diff --git a/crates/fj-kernel/src/algorithms/approx/curve.rs b/crates/fj-kernel/src/algorithms/approx/curve.rs
index a77cf749a..ba4169ffa 100644
--- a/crates/fj-kernel/src/algorithms/approx/curve.rs
+++ b/crates/fj-kernel/src/algorithms/approx/curve.rs
@@ -83,6 +83,10 @@ fn approx_circle(
         points.push(ApproxPoint::new(point_curve, point_global));
     }
 
+    if range.is_reversed() {
+        points.reverse();
+    }
+
     points
 }
 
@@ -102,12 +106,40 @@ fn number_of_vertices_for_circle(
 #[derive(Clone, Copy, Debug)]
 pub struct RangeOnCurve {
     boundary: [Vertex; 2],
+    is_reversed: bool,
 }
 
 impl RangeOnCurve {
     /// Construct an instance of `RangeOnCurve`
-    pub fn new(boundary: [Vertex; 2]) -> Self {
-        Self { boundary }
+    ///
+    /// Ranges are normalized on construction, meaning that the order of
+    /// vertices passed to this constructor does not influence the range that is
+    /// constructed.
+    ///
+    /// This is done to prevent bugs during mesh construction: The curve
+    /// approximation code is regularly faced with ranges that are reversed
+    /// versions of each other. This can lead to slightly different
+    /// approximations, which in turn leads to the aforementioned invalid
+    /// meshes.
+    ///
+    /// The caller can use `is_reversed` to determine, if the range was reversed
+    /// during normalization, to adjust the approximation accordingly.
+    pub fn new([a, b]: [Vertex; 2]) -> Self {
+        let (boundary, is_reversed) = if a < b {
+            ([a, b], false)
+        } else {
+            ([b, a], true)
+        };
+
+        Self {
+            boundary,
+            is_reversed,
+        }
+    }
+
+    /// Indicate whether the range was reversed during normalization
+    pub fn is_reversed(&self) -> bool {
+        self.is_reversed
     }
 
     /// Access the start of the range