diff --git a/crates/fj-kernel/src/algorithms/approx/edge.rs b/crates/fj-kernel/src/algorithms/approx/edge.rs
index a3542dbb4..95bc0f724 100644
--- a/crates/fj-kernel/src/algorithms/approx/edge.rs
+++ b/crates/fj-kernel/src/algorithms/approx/edge.rs
@@ -30,7 +30,7 @@ impl Approx for (&Handle<HalfEdge>, &Surface) {
         let range = RangeOnPath { boundary };
 
         let first = ApproxPoint::new(
-            half_edge.start_vertex().position(),
+            half_edge.start_position(),
             half_edge.start_vertex().global_form().position(),
         )
         .with_source((half_edge.clone(), half_edge.boundary()[0]));
diff --git a/crates/fj-kernel/src/algorithms/intersect/face_point.rs b/crates/fj-kernel/src/algorithms/intersect/face_point.rs
index 1f13c0a8e..6d6924570 100644
--- a/crates/fj-kernel/src/algorithms/intersect/face_point.rs
+++ b/crates/fj-kernel/src/algorithms/intersect/face_point.rs
@@ -318,10 +318,7 @@ mod tests {
         let edge = face
             .exterior()
             .half_edges()
-            .find(|edge| {
-                let vertex = edge.start_vertex();
-                vertex.position() == Point::from([0., 0.])
-            })
+            .find(|edge| edge.start_position() == Point::from([0., 0.]))
             .unwrap();
         assert_eq!(
             intersection,
@@ -352,10 +349,10 @@ mod tests {
         let vertex = face
             .exterior()
             .half_edges()
-            .map(|half_edge| half_edge.start_vertex().clone())
-            .find(|surface_vertex| {
-                surface_vertex.position() == Point::from([1., 0.])
+            .find(|half_edge| {
+                half_edge.start_position() == Point::from([1., 0.])
             })
+            .map(|half_edge| half_edge.start_vertex().clone())
             .unwrap();
         assert_eq!(
             intersection,
diff --git a/crates/fj-kernel/src/algorithms/intersect/ray_face.rs b/crates/fj-kernel/src/algorithms/intersect/ray_face.rs
index df4937d90..f117e480f 100644
--- a/crates/fj-kernel/src/algorithms/intersect/ray_face.rs
+++ b/crates/fj-kernel/src/algorithms/intersect/ray_face.rs
@@ -256,10 +256,7 @@ mod tests {
         let edge = face
             .exterior()
             .half_edges()
-            .find(|edge| {
-                let vertex = edge.start_vertex();
-                vertex.position() == Point::from([-1., 1.])
-            })
+            .find(|edge| edge.start_position() == Point::from([-1., 1.]))
             .unwrap();
         assert_eq!(
             (&ray, &face).intersect(),
@@ -291,10 +288,10 @@ mod tests {
         let vertex = face
             .exterior()
             .half_edges()
-            .map(|half_edge| half_edge.start_vertex().clone())
-            .find(|surface_vertex| {
-                surface_vertex.position() == Point::from([-1., -1.])
+            .find(|half_edge| {
+                half_edge.start_position() == Point::from([-1., -1.])
             })
+            .map(|half_edge| half_edge.start_vertex().clone())
             .unwrap();
         assert_eq!(
             (&ray, &face).intersect(),
diff --git a/crates/fj-kernel/src/objects/full/cycle.rs b/crates/fj-kernel/src/objects/full/cycle.rs
index be42f3fda..dd2abbb35 100644
--- a/crates/fj-kernel/src/objects/full/cycle.rs
+++ b/crates/fj-kernel/src/objects/full/cycle.rs
@@ -77,8 +77,7 @@ impl Cycle {
         let mut sum = Scalar::ZERO;
 
         for [a, b] in self.half_edges.as_slice().array_windows_ext() {
-            let [a, b] =
-                [a, b].map(|half_edge| half_edge.start_vertex().position());
+            let [a, b] = [a, b].map(|half_edge| half_edge.start_position());
 
             sum += (b.u - a.u) * (b.v + a.v);
         }
diff --git a/crates/fj-kernel/src/objects/full/edge.rs b/crates/fj-kernel/src/objects/full/edge.rs
index f0a0a4915..a40b1b193 100644
--- a/crates/fj-kernel/src/objects/full/edge.rs
+++ b/crates/fj-kernel/src/objects/full/edge.rs
@@ -79,6 +79,16 @@ impl HalfEdge {
         self.boundary
     }
 
+    /// Compute the surface position where the half-edge starts
+    pub fn start_position(&self) -> Point<2> {
+        // Computing the surface position from the curve position is fine.
+        // `HalfEdge` "owns" its start position. There is no competing code that
+        // could compute the surface position from slightly different data.
+
+        let [start, _] = self.boundary;
+        self.curve.point_from_path_coords(start)
+    }
+
     /// Access the vertex from where this half-edge starts
     pub fn start_vertex(&self) -> &Handle<SurfaceVertex> {
         &self.start_vertex