UI: datum planes and axes in the viewport, datums and partitions in the browser

Datum planes draw as a hatched square around the model, axes as a line through
it, each with its name, in the desktop viewport and the headless render. The
browser's Geometry node lists the datums and the partitions with the datum
each cuts by.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo

crates/ui-egui/src/browser.rs

@@ -1,4 +1,5 @@
-//! The browser (left): the model as a tree. Geometry and Mesh with eye toggles, then the model's
+//! The browser (left): the model as a tree. Geometry (the design's bodies, datums and
+//! partitions) and Mesh with eye toggles, then the model's
 //! definitions (sets, materials, sections, steps, loads and boundary conditions, interactions)
 //! with counts (Loads & BCs and Interactions with eye toggles for their viewport symbols), and
 //! the solved steps' results. Clicking a definition selects it (its properties show on the
@@ -388,6 +389,26 @@ fn rows(app: &mut ModelApp, ui: &mut egui::Ui, acts: &mut Vec<Act>) {
                 &Row { depth: 2, icon: Some("geometry.import.mesh"), label: s, ..Default::default() },
             );
         }
+        // Datum planes and axes, then the partitions in the order they cut.
+        let datums: Vec<(String, &'static str)> =
+            app.session.model.datums().iter().map(|(n, d)| (n.clone(), if d.plane().is_some() { "plane" } else { "axis" })).collect();
+        for (i, (n, kind)) in datums.iter().enumerate() {
+            draw_row(
+                app,
+                ui,
+                egui::Id::new(("fc_row_datum", i)),
+                &Row { depth: 2, icon: Some("geometry.datum"), label: n, note: Some((*kind).into()), ..Default::default() },
+            );
+        }
+        let partitions: Vec<(String, String)> = app.session.model.partitions().iter().map(|p| (p.name.clone(), p.datum.clone())).collect();
+        for (i, (n, datum)) in partitions.iter().enumerate() {
+            draw_row(
+                app,
+                ui,
+                egui::Id::new(("fc_row_partition", i)),
+                &Row { depth: 2, icon: Some("geometry.partition"), label: n, note: Some(format!("by {datum}")), ..Default::default() },
+            );
+        }
         if design.is_none() && surfaces.is_empty() {
             draw_row(
                 app,