diff --git a/crates/fj-math/src/triangle.rs b/crates/fj-math/src/triangle.rs
index cbafd436e..2c3cffb32 100644
--- a/crates/fj-math/src/triangle.rs
+++ b/crates/fj-math/src/triangle.rs
@@ -1,4 +1,4 @@
-use parry2d_f64::utils::point_in_triangle::{corner_direction, Orientation};
+use parry2d_f64::utils::point_in_triangle::Orientation;
 use parry3d_f64::query::{Ray, RayCast as _};
 
 use crate::Vector;
@@ -59,8 +59,17 @@ impl<const D: usize> Triangle<D> {
 impl Triangle<2> {
     /// Returns the direction of the line through the points of the triangle.
     pub fn winding_direction(&self) -> Winding {
-        let [v0, v1, v2] = self.points.map(|point| point.to_na());
-        corner_direction(&v0, &v1, &v2).into()
+        let [pa, pb, pc] = self.points.map(|point| point.into());
+        let orient2d = robust_predicates::orient2d(&pa, &pb, &pc);
+
+        if orient2d < 0. {
+            return Winding::Cw;
+        }
+        if orient2d > 0. {
+            return Winding::Ccw;
+        }
+
+        unreachable!("not a triangle")
     }
 }