fix(humanize): preserve gaussian magnitude in jitter_point; unify swipe return shape

tests/test_humanize.py

@@ -27,6 +27,28 @@ def test_jitter_point_centered_on_input():
     assert abs(sum(xs) / len(xs)) < 0.3
 
 
+def test_jitter_point_concentrated_near_target():
+    """Regression: jitter must be polar-Gaussian (concentrated near target),
+    not uniform-on-circle (all points at exactly ``radius``).
+
+    For a folded Gaussian with sigma=radius/2, the expected mean distance is
+    ~0.8*sigma ~= 0.4*radius. Using ``< 0.7*radius`` gives a safe margin that
+    fails the previous reprojection bug (mean distance == radius exactly).
+    """
+    rng = random.Random(1234)
+    radius = 5.0
+    n = 5000
+    distances = [
+        math.hypot(x - 0.0, y - 0.0)
+        for x, y in (jitter_point(0.0, 0.0, radius=radius, rng=rng) for _ in range(n))
+    ]
+    mean_distance = sum(distances) / n
+    assert mean_distance < radius * 0.7, (
+        f"mean distance {mean_distance:.3f} is too large; jitter looks like "
+        "uniform-on-circle rather than polar-Gaussian"
+    )
+
+
 def test_jitter_duration_within_spread():
     rng = random.Random(3)
     for _ in range(200):

tools/humanize.py

@@ -90,23 +90,31 @@ def set_rng(rng: random.Random | None) -> None:
 def jitter_point(
     x: float, y: float, *, radius: float, rng: random.Random
 ) -> tuple[float, float]:
-    """Gaussian offset clamped to a ``radius``-px circle around the target."""
+    """Polar-Gaussian offset around the target.
+
+    Magnitude is drawn from a folded Gaussian with sigma=radius/2, then
+    capped at ``radius``. The angle is uniform on [0, 2*pi). This concentrates
+    jittered points near the target rather than uniformly on the circle edge,
+    matching how humans tap close to (but not exactly on) a button center.
+    """
     r = abs(rng.gauss(0.0, radius / 2.0))
     r = min(r, radius)
     angle = rng.uniform(0, 2 * math.pi)
     dx = r * math.cos(angle)
     dy = r * math.sin(angle)
-    # Reproject to exact radius to absorb FP drift in cos/sin
+    # Guard against cos/sin FP drift pushing distance slightly past radius.
-    d = math.sqrt(dx * dx + dy * dy)
+    fd = math.hypot(dx, dy)
-    if d > 0:
+    if fd > radius:
-        dx = dx / d * radius
+        scale = radius / fd
-        dy = dy / d * radius
+        dx *= scale
+        dy *= scale
+    # Final clamp: hypot of the returned offset may overshoot by ulps; tighten
+    # to ``radius - 1e-10`` to keep ``<= radius`` after subtraction/hypot.
     fx = x + dx
     fy = y + dy
-    fd = math.hypot(fx - x, fy - y)
+    fd_final = math.hypot(fx - x, fy - y)
-    if fd > radius:
+    if fd_final > radius:
-        # Scale to a slightly tighter radius to absorb FP rounding in addition
+        scale = (radius - 1e-10) / fd_final
-        scale = (radius - 1e-10) / fd
         fx = x + dx * scale
         fy = y + dy * scale
     return (fx, fy)

tools/swipe.py

@@ -35,6 +35,8 @@ def swipe(
         return {
             "ok": True,
             "action": "swipe",
+            "start": {"x": start_x, "y": start_y},
+            "end": {"x": end_x, "y": end_y},
             "waypoints": waypoints,
             "duration_ms": dms,
         }