Carry first-person facing into orbit camera on mode switch

When leaving first person for an orbit mode (Paint / Player Control), snap
the orbit axes to Camera.main's current view direction instead of restoring
the orbit's last-used angle. With WorldSpace binding + Sphere orbit + a
centered composer the camera look rotation is exactly
Euler(VerticalAxis, HorizontalAxis, 0), so the inverse mapping is exact.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

Assets/Scripts/FirstPersonMode.cs

@@ -36,6 +36,12 @@ public class FirstPersonMode : GameMode
             Manager.FirstPerson.SetActive(false);
 
         if (Manager.CameraInput)
+        {
             Manager.CameraInput.enabled = true;
+            // Carry the first-person facing into the orbit camera so the next orbit mode (Paint / Player
+            // Control) keeps the current view angle instead of snapping back to the orbit's last-used angle.
+            // Camera.main still shows the first-person view this frame (the brain hasn't blended yet).
+            Manager.CameraInput.SyncToView();
+        }
     }
 }

Assets/Scripts/ThirdPersonOrbitInput.cs

@@ -123,6 +123,27 @@ public class ThirdPersonOrbitInput : MonoBehaviour
         _zoomInit = true;
     }
 
+    /// <summary>Snaps the orbit axes so the camera faces along Camera.main's current view direction, so the
+    /// next orbit mode keeps that facing instead of restoring the orbit's last-used angle. Called when
+    /// switching out of a non-orbit rig (first person): Camera.main still shows that rig's view this frame
+    /// (the brain hasn't blended yet), so the read is exact. With WorldSpace binding + Sphere orbit + a
+    /// centered composer the camera look rotation is exactly Euler(VerticalAxis, HorizontalAxis, 0), so
+    /// HorizontalAxis = world yaw and VerticalAxis = world pitch (positive = looking down). No-op without a
+    /// live camera/orbit.</summary>
+    public void SyncToView()
+    {
+        if (!_orbit) return;
+        var cam = Camera.main;
+        if (!cam) return;
+
+        Vector3 e = cam.transform.rotation.eulerAngles;
+        SetAxisValue(ref _orbit.HorizontalAxis, e.y > 180f ? e.y - 360f : e.y);
+        SetAxisValue(ref _orbit.VerticalAxis, e.x > 180f ? e.x - 360f : e.x);
+
+        // Drop any eased look carry-over so the snapped angle isn't immediately dragged back.
+        _smoothedLook = Vector2.zero;
+    }
+
     void Update()
     {
         if (!_orbit)
@@ -210,8 +231,11 @@ public class ThirdPersonOrbitInput : MonoBehaviour
 
     /// <summary>Adds to an input axis; wrapping axes wrap, others clamp to their range.</summary>
     static void ApplyAxisDelta(ref InputAxis axis, float amount)
+        => SetAxisValue(ref axis, axis.Value + amount);
+
+    /// <summary>Sets an input axis to an absolute value; wrapping axes wrap, others clamp to their range.</summary>
+    static void SetAxisValue(ref InputAxis axis, float value)
     {
-        float value = axis.Value + amount;
         float min = axis.Range.x;
         float max = axis.Range.y;