diff --git a/crates/fj-core/src/geometry/geometry.rs b/crates/fj-core/src/geometry/geometry.rs
index 5b180ccf0..267696617 100644
--- a/crates/fj-core/src/geometry/geometry.rs
+++ b/crates/fj-core/src/geometry/geometry.rs
@@ -108,10 +108,8 @@ impl Geometry {
     /// ## Panics
     ///
     /// Panics, if the geometry of the curve is not defined.
-    pub fn of_curve(&self, curve: &Handle<Curve>) -> &CurveGeom {
-        self.curve
-            .get(curve)
-            .expect("Expected geometry of half-edge to be defined")
+    pub fn of_curve(&self, curve: &Handle<Curve>) -> Option<&CurveGeom> {
+        self.curve.get(curve)
     }
 
     /// # Access the geometry of the provided half-edge
diff --git a/crates/fj-core/src/operations/build/half_edge.rs b/crates/fj-core/src/operations/build/half_edge.rs
index 37532c4fb..6e931248e 100644
--- a/crates/fj-core/src/operations/build/half_edge.rs
+++ b/crates/fj-core/src/operations/build/half_edge.rs
@@ -133,6 +133,7 @@ pub trait BuildHalfEdge {
                     .layers
                     .geometry
                     .of_curve(half_edge.curve())
+                    .expect("Curve geometry was just defined in same function")
                     .local_on(&surface)
                     .path,
                 boundary: boundary.unwrap_or_default(),
diff --git a/crates/fj-core/src/operations/build/shell.rs b/crates/fj-core/src/operations/build/shell.rs
index 7d4b955fd..211bd80ea 100644
--- a/crates/fj-core/src/operations/build/shell.rs
+++ b/crates/fj-core/src/operations/build/shell.rs
@@ -107,6 +107,10 @@ pub trait BuildShell {
                                             .layers
                                             .geometry
                                             .of_curve(&curve)
+                                            .expect(
+                                                "Curve geometry was just \
+                                                defined in same function",
+                                            )
                                             .local_on(&surface)
                                             .path,
                                         boundary,
diff --git a/crates/fj-core/src/operations/transform/curve.rs b/crates/fj-core/src/operations/transform/curve.rs
index 4457a35b4..7f878009b 100644
--- a/crates/fj-core/src/operations/transform/curve.rs
+++ b/crates/fj-core/src/operations/transform/curve.rs
@@ -1,19 +1,41 @@
 use fj_math::Transform;
 
-use crate::{topology::Curve, Core};
+use crate::{
+    operations::insert::Insert, storage::Handle, topology::Curve, Core,
+};
 
 use super::{TransformCache, TransformObject};
 
-impl TransformObject for Curve {
+impl TransformObject for Handle<Curve> {
     fn transform_with_cache(
         &self,
         _: &Transform,
-        _: &mut Core,
-        _: &mut TransformCache,
+        core: &mut Core,
+        cache: &mut TransformCache,
     ) -> Self {
-        // There's nothing to actually transform here, as `Curve` holds no data.
-        // We still need this implementation though, as a new `Curve` object
-        // must be created to represent the new and transformed curve.
-        Self::new()
+        cache
+            .entry(self)
+            .or_insert_with(|| {
+                // We don't actually need to transform the curve, as its
+                // geometry is locally defined on a surface. We need to set that
+                // geometry for the new object though, that we created here to
+                // represent the transformed curve.
+
+                let curve = Curve::new().insert(core);
+
+                let curve_geom = core.layers.geometry.of_curve(self).cloned();
+                if let Some(curve_geom) = curve_geom {
+                    for (surface, local_definition) in curve_geom.definitions {
+                        core.layers.geometry.define_curve(
+                            curve.clone(),
+                            surface,
+                            local_definition,
+                        );
+                    }
+                }
+
+                curve
+            })
+            .clone()
     }
 }