Use the other eye when the tracker loses one, and add a headset fit check

SteamVR's combined gaze keeps going on one eye, but it holds the lost
eye's yaw, so the gaze moves half as far sideways as the eyes do.
ft-gaze now reads each eye's tracking uncertainty and raw measurement
from eye-server.mmap. When the tracker loses an eye, ft-gazed takes the
gaze from the other one, plus the offset that eye usually shows
against both, learned while both are seen. On a recording, one eye
alone came out a median 0.8 degrees from both eyes' gaze.

Glances down at the keyboard, past every screen, aren't sent. The
pointer stays put, and eyes lost there don't count as lost.

The gaze probe gets a Headset fit mode. It shows per-eye tracking,
openness and confidence, maps where each eye gets lost, gives hints,
and has a guided check. The settings app opens it from the Gaze page
and shows how often each eye is lost. The probe can also test each eye
alone, and its side panel now collapses to a title bar so the dot
isn't hidden behind it.

Snapping to UI elements is deferred; the mouse drag is the correction.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

gaze/gazecal.py

@@ -2,8 +2,8 @@
 
 The correction models (Correction: the calibration fitted from calibration dots;
 LiveCorrection: what clicks teach on the fly, on top of it), the smoothing filters, the
-blink and dropout filter for one look at a spot, and SteamEyeLog, which follows SteamVR's
-eye tracking log. Angles are head-relative degrees (yaw +left, pitch +up), as ft-gaze
+blink and dropout filter for one look at a spot, EyeFallback (the gaze from one eye while
+the tracker has lost the other), and SteamEyeLog, which follows SteamVR's eye tracking log. Angles are head-relative degrees (yaw +left, pitch +up), as ft-gaze
 reports them.
 """
 
@@ -391,6 +391,90 @@ class LiveCorrection:
         return self.cy[0], self.cp[0]
 
 
+# The tracker's variance for an eye's direction (ft-gaze's "unc"): 0.0005-0.002 while it
+# sees the eye, 0.015-0.03 once it's lost it, falling back through 0.008-0.002 in the 0.1 s
+# after it finds it again.
+EYE_LOST = 0.004
+EYE_FOUND = 0.0025
+
+
+class EyeFallback:
+    """The gaze from one eye, while the tracker has lost the other.
+
+    SteamVR's combined gaze (mmap set 1) keeps going with one eye lost, but badly: it holds
+    the lost eye's yaw where it was and gives it the other eye's pitch, so the gaze moves
+    half as far sideways as the eyes do (seen: the right eye swung 5 degrees, the combined
+    gaze 2.5). Set 2's eyes are each eye's own reading. While both are seen, this learns what
+    each eye reads against the combined gaze (an offset: half the angle between the eyes,
+    plus how differently the tracker reads each), in 10 degree cells of where that eye
+    looks, blended over the four nearest; while one is lost, the other eye plus its offset
+    stands in for the combined gaze. So the rest (fixation lock, calibration, lessons)
+    carries on as if nothing happened.
+
+    On a recording, one eye alone came out 1.1 degrees (median) from both eyes' gaze, 0.8
+    over a tenth of a second of a steady look, and a little more jittery (0.31-0.37 degrees
+    against 0.28). Carrying on the offset from just before a loss did no better: what's
+    left is fast noise, not something particular to that look.
+
+    `update` and `get` take head-relative degrees (yaw, pitch)."""
+
+    CELL = 10.0
+    GLOBAL_RATE = 0.01   # per sample: about a second at 90 Hz
+    CELL_RATE = 0.02     # the least a cell learns per sample, once it has CELL_FULL
+    CELL_FULL = 30       # samples before a cell counts fully
+    READY = 45           # samples of both eyes before an eye can stand in
+
+    def __init__(self):
+        self.glob = [None, None]      # per eye: [oy, op]
+        self.seen = [0, 0]
+        self.cells = [{}, {}]         # per eye: (i, j) -> [oy, op, n]
+
+    def ready(self, eye):
+        return self.seen[eye] >= self.READY
+
+    def update(self, eye, ey, ep, cy, cp):
+        oy, op = cy - ey, cp - ep
+        g = self.glob[eye]
+        if g is None:
+            self.glob[eye] = [oy, op]
+        else:
+            g[0] += self.GLOBAL_RATE * (oy - g[0])
+            g[1] += self.GLOBAL_RATE * (op - g[1])
+        self.seen[eye] += 1
+        key = (math.floor(ey / self.CELL), math.floor(ep / self.CELL))
+        c = self.cells[eye].setdefault(key, [oy, op, 0])
+        c[2] += 1
+        a = max(1.0 / c[2], self.CELL_RATE)
+        c[0] += a * (oy - c[0])
+        c[1] += a * (op - c[1])
+
+    def offset(self, eye, ey, ep):
+        g = self.glob[eye]
+        if g is None:
+            return None
+        # Bilinear over the four cells whose centres surround the point.
+        fy, fp = ey / self.CELL - 0.5, ep / self.CELL - 0.5
+        i0, j0 = math.floor(fy), math.floor(fp)
+        ty, tp = fy - i0, fp - j0
+        sy = sp = used = 0.0
+        for di, wi in ((0, 1 - ty), (1, ty)):
+            for dj, wj in ((0, 1 - tp), (1, tp)):
+                c = self.cells[eye].get((i0 + di, j0 + dj))
+                if c:
+                    w = wi * wj * min(1.0, c[2] / self.CELL_FULL)
+                    sy += w * c[0]
+                    sp += w * c[1]
+                    used += w
+        return sy + (1 - used) * g[0], sp + (1 - used) * g[1]
+
+    def get(self, eye, ey, ep):
+        """The combined gaze from this eye's reading, or None before it has learned enough."""
+        if not self.ready(eye):
+            return None
+        oy, op = self.offset(eye, ey, ep)
+        return ey + oy, ep + op
+
+
 class SteamEyeLog:
     """Follows SteamVR's eye tracking log (read only) for what moves the raw gaze under a
     calibration.
@@ -494,7 +578,8 @@ def cross_validate(points, mode):
 
 def steady_samples(samples, vergence_jump=1.5):
     """The samples of one look at one spot where the tracker had both eyes: none in a blink
-    (openness under half its median over the samples), and none where the angle between the eyes' directions (`lr`, the
+    (openness under half its median over the samples), none where it had lost an eye (its
+    variance over EYE_LOST), and none where the angle between the eyes' directions (`lr`, the
     vergence) is more than `vergence_jump` degrees from its median over the samples. The
     vergence itself depends on distance (about 2.8 degrees for a screen 1.3 m away, a
     fraction of one far off), so only a jump away from what it was during this look means
@@ -513,6 +598,7 @@ def steady_samples(samples, vergence_jump=1.5):
 
     def vergence(smp):
         return (smp["src"].get("mmap1") or {}).get("lr", (smp["src"].get("mmap2") or {}).get("lr"))
+    opened = [smp for smp in opened if max((smp["src"].get("mmap1") or {}).get("unc") or [0]) <= EYE_LOST]
     have = [v for v in map(vergence, opened) if v is not None]
     if len(have) < 5:
         return opened