Add binaural triangulation + smooth gaze tracking

spatial.py: Triangulates sound source position from two DoA angles using
ray intersection. Exponential smoothing prevents jitter. Gaze drifts back
to center after 2s of silence. Converts position (mm) to gaze (0-255).

headmic.py: Replaces simple doa_poll_loop with doa_track_loop that runs
the spatial tracker and pushes gaze to the eye service when the position
changes. Rate-limited to 10 pushes/sec with minimum delta threshold.

/doa endpoint now returns triangulated position + gaze coordinates.
Array separation (175mm) stored in config, overridable.

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

headmic.py

@@ -159,6 +159,7 @@ class ServiceState:
         self.enrolling: bool = False
         self.active_side: str = "left"    # which mic array is currently active
         self.doa: dict = {}               # latest DoA from both arrays
+        self.spatial: Optional[dict] = None  # triangulated position + gaze
 
 state = ServiceState()
 
@@ -390,34 +391,58 @@ def sound_classifier_loop():
 
 
 # ============================================================================
-# DoA Polling Thread
+# Spatial Tracking + Gaze (DoA → triangulation → eye service)
 # ============================================================================
 
-def doa_poll_loop():
-    """Poll Direction of Arrival from both XVF3800 arrays."""
+from spatial import SpatialTracker
+
+spatial_tracker: Optional[SpatialTracker] = None
+_last_gaze_push: tuple[int, int] = (GAZE_CENTER, GAZE_CENTER)
+GAZE_CENTER = 127
+GAZE_PUSH_MIN_DELTA = 3    # don't push gaze unless it moved by at least this much
+GAZE_PUSH_INTERVAL = 0.1   # max 10 gaze pushes/sec to eye service
+
+
+def doa_track_loop():
+    """Poll DoA, triangulate, smooth, push gaze to eye service."""
+    global _last_gaze_push
     interval = 1.0 / DOA_POLL_HZ
+    last_push_time = 0.0
+
     while state.running:
         try:
             state.doa = xvf_manager.read_both_doa()
+
+            if spatial_tracker:
+                result = spatial_tracker.update(state.doa)
+                if result:
+                    state.spatial = result
+                    gx, gy = result["gaze_x"], result["gaze_y"]
+
+                    # Push to eye service if changed enough and not too frequent
+                    dx = abs(gx - _last_gaze_push[0])
+                    dy = abs(gy - _last_gaze_push[1])
+                    now = time.monotonic()
+
+                    if ((dx >= GAZE_PUSH_MIN_DELTA or dy >= GAZE_PUSH_MIN_DELTA)
+                            and now - last_push_time >= GAZE_PUSH_INTERVAL):
+                        _push_gaze(gx, gy)
+                        _last_gaze_push = (gx, gy)
+                        last_push_time = now
         except Exception as e:
-            logger.debug("DoA poll error: %s", e)
+            logger.debug("DoA/spatial error: %s", e)
+
         time.sleep(interval)
 
 
-def doa_to_gaze() -> Optional[tuple[int, int]]:
-    """Convert the active side's DoA angle to gaze coordinates for the eye service."""
-    doa = state.doa
-    side = state.active_side
-    if not doa or side not in doa or doa[side] is None:
-        return None
-    if not doa[side].get("vad"):
-        return None
-    import math
-    angle = doa[side]["angle"]
-    rad = math.radians(angle)
-    x = int(127 - 80 * math.sin(rad))
-    y = int(127 - 40 * math.cos(rad))
-    return max(0, min(255, x)), max(0, min(255, y))
+def _push_gaze(x: int, y: int):
+    """Fire-and-forget gaze push to eye service."""
+    try:
+        import httpx
+        httpx.post(f"{EYE_SERVICE_URL}/gaze",
+                   json={"x": x, "y": y}, timeout=0.5)
+    except Exception:
+        pass  # eye service may be down, don't spam logs
 
 
 # ============================================================================
@@ -497,10 +522,13 @@ async def startup():
     except Exception as e:
         logger.warning("Speaker recognition unavailable: %s", e)
 
-    # --- DoA polling ---
+    # --- Spatial tracking (DoA → triangulation → gaze) ---
     if xvf_manager.left or xvf_manager.right:
-        threading.Thread(target=doa_poll_loop, daemon=True).start()
-        logger.info("DoA polling started at %d Hz", DOA_POLL_HZ)
+        array_sep = cfg.get("array_separation_mm", 175.0)
+        spatial_tracker = SpatialTracker(array_separation_mm=array_sep)
+        threading.Thread(target=doa_track_loop, daemon=True).start()
+        logger.info("Spatial tracking started (%d Hz, %.0fmm baseline, pushing gaze to %s)",
+                     DOA_POLL_HZ, array_sep, EYE_SERVICE_URL)
 
     # --- Main listener ---
     thread = threading.Thread(target=listener_loop, daemon=True)
@@ -570,11 +598,11 @@ async def last():
 
 @app.get("/doa")
 async def doa():
-    """Direction of Arrival from both mic arrays."""
+    """Direction of Arrival from both mic arrays + triangulated position."""
     return {
         "doa": state.doa,
         "active_side": state.active_side,
-        "gaze": doa_to_gaze(),
+        "spatial": state.spatial,
     }