Feat: implement WCS↔UCS coordinate transform pipeline

- Add `active_ucs: Option<Ucs>` per-tab state to DocumentTab
- Add `ucs_to_wcs`, `wcs_to_ucs`, `ucs_z_axis`, `ucs_rotated_z` helpers
- Add `Camera::pick_on_plane` for ray–plane intersection against any plane
- Mouse picks project onto the active UCS XY plane instead of world XY
- Typed coordinates are converted from UCS space to WCS before dispatch
- UCS command now really activates/deactivates a UCS:
  - `UCS W` resets to WCS (clears active_ucs)
  - `UCS <name>` activates a named UCS
  - `UCS SAVE <name>` saves the current active UCS
  - `UCS ORIGIN x,y,z` shifts origin (in current UCS space)
  - `UCS X/Y/Z <angle>` rotates the UCS around its own axes

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

src/app/helpers.rs

@@ -1,5 +1,6 @@
 use crate::ui::overlay::GridPlane;
 use crate::scene::WireModel;
+use acadrust::tables::Ucs;
 
 // ── Coordinate parsing ─────────────────────────────────────────────────────
 
@@ -20,6 +21,50 @@ pub(super) fn parse_coord(text: &str) -> Option<glam::Vec3> {
     }
 }
 
+// ── UCS ↔ WCS transforms ───────────────────────────────────────────────────
+
+/// Convert a point from UCS local coordinates to WCS.
+///
+/// WCS = origin + x_axis*u + y_axis*v + z_axis*w
+pub(super) fn ucs_to_wcs(pt: glam::Vec3, ucs: &Ucs) -> glam::Vec3 {
+    let o = glam::Vec3::new(ucs.origin.x as f32, ucs.origin.y as f32, ucs.origin.z as f32);
+    let x = glam::Vec3::new(ucs.x_axis.x as f32, ucs.x_axis.y as f32, ucs.x_axis.z as f32);
+    let y = glam::Vec3::new(ucs.y_axis.x as f32, ucs.y_axis.y as f32, ucs.y_axis.z as f32);
+    let z_ax = ucs_z_axis(ucs);
+    o + x * pt.x + y * pt.y + z_ax * pt.z
+}
+
+/// Convert a WCS point back to UCS local coordinates.
+#[allow(dead_code)]
+pub(super) fn wcs_to_ucs(pt: glam::Vec3, ucs: &Ucs) -> glam::Vec3 {
+    let o = glam::Vec3::new(ucs.origin.x as f32, ucs.origin.y as f32, ucs.origin.z as f32);
+    let x = glam::Vec3::new(ucs.x_axis.x as f32, ucs.x_axis.y as f32, ucs.x_axis.z as f32);
+    let y = glam::Vec3::new(ucs.y_axis.x as f32, ucs.y_axis.y as f32, ucs.y_axis.z as f32);
+    let z_ax = ucs_z_axis(ucs);
+    let d = pt - o;
+    glam::Vec3::new(d.dot(x), d.dot(y), d.dot(z_ax))
+}
+
+/// Return the normalised Z axis of a UCS (cross product of X and Y axes).
+pub(super) fn ucs_z_axis(ucs: &Ucs) -> glam::Vec3 {
+    let x = glam::Vec3::new(ucs.x_axis.x as f32, ucs.x_axis.y as f32, ucs.x_axis.z as f32);
+    let y = glam::Vec3::new(ucs.y_axis.x as f32, ucs.y_axis.y as f32, ucs.y_axis.z as f32);
+    x.cross(y).normalize_or_zero()
+}
+
+/// Build a UCS with `origin` and axes rotated by `angle_z_rad` around the Z axis.
+pub(super) fn ucs_rotated_z(origin: glam::Vec3, angle_z: f32) -> Ucs {
+    let cos = angle_z.cos() as f64;
+    let sin = angle_z.sin() as f64;
+    let mut ucs = Ucs::new("*ACTIVE*");
+    ucs.origin = acadrust::types::Vector3::new(
+        origin.x as f64, origin.y as f64, origin.z as f64,
+    );
+    ucs.x_axis = acadrust::types::Vector3::new(cos, sin, 0.0);
+    ucs.y_axis = acadrust::types::Vector3::new(-sin, cos, 0.0);
+    ucs
+}
+
 pub(super) fn angle_close(a: f32, b: f32, tol: f32) -> bool {
     let diff = (a - b).rem_euclid(std::f32::consts::TAU);
     let diff = if diff > std::f32::consts::PI {