diff --git a/crates/fj-core/src/algorithms/transform/edge.rs b/crates/fj-core/src/algorithms/transform/edge.rs
index f1b47c28a..b690751d1 100644
--- a/crates/fj-core/src/algorithms/transform/edge.rs
+++ b/crates/fj-core/src/algorithms/transform/edge.rs
@@ -18,6 +18,10 @@ impl TransformObject for HalfEdge {
         // coordinates.
         let path = self.path();
         let boundary = self.boundary();
+        let curve = self
+            .curve()
+            .clone()
+            .transform_with_cache(transform, services, cache);
         let start_vertex = self
             .start_vertex()
             .clone()
@@ -27,7 +31,7 @@ impl TransformObject for HalfEdge {
             .clone()
             .transform_with_cache(transform, services, cache);
 
-        Self::new(path, boundary, start_vertex, global_form)
+        Self::new(path, boundary, curve, start_vertex, global_form)
     }
 }
 
diff --git a/crates/fj-core/src/objects/kinds/edge.rs b/crates/fj-core/src/objects/kinds/edge.rs
index 5154fd799..153f82ac2 100644
--- a/crates/fj-core/src/objects/kinds/edge.rs
+++ b/crates/fj-core/src/objects/kinds/edge.rs
@@ -2,7 +2,7 @@ use fj_math::Point;
 
 use crate::{
     geometry::{BoundaryOnCurve, SurfacePath},
-    objects::Vertex,
+    objects::{Curve, Vertex},
     storage::{Handle, HandleWrapper},
 };
 
@@ -42,6 +42,7 @@ use crate::{
 pub struct HalfEdge {
     path: SurfacePath,
     boundary: BoundaryOnCurve,
+    curve: HandleWrapper<Curve>,
     start_vertex: HandleWrapper<Vertex>,
     global_form: HandleWrapper<GlobalEdge>,
 }
@@ -51,12 +52,14 @@ impl HalfEdge {
     pub fn new(
         path: SurfacePath,
         boundary: impl Into<BoundaryOnCurve>,
+        curve: Handle<Curve>,
         start_vertex: Handle<Vertex>,
         global_form: Handle<GlobalEdge>,
     ) -> Self {
         Self {
             path,
             boundary: boundary.into(),
+            curve: curve.into(),
             start_vertex: start_vertex.into(),
             global_form: global_form.into(),
         }
@@ -82,6 +85,11 @@ impl HalfEdge {
         self.path.point_from_path_coords(start)
     }
 
+    /// Access the curve of the half-edge
+    pub fn curve(&self) -> &Handle<Curve> {
+        &self.curve
+    }
+
     /// Access the vertex from where this half-edge starts
     pub fn start_vertex(&self) -> &Handle<Vertex> {
         &self.start_vertex
diff --git a/crates/fj-core/src/operations/build/edge.rs b/crates/fj-core/src/operations/build/edge.rs
index 6e850e549..3552ada11 100644
--- a/crates/fj-core/src/operations/build/edge.rs
+++ b/crates/fj-core/src/operations/build/edge.rs
@@ -3,7 +3,7 @@ use fj_math::{Arc, Point, Scalar};
 
 use crate::{
     geometry::{BoundaryOnCurve, SurfacePath},
-    objects::{GlobalEdge, HalfEdge, Vertex},
+    objects::{Curve, GlobalEdge, HalfEdge, Vertex},
     operations::Insert,
     services::Services,
 };
@@ -16,10 +16,11 @@ pub trait BuildHalfEdge {
         boundary: impl Into<BoundaryOnCurve>,
         services: &mut Services,
     ) -> HalfEdge {
+        let curve = Curve::new().insert(services);
         let start_vertex = Vertex::new().insert(services);
         let global_form = GlobalEdge::new().insert(services);
 
-        HalfEdge::new(path, boundary, start_vertex, global_form)
+        HalfEdge::new(path, boundary, curve, start_vertex, global_form)
     }
 
     /// Create an arc
diff --git a/crates/fj-core/src/operations/reverse/cycle.rs b/crates/fj-core/src/operations/reverse/cycle.rs
index 62cac2ef1..7d2fdc3af 100644
--- a/crates/fj-core/src/operations/reverse/cycle.rs
+++ b/crates/fj-core/src/operations/reverse/cycle.rs
@@ -14,6 +14,7 @@ impl Reverse for Cycle {
                 HalfEdge::new(
                     current.path(),
                     current.boundary().reverse(),
+                    current.curve().clone(),
                     next.start_vertex().clone(),
                     current.global_form().clone(),
                 )
diff --git a/crates/fj-core/src/operations/update/edge.rs b/crates/fj-core/src/operations/update/edge.rs
index 91f400759..d065cee69 100644
--- a/crates/fj-core/src/operations/update/edge.rs
+++ b/crates/fj-core/src/operations/update/edge.rs
@@ -19,6 +19,7 @@ impl UpdateHalfEdge for HalfEdge {
         HalfEdge::new(
             self.path(),
             self.boundary(),
+            self.curve().clone(),
             start_vertex,
             self.global_form().clone(),
         )
@@ -28,6 +29,7 @@ impl UpdateHalfEdge for HalfEdge {
         HalfEdge::new(
             self.path(),
             self.boundary(),
+            self.curve().clone(),
             self.start_vertex().clone(),
             global_form,
         )
diff --git a/crates/fj-core/src/validate/edge.rs b/crates/fj-core/src/validate/edge.rs
index 9516664b6..899a33b7b 100644
--- a/crates/fj-core/src/validate/edge.rs
+++ b/crates/fj-core/src/validate/edge.rs
@@ -95,6 +95,7 @@ mod tests {
             HalfEdge::new(
                 valid.path(),
                 boundary,
+                valid.curve().clone(),
                 valid.start_vertex().clone(),
                 valid.global_form().clone(),
             )