Fix: Window position creeps between executions on scaled monitors (#4443)

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* Closes <https://github.com/emilk/egui/issues/4442>
* Refactors active monitor detection so it can be called from multiple
locations.

Compare this gif to the one on the issue report.

![egui_window_position_no_creep](https://github.com/emilk/egui/assets/45777186/8e05d4fb-266e-48b9-9223-b65f16500a99)

### Investigation notes

- [`WindowSettings.inner_position_pixels` and
`WindowSettings.outer_position_pixels`](https://github.com/emilk/egui/blob/master/crates/egui-winit/src/window_settings.rs#L8-L12)
are stored in physical/pixel coordinates.
- `ViewportBuilder::with_position` expects to be passed a position in
_logical_ coordinates.
- Prior to this PR, the position was being passed from `WindowSettings`
to `with_position` [without any
scaling](https://github.com/emilk/egui/blob/master/crates/egui-winit/src/window_settings.rs#L61-L68).
This was the root cause of the issue.
- The fix is to first convert the position to logical coordinates,
respecting the scaling factor of the active monitor. This requires us to
first determine the active monitor, so I factored out some of the logic
in
[`clamp_pos_to_monitor`](https://github.com/emilk/egui/blob/master/crates/egui-winit/src/window_settings.rs#L130)
to find the active monitor.

crates/eframe/src/native/epi_integration.rs

@@ -38,7 +38,11 @@ pub fn viewport_builder<E>(
         }
         window_settings.clamp_position_to_monitors(egui_zoom_factor, event_loop);
 
-        viewport_builder = window_settings.initialize_viewport_builder(viewport_builder);
+        viewport_builder = window_settings.initialize_viewport_builder(
+            egui_zoom_factor,
+            event_loop,
+            viewport_builder,
+        );
         window_settings.inner_size_points()
     } else {
         if let Some(pos) = viewport_builder.position {

crates/egui-winit/src/window_settings.rs

@@ -50,8 +50,10 @@ impl WindowSettings {
         self.inner_size_points
     }
 
-    pub fn initialize_viewport_builder(
+    pub fn initialize_viewport_builder<E>(
         &self,
+        egui_zoom_factor: f32,
+        event_loop: &winit::event_loop::EventLoopWindowTarget<E>,
         mut viewport_builder: ViewportBuilder,
     ) -> ViewportBuilder {
         crate::profile_function!();
@@ -64,7 +66,15 @@ impl WindowSettings {
             self.outer_position_pixels
         };
         if let Some(pos) = pos_px {
-            viewport_builder = viewport_builder.with_position(pos);
+            let monitor_scale_factor = if let Some(inner_size_points) = self.inner_size_points {
+                find_active_monitor(egui_zoom_factor, event_loop, inner_size_points, &pos)
+                    .map_or(1.0, |monitor| monitor.scale_factor() as f32)
+            } else {
+                1.0
+            };
+
+            let scaled_pos = pos / (egui_zoom_factor * monitor_scale_factor);
+            viewport_builder = viewport_builder.with_position(scaled_pos);
         }
 
         if let Some(inner_size_points) = self.inner_size_points {
@@ -127,12 +137,12 @@ impl WindowSettings {
     }
 }
 
-fn clamp_pos_to_monitors<E>(
+fn find_active_monitor<E>(
     egui_zoom_factor: f32,
     event_loop: &winit::event_loop::EventLoopWindowTarget<E>,
     window_size_pts: egui::Vec2,
-    position_px: &mut egui::Pos2,
-) {
+    position_px: &egui::Pos2,
+) -> Option<winit::monitor::MonitorHandle> {
     crate::profile_function!();
 
     let monitors = event_loop.available_monitors();
@@ -142,7 +152,7 @@ fn clamp_pos_to_monitors<E>(
         .primary_monitor()
         .or_else(|| event_loop.available_monitors().next())
     else {
-        return; // no monitors 🤷
+        return None; // no monitors 🤷
     };
 
     for monitor in monitors {
@@ -159,6 +169,23 @@ fn clamp_pos_to_monitors<E>(
         }
     }
 
+    Some(active_monitor)
+}
+
+fn clamp_pos_to_monitors<E>(
+    egui_zoom_factor: f32,
+    event_loop: &winit::event_loop::EventLoopWindowTarget<E>,
+    window_size_pts: egui::Vec2,
+    position_px: &mut egui::Pos2,
+) {
+    crate::profile_function!();
+
+    let Some(active_monitor) =
+        find_active_monitor(egui_zoom_factor, event_loop, window_size_pts, position_px)
+    else {
+        return; // no monitors 🤷
+    };
+
     let mut window_size_px =
         window_size_pts * (egui_zoom_factor * active_monitor.scale_factor() as f32);
     // Add size of title bar. This is 32 px by default in Win 10/11.