feat(camera): centered_window_origin — place a window at the viewport center

The mirror of center_on: that moves the camera to a window, this moves a window to the camera. Per axis, from the projection this module already documents — the viewport shows [pan, pan + extent/zoom), so its virtual midpoint is pan + extent/(2*zoom) and the window starts half its own (virtual, unscaled) length before it.

Consumed by the compositor to open session modals where the user is currently looking: on a panning desktop a remembered position is usually off-view by the time the window reopens, which for the polkit agent means the prompt reads as never having appeared.

Tested at zoom 1, zoomed in and out, under pan, and round-tripped against (virtual - pan) * zoom so the window's screen midpoint lands on the viewport's at any camera; an oversized window overhangs symmetrically rather than clamping, since this centers rather than fits.

Co-Authored-By: Claude <[email protected]>

 src/camera.rs | 47 +++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 47 insertions(+)

diff --git a/src/camera.rs b/src/camera.rs
index 117e977..34aba20 100644
--- a/src/camera.rs
+++ b/src/camera.rs
@@ -77,6 +77,23 @@ pub fn center_on(cx: f64, cy: f64, vw: f64, vh: f64, zoom: f64) -> Camera {
     }
 }
 
+/// Virtual top-left that puts a `win`-long window in the middle of the
+/// viewport, on one axis. The mirror of [`center_on`]: that moves the camera
+/// to a window, this moves a window to the camera.
+///
+/// The viewport shows `[pan, pan + extent/zoom)`, so its virtual midpoint is
+/// `pan + extent/(2*zoom)` and the window starts half its own length before
+/// it. `extent` is the output's length in px; `win` is virtual (unscaled),
+/// because a window's stored geometry is virtual and zoom is applied when it
+/// is drawn.
+///
+/// Session modals place with this so they open where the user is currently
+/// looking rather than wherever they last sat — on a panning desktop a
+/// remembered position is usually off-view by the time the window reopens.
+pub fn centered_window_origin(pan: f64, extent: f64, zoom: f64, win: f64) -> f64 {
+    pan + (extent / zoom - win) / 2.0
+}
+
 /// Anchor-stable zoom-pan interpolation between two cameras at progress
 /// `p` ∈ [0, 1]: zoom log-lerps, and pan is DERIVED from the unique world
 /// point that maps to the same screen position under both cameras — so the
@@ -247,6 +264,36 @@ mod tests {
         assert_eq!(keyed_zoom(3.7, 0.0), 1.0);
     }
 
+    #[test]
+    fn centered_window_origin_puts_the_window_mid_viewport() {
+        // Zoom 1: a 640-wide window in a 1920 viewport starts 640 in, and
+        // the whole thing shifts with the pan.
+        assert_eq!(centered_window_origin(0.0, VW, 1.0, 640.0), 640.0);
+        assert_eq!(centered_window_origin(5000.0, VW, 1.0, 640.0), 5640.0);
+        // Vertical axis is the same call.
+        assert_eq!(centered_window_origin(0.0, VH, 1.0, 400.0), 340.0);
+
+        // Zoomed out to 0.5 the viewport covers 3840 virtual px, so the same
+        // window centers further from the pan origin — the point of dividing
+        // the extent by zoom rather than scaling the window.
+        assert_eq!(centered_window_origin(0.0, VW, 0.5, 640.0), 1600.0);
+        // Zoomed in 2x it covers only 960, so the window sits nearer.
+        assert_eq!(centered_window_origin(0.0, VW, 2.0, 640.0), 160.0);
+
+        // Round-trip against the projection the module documents:
+        // screen = (virtual - pan) * zoom. The window's screen midpoint must
+        // land on the viewport's screen midpoint at any camera.
+        for &(pan, zoom, win) in &[(0.0, 1.0, 640.0), (1234.5, 0.75, 500.0), (-800.0, 1.6, 900.0)] {
+            let v = centered_window_origin(pan, VW, zoom, win);
+            let screen_mid = (v - pan) * zoom + (win * zoom) / 2.0;
+            assert!((screen_mid - VW / 2.0).abs() < 1e-9, "pan={pan} zoom={zoom}");
+        }
+
+        // A window wider than the viewport overhangs symmetrically (negative
+        // origin) rather than being clamped — centering, not fitting.
+        assert_eq!(centered_window_origin(0.0, VW, 1.0, 2920.0), -500.0);
+    }
+
     #[test]
     fn pinch_zoom_maps_off_the_begin_zoom_and_clamps() {
         // Absolute-scale semantics: spreading to 2x from zoom 1.5 lands on