feat(polar): angle picker dropdown on the POLAR pill (#264)

The polar-tracking pill only right-click-cycled 15→30→45→90. Add an
AutoCAD-style angle picker opened from a caret on the pill: presets
90/45/30/22.5/18/15/10/5/1 plus a free-text field for any custom angle,
mirroring the existing units / scale status-bar popups. The chosen angle
persists like the other user settings.

Factor the shared chrome into one `split_pill(main, caret_msg, active,
open)` helper (+ `pill_text_color`) so the OSNAP and POLAR pills stop
hand-rolling the same outer border, background, caret and sizing — each
pill now only supplies its own main region. The caret is sized and
aligned to sit inside the single pill border on both.

Co-Authored-By: Claude Opus 4.8 <[email protected]>

src/app/mod.rs

@@ -252,6 +252,10 @@ pub(super) struct OpenCADStudio {
     snapper: Snapper,
     snap_popup_open: bool,
     scale_popup_open: bool,
+    /// True while the polar-tracking angle picker is open.
+    polar_popup_open: bool,
+    /// Live text of the polar picker's custom-angle field.
+    polar_custom_input: String,
     /// True while the status-bar customization menu is open.
     statusbar_menu_open: bool,
     /// True while the leftmost hamburger's Model/layout list dropdown is open.
@@ -1404,8 +1408,16 @@ pub enum Message {
     ToggleLineweightDisplay,
     /// Toggle polar-angle constraint — F10 / POLAR status-bar button.
     TogglePolar,
-    /// Set polar tracking angle increment (right-click POLAR button).
+    /// Set polar tracking angle increment (POLAR picker / right-click cycle).
     SetPolarAngle(f32),
+    /// Open/close the polar-tracking angle picker (POLAR pill caret).
+    TogglePolarPopup,
+    /// Close the polar-tracking angle picker.
+    ClosePolarPopup,
+    /// Live text edit of the polar picker's custom-angle field.
+    PolarCustomInput(String),
+    /// Apply the typed custom polar angle (Enter in the picker's field).
+    SubmitPolarCustom,
     /// Set the model-space annotation scale (CANNOSCALE equivalent).
     SetAnnotationScale(f32),
     /// Set the active viewport's custom_scale (paper space).
@@ -2045,6 +2057,8 @@ impl OpenCADStudio {
             snapper: Snapper::default(),
             snap_popup_open: false,
             scale_popup_open: false,
+            polar_popup_open: false,
+            polar_custom_input: String::new(),
             statusbar_menu_open: false,
             layout_list_open: false,
             units_popup_open: false,

src/app/update/mod.rs

@@ -1561,6 +1561,37 @@ impl OpenCADStudio {
                 self.polar_increment_deg = deg;
                 self.polar_mode = true;
                 self.ortho_mode = false;
+                self.polar_popup_open = false;
+                Task::none()
+            }
+            Message::TogglePolarPopup => {
+                self.polar_popup_open ^= true;
+                if self.polar_popup_open {
+                    // Start the custom field empty each time; picking a preset or
+                    // typing a value is what actually enables polar tracking.
+                    self.polar_custom_input.clear();
+                }
+                Task::none()
+            }
+            Message::ClosePolarPopup => {
+                self.polar_popup_open = false;
+                Task::none()
+            }
+            Message::PolarCustomInput(s) => {
+                self.polar_custom_input = s;
+                Task::none()
+            }
+            Message::SubmitPolarCustom => {
+                // Accept any positive angle up to a full turn; ignore garbage.
+                if let Ok(v) = self.polar_custom_input.trim().parse::<f32>() {
+                    if v > 0.0 && v <= 360.0 {
+                        self.polar_increment_deg = v;
+                        self.polar_mode = true;
+                        self.ortho_mode = false;
+                    }
+                }
+                self.polar_custom_input.clear();
+                self.polar_popup_open = false;
                 Task::none()
             }
             Message::SetAnnotationScale(scale) => {

src/app/view/mod.rs

@@ -1253,6 +1253,7 @@ impl OpenCADStudio {
                         self.ortho_mode,
                         self.polar_mode,
                         self.polar_increment_deg,
+                        self.polar_popup_open,
                         self.dyn_input,
                         self.snapper.otrack_enabled,
                         tab.scene.layout_names(),
@@ -1320,6 +1321,17 @@ impl OpenCADStudio {
             iced::widget::Space::new().width(0).height(0).into()
         };
 
+        let polar_layer: Element<'_, Message> = if self.polar_popup_open {
+            crate::ui::popup::polar_popup::polar_popup_overlay(
+                self.polar_increment_deg,
+                &self.polar_custom_input,
+                sb_pill(crate::ui::statusbar::SB_POLAR_ID),
+                win,
+            )
+        } else {
+            iced::widget::Space::new().width(0).height(0).into()
+        };
+
         let statusbar_menu_layer: Element<'_, Message> = if self.statusbar_menu_open {
             crate::ui::statusbar::statusbar_menu::statusbar_menu_overlay(
                 &self.statusbar_config,
@@ -1412,6 +1424,7 @@ impl OpenCADStudio {
             main_ui,
             snap_layer,
             scale_layer,
+            polar_layer,
             statusbar_menu_layer,
             layout_list_layer,
             units_layer,