fix: UCS FACE/OBJECT pick from the interactive prompt; reuse ocs_axes

Follow-up to #1341:
- interactive UCS offers Face / OBject; bare UCS OBJECT starts an entity pick
- one UcsPickCommand serves both FACE and OBJECT
- ucs_from_normal calls the existing arbitrary-axis helper instead of a copy
- prompt catalogue key and en-US text follow the new option list

Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>

src/app/commands/layerprops.rs

@@ -338,7 +338,7 @@ impl OpenCADStudio {
                             // surface point, so both entry points share the
                             // plane construction below.
                             None => {
-                                let picker = crate::command::UcsFaceCommand;
+                                let picker = crate::command::UcsPickCommand { face: true };
                                 self.command_line.push_info(&picker.prompt());
                                 self.tabs[i].active_cmd = Some(Box::new(picker));
                             }
@@ -386,9 +386,13 @@ impl OpenCADStudio {
                             })
                             .map(acadrust::Handle::new);
                         match target {
-                            None => self
-                                .command_line
-                                .push_error(crate::t!("Usage: UCS OBJECT <handle>").as_ref()),
+                            // Bare `UCS OBJECT` starts the pick; the click
+                            // comes back through this arm with the handle.
+                            None => {
+                                let picker = crate::command::UcsPickCommand { face: false };
+                                self.command_line.push_info(&picker.prompt());
+                                self.tabs[i].active_cmd = Some(Box::new(picker));
+                            }
                             Some(handle) => {
                                 let built = self.tabs[i]
                                     .scene

src/app/commands/mod.rs

@@ -739,9 +739,10 @@ inventory::submit!(crate::command::CommandRegistration {
         "SELSIM",
         // Draw a new object of the same type as the selected one. (#239)
         "ADDSELECTED",
+        // Outline of origin planes, open sketch and solid bodies.
+        "BROWSER",
         // Open and close a sketch: a drawing plane, a square-on view and
         // snapping, held together until the profile is done.
-        "BROWSER",
         "CREATESKETCH",
         "FINISHSKETCH",
         "SHEETSET",

src/app/helpers.rs

@@ -249,35 +249,20 @@ pub(super) fn ucs_z_axis(ucs: &Ucs) -> glam::DVec3 {
 
 /// Build a UCS whose Z axis is `normal`, anchored at `origin`.
 ///
-/// X and Y come from the Arbitrary Axis Algorithm, the same rule DWG uses to
-/// turn an extrusion direction into an object coordinate system. Picking the
-/// world axis that is *least* parallel to the normal keeps the cross product
-/// well conditioned, and makes the result stable: the same face always yields
-/// the same X axis, so a sketch drawn on it does not spin when the UCS is
-/// rebuilt.
-///
-/// Returns `None` when `normal` is degenerate and defines no plane.
+/// X and Y come from the arbitrary-axis algorithm in
+/// [`crate::scene::view::transform::ocs_axes`], the same frame entities get
+/// from their extrusion direction, so the same face always yields the same X
+/// axis. Returns `None` when `normal` is degenerate and defines no plane.
 pub(super) fn ucs_from_normal(origin: glam::DVec3, normal: glam::DVec3) -> Option<Ucs> {
     let z = normal.normalize_or_zero();
     if z.length_squared() < 1e-12 {
         return None;
     }
-    // 1/64 is the threshold the DWG spec names for "close enough to the world
-    // Z axis that using it as the reference would be ill conditioned".
-    let reference = if z.x.abs() < 1.0 / 64.0 && z.y.abs() < 1.0 / 64.0 {
-        glam::DVec3::Y
-    } else {
-        glam::DVec3::Z
-    };
-    let x = reference.cross(z).normalize_or_zero();
-    if x.length_squared() < 1e-12 {
-        return None;
-    }
-    let y = z.cross(x).normalize_or_zero();
+    let ((xx, xy, xz), (yx, yy, yz)) = crate::scene::view::transform::ocs_axes((z.x, z.y, z.z));
     let mut ucs = Ucs::new("*ACTIVE*");
     ucs.origin = acadrust::types::Vector3::new(origin.x, origin.y, origin.z);
-    ucs.x_axis = acadrust::types::Vector3::new(x.x, x.y, x.z);
-    ucs.y_axis = acadrust::types::Vector3::new(y.x, y.y, y.z);
+    ucs.x_axis = acadrust::types::Vector3::new(xx, xy, xz);
+    ucs.y_axis = acadrust::types::Vector3::new(yx, yy, yz);
     Some(ucs)
 }