diff --git a/crates/fj-core/src/objects/kinds/cycle.rs b/crates/fj-core/src/objects/kinds/cycle.rs
index 61bb4179a..2e0ac0cf9 100644
--- a/crates/fj-core/src/objects/kinds/cycle.rs
+++ b/crates/fj-core/src/objects/kinds/cycle.rs
@@ -1,7 +1,7 @@
 use fj_math::{Scalar, Winding};
 
 use crate::{
-    geometry::SurfacePath,
+    geometry::{Geometry, SurfacePath},
     objects::{HalfEdge, ObjectSet},
     storage::Handle,
 };
@@ -29,7 +29,7 @@ impl Cycle {
     /// Please note that this is not *the* winding of the cycle, only one of the
     /// two possible windings, depending on the direction you look at the
     /// surface that the cycle is defined on from.
-    pub fn winding(&self) -> Winding {
+    pub fn winding(&self, _: &Geometry) -> Winding {
         // The cycle could be made up of one or two circles. If that is the
         // case, the winding of the cycle is determined by the winding of the
         // first circle.
diff --git a/crates/fj-core/src/objects/kinds/face.rs b/crates/fj-core/src/objects/kinds/face.rs
index 5f65e8c8b..c0f22fc7a 100644
--- a/crates/fj-core/src/objects/kinds/face.rs
+++ b/crates/fj-core/src/objects/kinds/face.rs
@@ -65,8 +65,8 @@ impl Face {
     /// Faces *do* have an orientation, meaning they have definite front and
     /// back sides. The front side is the side, where the face's exterior cycle
     /// is wound counter-clockwise.
-    pub fn coord_handedness(&self, _: &Geometry) -> Handedness {
-        match self.region.exterior().winding() {
+    pub fn coord_handedness(&self, geometry: &Geometry) -> Handedness {
+        match self.region.exterior().winding(geometry) {
             Winding::Ccw => Handedness::RightHanded,
             Winding::Cw => Handedness::LeftHanded,
         }
diff --git a/crates/fj-core/src/operations/sweep/sketch.rs b/crates/fj-core/src/operations/sweep/sketch.rs
index 087ad51a6..d2f6d33a9 100644
--- a/crates/fj-core/src/operations/sweep/sketch.rs
+++ b/crates/fj-core/src/operations/sweep/sketch.rs
@@ -40,7 +40,10 @@ impl SweepSketch for Sketch {
             let region = {
                 // The following code assumes that the sketch is winded counter-
                 // clockwise. Let's check that real quick.
-                assert!(region.exterior().winding().is_ccw());
+                assert!(region
+                    .exterior()
+                    .winding(&core.layers.geometry)
+                    .is_ccw());
 
                 let is_negative_sweep = {
                     let u = match core.layers.geometry.of_surface(&surface).u {
diff --git a/crates/fj-core/src/validate/face.rs b/crates/fj-core/src/validate/face.rs
index fc0bc81ad..3a7c04756 100644
--- a/crates/fj-core/src/validate/face.rs
+++ b/crates/fj-core/src/validate/face.rs
@@ -58,7 +58,7 @@ impl FaceValidationError {
 
     fn check_interior_winding(
         face: &Face,
-        _: &Geometry,
+        geometry: &Geometry,
         errors: &mut Vec<ValidationError>,
     ) {
         if face.region().exterior().half_edges().is_empty() {
@@ -67,7 +67,7 @@ impl FaceValidationError {
             return;
         }
 
-        let exterior_winding = face.region().exterior().winding();
+        let exterior_winding = face.region().exterior().winding(geometry);
 
         for interior in face.region().interiors() {
             if interior.half_edges().is_empty() {
@@ -75,7 +75,7 @@ impl FaceValidationError {
                 // like a job for a different validation check.
                 continue;
             }
-            let interior_winding = interior.winding();
+            let interior_winding = interior.winding(geometry);
 
             if exterior_winding == interior_winding {
                 errors.push(
diff --git a/crates/fj-core/src/validate/sketch.rs b/crates/fj-core/src/validate/sketch.rs
index 53eb034e0..6a23c46ab 100644
--- a/crates/fj-core/src/validate/sketch.rs
+++ b/crates/fj-core/src/validate/sketch.rs
@@ -78,13 +78,13 @@ impl SketchValidationError {
 
     fn check_exterior_cycles(
         sketch: &Sketch,
-        _: &Geometry,
+        geometry: &Geometry,
         _config: &ValidationConfig,
         errors: &mut Vec<ValidationError>,
     ) {
         sketch.regions().iter().for_each(|region| {
             let cycle = region.exterior();
-            if cycle.winding() == Winding::Cw {
+            if cycle.winding(geometry) == Winding::Cw {
                 errors.push(ValidationError::Sketch(
                     SketchValidationError::ClockwiseExteriorCycle {
                         cycle: cycle.clone(),
@@ -96,7 +96,7 @@ impl SketchValidationError {
 
     fn check_interior_cycles(
         sketch: &Sketch,
-        _: &Geometry,
+        geometry: &Geometry,
         _config: &ValidationConfig,
         errors: &mut Vec<ValidationError>,
     ) {
@@ -104,7 +104,7 @@ impl SketchValidationError {
             region
                 .interiors()
                 .iter()
-                .filter(|interior| interior.winding() == Winding::Ccw)
+                .filter(|interior| interior.winding(geometry) == Winding::Ccw)
                 .for_each(|cycle| {
                     errors.push(ValidationError::Sketch(
                         SketchValidationError::CounterClockwiseInteriorCycle {