diff --git a/src/bin/flat/tube/mod.rs b/src/bin/flat/tube/mod.rs
index 1681647..81f06a3 100644
--- a/src/bin/flat/tube/mod.rs
+++ b/src/bin/flat/tube/mod.rs
@@ -203,6 +203,23 @@ mod coords {
 		fn global_metric(&self) -> &impl Metric;
 	}
 
+	impl<T: FlatCoordinateSystem<Vec2> + MetricCS> FlatCoordinateSystem<Ray> for T {
+		fn flat_to_global(&self, ray: Ray) -> Ray {
+			let pos = self.flat_to_global(ray.pos);
+			Ray {
+				pos,
+				dir: Mat2::from(self.global_metric().sqrt_at(pos).inverse()) * ray.dir,
+			}
+		}
+
+		fn global_to_flat(&self, ray: Ray) -> Ray {
+			Ray {
+				pos: self.global_to_flat(ray.pos),
+				dir: Mat2::from(self.global_metric().sqrt_at(ray.pos)) * ray.dir,
+			}
+		}
+	}
+
 	impl<T: FlatCoordinateSystem<Vec2> + MetricCS> FlatCoordinateSystem<Location> for T {
 		fn flat_to_global(&self, loc: Location) -> Location {
 			let pos = self.flat_to_global(loc.pos);
@@ -235,22 +252,6 @@ mod coords {
 		}
 	}
 
-	impl FlatCoordinateSystem<Ray> for InnerCS {
-		fn flat_to_global(&self, ray: Ray) -> Ray {
-			Ray {
-				pos: self.flat_to_global(ray.pos),
-				dir: vec2(ray.dir.x, self.0.dy(ray.pos.y) * ray.dir.y),
-			}
-		}
-
-		fn global_to_flat(&self, ray: Ray) -> Ray {
-			Ray {
-				pos: self.global_to_flat(ray.pos),
-				dir: vec2(ray.dir.x, self.0.dv(ray.pos.y) * ray.dir.y),
-			}
-		}
-	}
-
 	impl FlatRegion for InnerCS {
 		fn distance_to_boundary(&self, ray: Ray) -> Option<f32> {
 			Rect { size: vec2(self.0.inner_radius, self.0.internal_halflength) }.trace_out_of(ray)
@@ -285,8 +286,6 @@ mod coords {
 		}
 	}
 
-	impl FlatCoordinateSystem<Ray> for OuterCS {}
-
 	impl FlatRegion for OuterCS {
 		fn distance_to_boundary(&self, ray: Ray) -> Option<f32> {
 			Rect { size: vec2(self.0.outer_radius, self.0.external_halflength) }.trace_into(ray)