOT CERTIFICATION

Three different questions.
One wall to test.

Eye detection distance, gaze directions needed by the wall, and angular tile separation are separate constraints. This offline planner computes geometry only—it cannot tell whether a tracker will select a screen correctly.

PHYSICAL WALL

—

REQUIRED GAZE · HALF ANGLE

—

About nominal forward, including eye motion

SAME-ANGLE DESKTOP REFERENCE

—

Centered-eye equivalence, not coverage

APERTURE / ASSUMED ENVELOPE

—

Optional geometric bound; not tracker coverage

CAMERA → EYE DISTANCE

—

Euclidean range across eye-motion box

WALL FRONT · PHYSICAL PLANE AT z = D

Screen layout & visibility

Click a tile for its geometry

Physical screenDesktop angular referenceAssumed gaze / errorAperture clippingSelected target

SELECTED TILE

—

Center direction—

Nearest physical decision midline—

Entire screen visible—

Visibility means each point lies inside the opening from every eye position in the entered rectangle. Tile-selection decision boundaries are physical screen-cell midlines projected onto the wall, not angular bisectors or a tracker SDK mapping.

PLAN VIEW · TOP

Eye, camera & aperture

Eye movement rectangle, camera position, aperture plane and extreme opening sightlines are drawn separately.

ELEVATION · SIDE

Vertical sightlines

The camera supports eye detection at z_camera; gaze rays continue to wall targets at z_wall.

DISTANCE TRADE-OFF · GEOMETRY ONLY

What changes as the wall moves?

Wall width (m) vs eye → wall distance (m) · geometry only

A farther wall increases physical width for a fixed assumed angle, but fixed physical tiles subtend smaller angles. The aperture and optional envelope are geometric bounds, never vendor-supported wall sizes. Camera depth and desktop reference distance stay fixed.

TRACKER SOURCE & SPECIFICATION

—

Open manufacturer/source page ↗

MODEL BOUNDARIES

What these diagrams omit

Flat centered wall/opening; no depth movement, opening thickness, lenses, occlusion or installation survey.
Head-box dimensions apply only on the aligned 0.65 m reference plane; otherwise not extrapolated.
Angular error bands are separable yaw/elevation at the nominal eye, not a 3D spherical cone or measured distribution.
Aperture “fully visible” tests the whole physical screen from every modeled eye location; classification margins use physical wall-cell midlines projected as rays.
No calibration, gaze SDK, actual visitor data, confidence, latency, bystanders or tracking-loss behavior is modeled.