feat(statusbar): honor $COORDS in the coordinate readout, click to cycle

The Coords pill always showed live absolute X,Y,Z, ignoring the drawing's
$COORDS (coords_mode) sysvar. Drive the readout from it:

- 0 static  — the last picked point; the readout freezes between picks.
- 1 live    — continuous absolute X,Y,Z (previous behavior, default).
- 2 polar   — distance<angle relative to the last point while a command is
              prompting for a point; absolute otherwise.

The cursor and last point are reported in the active UCS, matching the rest of
the readout. Clicking the pill cycles the mode 0→1→2→0 (CycleCoordsMode), marks
the tab dirty and echoes it; SETVAR COORDS still works. $COORDS round-trips per
drawing via acadrust's coords_mode.

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

src/app/mod.rs

@@ -1458,6 +1458,8 @@ pub enum Message {
     ToggleLayoutList,
     /// Close the Model/layout list dropdown.
     CloseLayoutList,
+    /// Cycle the coordinate readout mode ($COORDS): static → live → polar.
+    CycleCoordsMode,
     /// Toggle the status-bar customization menu open/closed.
     ToggleStatusBarMenu,
     /// Close the status-bar customization menu.

src/app/update/mod.rs

@@ -1541,6 +1541,26 @@ impl OpenCADStudio {
                 }
                 Task::none()
             }
+            Message::CycleCoordsMode => {
+                // $COORDS 0 (static) → 1 (live absolute) → 2 (polar) → 0.
+                let i = self.active_tab;
+                if i < self.tabs.len() {
+                    let mode = {
+                        let h = &mut self.tabs[i].scene.document.header;
+                        h.coords_mode = (h.coords_mode + 1).rem_euclid(3);
+                        h.coords_mode
+                    };
+                    self.tabs[i].dirty = true;
+                    let label = match mode {
+                        0 => "static",
+                        2 => "polar",
+                        _ => "live",
+                    };
+                    self.command_line
+                        .push_output(&format!("COORDS = {mode} ({label})"));
+                }
+                Task::none()
+            }
             Message::TogglePolar => {
                 self.polar_mode ^= true;
                 if self.polar_mode {

src/app/view/mod.rs

@@ -1303,16 +1303,21 @@ impl OpenCADStudio {
                     // drawing coordinates (paper space carries no offset), then
                     // report it in the active UCS — the readout follows the
                     // user's coordinate system, not raw WCS (no-op without UCS).
-                    let cursor_coord = {
-                        let lc = tab.last_cursor_world;
+                    let to_readout = |p: glam::Vec3| {
                         // The readout follows the active pane's UCS — model space
                         // or inside a floating viewport (no-op without a UCS).
                         if tab.editing_model_space() {
-                            tab.ucs_xform().to_ucs(lc)
+                            tab.ucs_xform().to_ucs(p)
                         } else {
-                            lc
+                            p
                         }
                     };
+                    let cursor_coord = to_readout(tab.last_cursor_world);
+                    // The last picked point (same UCS as the cursor) drives the
+                    // static ($COORDS 0) and polar ($COORDS 2) readouts.
+                    let last_coord = self.last_point.map(to_readout);
+                    let coords_mode = tab.scene.document.header.coords_mode;
+                    let picking = tab.active_cmd.is_some();
                     self.status_bar.view(
                         &self.snapper,
                         self.snap_popup_open,
@@ -1334,6 +1339,9 @@ impl OpenCADStudio {
                         scale_pill_enabled,
                         tab.scene.document.header.lineweight_display,
                         cursor_coord,
+                        coords_mode,
+                        last_coord,
+                        picking,
                         self.clean_screen,
                         tab.scene.document.header.insertion_units,
                         self.units_popup_open,

src/ui/statusbar/mod.rs

@@ -79,6 +79,13 @@ impl StatusBar {
         lineweight_display: bool,
         // Live cursor position in model coordinates, for the coordinate readout.
         cursor_world: glam::Vec3,
+        // $COORDS readout mode: 0 = static (updates only on a pick), 1 = live
+        // absolute, 2 = polar (distance<angle from the last point while picking).
+        coords_mode: i16,
+        // The last committed point, for the static (0) and polar (2) readouts.
+        last_point: Option<glam::Vec3>,
+        // True while a command is prompting for a point (enables the polar readout).
+        picking: bool,
         // True while clean-screen mode hides the ribbon and side panels.
         clean_screen: bool,
         // Drawing units (INSUNITS) for the units pill.
@@ -153,10 +160,11 @@ impl StatusBar {
         let vis = |p: StatusPill| config.is_visible(p);
         let mut pills: Vec<Element<'_, Message>> = Vec::new();
         if vis(StatusPill::Coords) {
+            let coords_label = format_coords(cursor_world, last_point, coords_mode, picking);
             pills.push(
                 tip(
-                    status_pill(format_coords(cursor_world)).into(),
-                    "Cursor coordinates (X, Y, Z)",
+                    popup_pill(&coords_label, false, Message::CycleCoordsMode),
+                    "Cursor coordinates ($COORDS)\nClick to cycle: static / live / polar",
                 )
                 .into(),
             );
@@ -377,8 +385,28 @@ impl StatusBar {
 
 // ── Coordinate readout ────────────────────────────────────────────────────
 
-fn format_coords(p: glam::Vec3) -> String {
-    format!("{:.4}, {:.4}, {:.4}", p.x, p.y, p.z)
+fn format_coords(cursor: glam::Vec3, last: Option<glam::Vec3>, mode: i16, picking: bool) -> String {
+    let abs = |p: glam::Vec3| format!("{:.4}, {:.4}, {:.4}", p.x, p.y, p.z);
+    match mode {
+        // Static: show the last picked point; the readout freezes between picks.
+        0 => abs(last.unwrap_or(cursor)),
+        // Polar: distance < angle relative to the last point while a command is
+        // prompting for a point; absolute otherwise.
+        2 => match (picking, last) {
+            (true, Some(l)) => {
+                let d = cursor - l;
+                let dist = (d.x * d.x + d.y * d.y).sqrt();
+                let mut ang = d.y.atan2(d.x).to_degrees();
+                if ang < 0.0 {
+                    ang += 360.0;
+                }
+                format!("{dist:.4} < {ang:.2}\u{b0}")
+            }
+            _ => abs(cursor),
+        },
+        // 1 (default) and anything else: live absolute.
+        _ => abs(cursor),
+    }
 }
 
 // ── Customization handle ──────────────────────────────────────────────────