diff --git a/src/bin/flat/tube/mod.rs b/src/bin/flat/tube/mod.rs
index b5cac7a..41e6553 100644
--- a/src/bin/flat/tube/mod.rs
+++ b/src/bin/flat/tube/mod.rs
@@ -230,9 +230,10 @@ mod coords {
 
 	impl FlatCoordinateSystem<Location> for InnerCS {
 		fn flat_to_global(&self, loc: Location) -> Location {
+			let pos = self.flat_to_global(loc.pos);
 			Location {
-				pos: self.flat_to_global(loc.pos),
-				rot: Mat2::from(self.0.sqrt_at(loc.pos).inverse()) * loc.rot,
+				pos,
+				rot: Mat2::from(self.0.sqrt_at(pos).inverse()) * loc.rot,
 			}
 		}
 
@@ -280,9 +281,10 @@ mod coords {
 
 	impl FlatCoordinateSystem<Location> for OuterCS {
 		fn flat_to_global(&self, loc: Location) -> Location {
+			let pos = self.flat_to_global(loc.pos);
 			Location {
-				pos: self.flat_to_global(loc.pos),
-				rot: Mat2::from(self.0.sqrt_at(loc.pos).inverse()) * loc.rot,
+				pos,
+				rot: Mat2::from(self.0.sqrt_at(pos).inverse()) * loc.rot,
 			}
 		}
 
@@ -340,6 +342,7 @@ mod coords {
 					check_range("global", pos_global, range_global, "flat", pos_flat, range_flat);
 					assert_eq_at!(pos_global, region.global_to_flat(Location { pos: pos_global, rot: Mat2::IDENTITY }).pos, pos_flat);
 					assert_eq_at!(pos_global, region.flat_to_global(pos_flat), pos_global);
+					assert_eq_at!(pos_global, region.flat_to_global(region.global_to_flat(Location { pos: pos_global, rot: Mat2::IDENTITY })).rot, Mat2::IDENTITY);
 				}
 			}
 			for x in linspace(range_flat.0.x, range_flat.1.x, 20) {
@@ -349,6 +352,7 @@ mod coords {
 					check_range("flat", pos_flat, range_flat, "global", pos_global, range_global);
 					assert_eq_at!(pos_flat, region.flat_to_global(Location { pos: pos_flat, rot: Mat2::IDENTITY }).pos, pos_global);
 					assert_eq_at!(pos_flat, region.global_to_flat(pos_global), pos_flat);
+					assert_eq_at!(pos_global, region.global_to_flat(region.flat_to_global(Location { pos: pos_global, rot: Mat2::IDENTITY })).rot, Mat2::IDENTITY);
 				}
 			}
 		}