diff --git a/crates/fj-core/src/algorithms/approx/curve.rs b/crates/fj-core/src/algorithms/approx/curve.rs
index db90e56b7..6a5dc4bfa 100644
--- a/crates/fj-core/src/algorithms/approx/curve.rs
+++ b/crates/fj-core/src/algorithms/approx/curve.rs
@@ -5,7 +5,10 @@ use std::collections::BTreeMap;
 use fj_math::Point;
 
 use crate::{
-    geometry::{CurveBoundary, GlobalPath, SurfaceGeometry, SurfacePath},
+    geometry::{
+        CurveBoundary, GlobalPath, HalfEdgeGeometry, SurfaceGeometry,
+        SurfacePath,
+    },
     objects::Curve,
     storage::Handle,
     Core,
@@ -13,14 +16,7 @@ use crate::{
 
 use super::{Approx, ApproxPoint, Tolerance};
 
-impl Approx
-    for (
-        &Handle<Curve>,
-        SurfacePath,
-        &SurfaceGeometry,
-        CurveBoundary<Point<1>>,
-    )
-{
+impl Approx for (&Handle<Curve>, &HalfEdgeGeometry, &SurfaceGeometry) {
     type Approximation = CurveApprox;
     type Cache = CurveApproxCache;
 
@@ -30,20 +26,20 @@ impl Approx
         cache: &mut Self::Cache,
         core: &mut Core,
     ) -> Self::Approximation {
-        let (curve, surface_path, surface, boundary) = self;
+        let (curve, half_edge, surface) = self;
 
-        match cache.get(curve, boundary) {
+        match cache.get(curve, half_edge.boundary) {
             Some(approx) => approx,
             None => {
                 let approx = approx_curve(
-                    &surface_path,
+                    &half_edge.path,
                     surface,
-                    boundary,
+                    half_edge.boundary,
                     tolerance,
                     core,
                 );
 
-                cache.insert(curve.clone(), boundary, approx)
+                cache.insert(curve.clone(), half_edge.boundary, approx)
             }
         }
     }
@@ -187,7 +183,10 @@ mod tests {
 
     use crate::{
         algorithms::approx::{Approx, ApproxPoint},
-        geometry::{CurveBoundary, GlobalPath, SurfaceGeometry, SurfacePath},
+        geometry::{
+            CurveBoundary, GlobalPath, HalfEdgeGeometry, SurfaceGeometry,
+            SurfacePath,
+        },
         objects::Curve,
         operations::insert::Insert,
         Core,
@@ -201,11 +200,12 @@ mod tests {
         let (path, boundary) =
             SurfacePath::line_from_points([[1., 1.], [2., 1.]]);
         let boundary = CurveBoundary::from(boundary);
+        let half_edge = HalfEdgeGeometry { path, boundary };
         let surface = core.layers.geometry.xz_plane();
 
         let tolerance = 1.;
         let approx =
-            (&curve, path, &surface, boundary).approx(tolerance, &mut core);
+            (&curve, &half_edge, &surface).approx(tolerance, &mut core);
 
         assert_eq!(approx.points, vec![]);
     }
@@ -218,6 +218,7 @@ mod tests {
         let (path, boundary) =
             SurfacePath::line_from_points([[1., 1.], [2., 1.]]);
         let boundary = CurveBoundary::from(boundary);
+        let half_edge = HalfEdgeGeometry { path, boundary };
         let surface = SurfaceGeometry {
             u: GlobalPath::circle_from_radius(1.),
             v: [0., 0., 1.].into(),
@@ -225,7 +226,7 @@ mod tests {
 
         let tolerance = 1.;
         let approx =
-            (&curve, path, &surface, boundary).approx(tolerance, &mut core);
+            (&curve, &half_edge, &surface).approx(tolerance, &mut core);
 
         assert_eq!(approx.points, vec![]);
     }
@@ -241,6 +242,7 @@ mod tests {
             ([TAU], [TAU, 1.]),
         ]);
         let boundary = CurveBoundary::from([[0.], [TAU]]);
+        let half_edge = HalfEdgeGeometry { path, boundary };
         let surface = SurfaceGeometry {
             u: global_path,
             v: [0., 0., 1.].into(),
@@ -248,7 +250,7 @@ mod tests {
 
         let tolerance = 1.;
         let approx =
-            (&curve, path, &surface, boundary).approx(tolerance, &mut core);
+            (&curve, &half_edge, &surface).approx(tolerance, &mut core);
 
         let expected_approx = (global_path, boundary)
             .approx(tolerance, &mut core)
@@ -270,11 +272,12 @@ mod tests {
         let curve = Curve::new().insert(&mut core);
         let path = SurfacePath::circle_from_center_and_radius([0., 0.], 1.);
         let boundary = CurveBoundary::from([[0.], [TAU]]);
+        let half_edge = HalfEdgeGeometry { path, boundary };
         let surface = core.layers.geometry.xz_plane();
 
         let tolerance = 1.;
         let approx =
-            (&curve, path, &surface, boundary).approx(tolerance, &mut core);
+            (&curve, &half_edge, &surface).approx(tolerance, &mut core);
 
         let expected_approx = (&path, boundary)
             .approx(tolerance, &mut core)
diff --git a/crates/fj-core/src/algorithms/approx/edge.rs b/crates/fj-core/src/algorithms/approx/edge.rs
index 356cb193d..5db47de99 100644
--- a/crates/fj-core/src/algorithms/approx/edge.rs
+++ b/crates/fj-core/src/algorithms/approx/edge.rs
@@ -50,9 +50,8 @@ impl Approx for (&Handle<HalfEdge>, &SurfaceGeometry) {
         let rest = {
             let approx = (
                 half_edge.curve(),
-                core.layers.geometry.of_half_edge(half_edge).path,
+                &core.layers.geometry.of_half_edge(half_edge),
                 surface,
-                half_edge.boundary(),
             )
                 .approx_with_cache(
                     tolerance,