diff --git a/src/app/document.rs b/src/app/document.rs
index c3471310d..288377ac2 100644
--- a/src/app/document.rs
+++ b/src/app/document.rs
@@ -192,13 +192,7 @@ impl DocumentTab {
     /// Push the active UCS rotation into the scene so the ViewCube composes with
     /// it. Call after any change to `active_ucs`.
     pub(super) fn sync_ucs_to_scene(&mut self) {
-        let (_, x, y, z) = self.ucs_xform().axes();
-        self.scene.viewcube_ucs = glam::Mat4::from_cols(
-            x.extend(0.0),
-            y.extend(0.0),
-            z.extend(0.0),
-            glam::Vec4::W,
-        );
+        self.scene.viewcube_ucs = self.ucs_xform().rotation_mat();
     }
 
     pub(super) fn new_drawing(n: usize) -> Self {
diff --git a/src/app/helpers.rs b/src/app/helpers.rs
index 4af495a81..a63e1c336 100644
--- a/src/app/helpers.rs
+++ b/src/app/helpers.rs
@@ -118,6 +118,17 @@ impl UcsXform {
     pub(super) fn axes(&self) -> (glam::Vec3, glam::Vec3, glam::Vec3, glam::Vec3) {
         (self.origin, self.x, self.y, self.z)
     }
+
+    /// UCS→world rotation matrix (columns = UCS axes). For consumers that take
+    /// a `Mat4` rotation directly (ViewCube, OTRACK ray directions).
+    pub(super) fn rotation_mat(&self) -> glam::Mat4 {
+        glam::Mat4::from_cols(
+            self.x.extend(0.0),
+            self.y.extend(0.0),
+            self.z.extend(0.0),
+            glam::Vec4::W,
+        )
+    }
 }
 
 // ── UCS ↔ WCS transforms (thin wrappers over `UcsXform`) ────────────────────
diff --git a/src/app/update.rs b/src/app/update.rs
index d7f9ef32d..7601d8fd7 100644
--- a/src/app/update.rs
+++ b/src/app/update.rs
@@ -2839,12 +2839,14 @@ impl OpenCADStudio {
                             } else {
                                 None
                             };
+                            let ucs = self.tabs[i].scene.viewcube_ucs_mat();
                             self.snapper.otrack_snap(
                                 cursor_world,
                                 view_proj,
                                 bounds,
                                 step,
                                 self.last_point,
+                                ucs,
                             )
                         } else {
                             None
@@ -3464,8 +3466,9 @@ impl OpenCADStudio {
                             } else {
                                 None
                             };
+                            let ucs = self.tabs[i].scene.viewcube_ucs_mat();
                             self.snapper
-                                .otrack_snap(raw, vp_mat, bounds, step, self.last_point)
+                                .otrack_snap(raw, vp_mat, bounds, step, self.last_point, ucs)
                         } else {
                             None
                         };
diff --git a/src/snap/mod.rs b/src/snap/mod.rs
index f5d82e4f3..641bfefab 100644
--- a/src/snap/mod.rs
+++ b/src/snap/mod.rs
@@ -263,6 +263,9 @@ impl Snapper {
         bounds: iced::Rectangle,
         polar_step_deg: Option<f32>,
         last_point: Option<Vec3>,
+        // UCS→world rotation: tracking rays run along the UCS axes, matching
+        // ortho/polar. Identity = world-aligned rays.
+        ucs: glam::Mat4,
     ) -> Option<OtrackHit> {
         if !self.otrack_enabled || self.tracking_points.is_empty() {
             return None;
@@ -307,7 +310,7 @@ impl Snapper {
                 let ar = adeg.to_radians();
                 rays.push(Ray {
                     origin: tp,
-                    dir: Vec3::new(ar.cos(), ar.sin(), 0.0),
+                    dir: ucs.transform_vector3(Vec3::new(ar.cos(), ar.sin(), 0.0)),
                     group: gi,
                 });
             }
@@ -322,7 +325,7 @@ impl Snapper {
                 let ar = a.to_radians();
                 rays.push(Ray {
                     origin: lp,
-                    dir: Vec3::new(ar.cos(), ar.sin(), 0.0),
+                    dir: ucs.transform_vector3(Vec3::new(ar.cos(), ar.sin(), 0.0)),
                     group: POLAR_GROUP,
                 });
                 a += step;