diff --git a/crates/fj-core/src/algorithms/approx/curve.rs b/crates/fj-core/src/algorithms/approx/curve.rs
new file mode 100644
index 000000000..b80419791
--- /dev/null
+++ b/crates/fj-core/src/algorithms/approx/curve.rs
@@ -0,0 +1,5 @@
+//! Curve approximation
+
+mod segment;
+
+pub use self::segment::CurveApproxSegment;
diff --git a/crates/fj-core/src/algorithms/approx/curve/segment.rs b/crates/fj-core/src/algorithms/approx/curve/segment.rs
new file mode 100644
index 000000000..d0d8fcb05
--- /dev/null
+++ b/crates/fj-core/src/algorithms/approx/curve/segment.rs
@@ -0,0 +1,50 @@
+use std::cmp;
+
+use fj_math::Point;
+
+use crate::{algorithms::approx::ApproxPoint, geometry::CurveBoundary};
+
+/// A segment of a curve approximation
+///
+/// A curve is potentially infinite (at least its local coordinate space is
+/// infinite, even if the curve itself isn't; a circle is an example of that).
+/// This means a curve can only be approximated locally, at a number of
+/// segments. This struct represents on such segment.
+#[derive(Clone, Debug, Eq, PartialEq, Hash)]
+pub struct CurveApproxSegment {
+    /// The boundary within which this segment approximates the curve
+    pub boundary: CurveBoundary<Point<1>>,
+
+    /// The points that approximate the curve segment
+    pub points: Vec<ApproxPoint<1>>,
+}
+
+impl CurveApproxSegment {
+    /// Reverse the orientation of the approximation
+    #[must_use]
+    pub fn reverse(mut self) -> Self {
+        self.boundary = self.boundary.reverse();
+        self.points.reverse();
+        self
+    }
+}
+
+impl Ord for CurveApproxSegment {
+    fn cmp(&self, other: &Self) -> cmp::Ordering {
+        let [a_start, a_end] = self.boundary.inner;
+        let [b_start, b_end] = other.boundary.inner;
+
+        let by_start = a_start.cmp(&b_start);
+        if by_start.is_ne() {
+            return by_start;
+        }
+
+        a_end.cmp(&b_end)
+    }
+}
+
+impl PartialOrd for CurveApproxSegment {
+    fn partial_cmp(&self, other: &Self) -> Option<cmp::Ordering> {
+        Some(self.cmp(other))
+    }
+}
diff --git a/crates/fj-core/src/algorithms/approx/edge.rs b/crates/fj-core/src/algorithms/approx/edge.rs
index a66d02e78..4f1030f3a 100644
--- a/crates/fj-core/src/algorithms/approx/edge.rs
+++ b/crates/fj-core/src/algorithms/approx/edge.rs
@@ -15,7 +15,7 @@ use crate::{
     storage::{Handle, HandleWrapper},
 };
 
-use super::{Approx, ApproxPoint, Tolerance};
+use super::{curve::CurveApproxSegment, Approx, ApproxPoint, Tolerance};
 
 impl Approx for (&HalfEdge, &Surface) {
     type Approximation = HalfEdgeApprox;
@@ -143,7 +143,7 @@ fn approx_edge(
     surface: &Surface,
     boundary: CurveBoundary<Point<1>>,
     tolerance: impl Into<Tolerance>,
-) -> GlobalEdgeApprox {
+) -> CurveApproxSegment {
     // There are different cases of varying complexity. Circles are the hard
     // part here, as they need to be approximated, while lines don't need to be.
     //
@@ -211,7 +211,7 @@ fn approx_edge(
             ApproxPoint::new(point_curve, point_global)
         })
         .collect();
-    GlobalEdgeApprox { points }
+    CurveApproxSegment { boundary, points }
 }
 
 /// A cache for results of an approximation
@@ -219,7 +219,7 @@ fn approx_edge(
 pub struct EdgeCache {
     edge_approx: BTreeMap<
         (HandleWrapper<GlobalEdge>, CurveBoundary<Point<1>>),
-        GlobalEdgeApprox,
+        CurveApproxSegment,
     >,
     vertex_approx: BTreeMap<HandleWrapper<Vertex>, Point<3>>,
 }
@@ -235,7 +235,7 @@ impl EdgeCache {
         &self,
         handle: Handle<GlobalEdge>,
         boundary: CurveBoundary<Point<1>>,
-    ) -> Option<GlobalEdgeApprox> {
+    ) -> Option<CurveApproxSegment> {
         if let Some(approx) =
             self.edge_approx.get(&(handle.clone().into(), boundary))
         {
@@ -257,8 +257,8 @@ impl EdgeCache {
         &mut self,
         handle: Handle<GlobalEdge>,
         boundary: CurveBoundary<Point<1>>,
-        approx: GlobalEdgeApprox,
-    ) -> GlobalEdgeApprox {
+        approx: CurveApproxSegment,
+    ) -> CurveApproxSegment {
         self.edge_approx
             .insert((handle.into(), boundary), approx.clone())
             .unwrap_or(approx)
@@ -279,21 +279,6 @@ impl EdgeCache {
     }
 }
 
-/// An approximation of a [`GlobalEdge`]
-#[derive(Clone, Debug, Eq, PartialEq, Hash, Ord, PartialOrd)]
-struct GlobalEdgeApprox {
-    /// The points that approximate the edge
-    points: Vec<ApproxPoint<1>>,
-}
-
-impl GlobalEdgeApprox {
-    /// Reverse the order of the approximation
-    fn reverse(mut self) -> Self {
-        self.points.reverse();
-        self
-    }
-}
-
 #[cfg(test)]
 mod tests {
     use std::{f64::consts::TAU, ops::Deref};
diff --git a/crates/fj-core/src/algorithms/approx/mod.rs b/crates/fj-core/src/algorithms/approx/mod.rs
index 7899320ea..236dfe751 100644
--- a/crates/fj-core/src/algorithms/approx/mod.rs
+++ b/crates/fj-core/src/algorithms/approx/mod.rs
@@ -1,5 +1,6 @@
 //! Approximation of objects
 
+pub mod curve;
 pub mod cycle;
 pub mod edge;
 pub mod face;