It only holds when the physical space is large enough

What it is

However gentle the curvature, it still needs enough radius to hide the discrepancy below detection threshold; a two-metre corridor cannot host that arc. Space requirement is the enabling condition for redirected walking: the physical empty patch must be large enough for sub-threshold gain to have somewhere to bend. Otherwise the algorithm can only supra-threshold twist or reset often, and the promise to expand range collapses.

This is not the psychophysics of whether a discrepancy is noticed. It is whether that arc fits in the room.

Why it happens

Sub-threshold curvature corresponds to a minimum turning radius. That radius has to land inside the play area so the physical trajectory can bend back before a wall. If the short side of the empty patch is below roughly twice that radius, a virtual straight hits the edge before the arc has finished turning. Rotation gain can save a little area when people turn themselves, but a straight corridor is mostly curvature, and with no space there is no turn to exploit.

Furniture fragments the empty patch, so usable radius is the largest inscribed empty circle, not the room’s outer walls. A nominal hall with a table in the middle may leave only the aisle from table to wall; redirection in that aisle will reset constantly. That is why lab demos and living-room deployments are not the same grade of technique: the demo chose a floor that can draw a sub-threshold arc.

Studying it

Make the short side of the empty patch the independent variable: one sub-threshold gain, the same virtual path, in successively smaller squares. Count resets, pad hits, and reported noticing. When resets densify, the patch is already below that gain’s geometric need. The inverse is also usable: fix the patch, find the longest virtual path that still keeps resets rare.

Measure walkable empty space, not the room’s nominal span. Draw tables and chairs on the plan, then take the largest empty circle or empty square. A condition labelled “four-metre room” that is actually tested in a cleared hall will fake external validity.

Where it stops holding

Translation gain can stretch virtual distance in a short patch, but it stretches step scale; it does not supply the radius a turn needs, and too much translation gain goes supra-threshold on its own. A hybrid of in-place turning plus teleport does not depend on this empty patch and cannot be used to claim redirected walking works in small spaces. When outside-in tracking covers less than the physical empty area, the constraint is tracking, not walls. If people hug the edge and the safety grid is drawn tight, usable radius loses another ring. Children have shorter strides, so the same radius is relatively more generous; adult data may overestimate the space children need — or underestimate it, if the predictor assumes adult speed.

Applying it

• Measure the target venue’s largest empty square before deciding that walking can be the main locomotion. If the short side cannot host a sub-threshold arc, do not sell redirection as a feature.
• When the patch is too small, switch to teleport or stick rather than raising gain to “force the bend.”
• In setup, refuse to enable redirection on an undersized play area, and state the area that must be cleared. Do not silently degrade into constant resets.
• How to check: on the claimed minimum patch, walk a virtual straight longer than that patch, at sub-threshold gain, with no reset and no pad hit. Fail any of the three and the minimum is written too small, or the technique should not be enabled at that area.

Related

• Same group: N4.05.1 Tiny rotational discrepancies expand the walkable range · N4.05.2 A discrepancy above threshold is noticed
• Nearby: N4.04 Room Scale and Safety Boundaries · N4.09 Wayfinding and Landmarks in Space
• Search terms: redirected walking space requirement · curvature radius · tracking area