diff --git a/src/bin/flat/tube/mod.rs b/src/bin/flat/tube/mod.rs
index 5a3ff2e..b8b5b03 100644
--- a/src/bin/flat/tube/mod.rs
+++ b/src/bin/flat/tube/mod.rs
@@ -3,7 +3,7 @@ use crate::riemann;
 use crate::riemann::Metric;
 use Subspace::{Boundary, Inner, Outer};
 use metric::Tube;
-use coords::Mapper;
+use coords::{MapperInner, MapperOuter};
 use crate::types::{FlatTraceResult, Hit, Location, Object, Ray};
 
 pub mod metric;
@@ -64,11 +64,11 @@ impl Space {
 
 	pub fn trace_inner(&self, ray: Ray) -> FlatTraceResult {
 		assert_eq!(self.which_subspace(ray.pos), Inner);
-		let size = vec2(self.tube.inner_radius, self.tube.internal_halflength);
-		let ray = self.tube.outer_to_inner(ray);
-		assert!(ray.pos.abs().cmple(size).all());
+		let inner = Rect { size: vec2(self.tube.inner_radius, self.tube.internal_halflength) };
+		let ray = self.tube.global_to_inner(ray);
+		assert!(inner.is_inside(ray.pos));
 		let objs = self.list_objects_inner();
-		let dist = Rect { size }.trace_out_of(ray).expect("Can't get outta here!");
+		let dist = inner.trace_out_of(ray).expect("Can't get outta here!");
 		FlatTraceResult {
 			end: Some(self.tube.inner_to_global(ray.forward(dist))),
 			objects: Self::hit_objects(objs.as_slice(), ray, dist, |pos| self.tube.inner_to_global(pos)),
@@ -101,30 +101,16 @@ impl Space {
 	fn list_objects_outer(&self) -> Vec<Object> {
 		self.list_objects(|loc|
 			match self.which_subspace(loc.pos) {
-				Outer => loc,
-				Inner => {
-					let Vec2 { x: u, y } = loc.pos; // в основной СК
-					let v = self.tube.v(y) + y.signum() * (self.tube.external_halflength - self.tube.internal_halflength);
-					Location {
-						pos: vec2(u, v), // в плоском продолжении СК Outer на область Inner
-						rot: self.global_to_flat(loc.pos) * loc.rot,
-					}
-				}
+				Inner | Outer => self.tube.global_to_outer(loc),
 				Boundary => panic!("Object at {} was destroyed by the space curvature", loc.pos),
 			})
 	}
 
 	fn list_objects_inner(&self) -> Vec<Object> {
-		self.list_objects(|Location { pos, rot }|
-			match self.which_subspace(pos) {
-				Inner | Outer => {
-					// NB: не работает для частей Outer с |y| < external_halflength. Но они и не нужны.
-					Location {
-						pos: vec2(pos.x, self.tube.v(pos.y)), // в плоской СК для Inner или её продолжении на Outer
-						rot: self.global_to_flat(pos) * rot,
-					}
-				}
-				Boundary => panic!("Object at {pos} was destroyed by the space curvature"),
+		self.list_objects(|loc|
+			match self.which_subspace(loc.pos) {
+				Inner | Outer => self.tube.global_to_inner(loc),
+				Boundary => panic!("Object at {} was destroyed by the space curvature", loc.pos),
 			})
 	}
 
@@ -225,16 +211,22 @@ fn test_rect() {
 }
 
 mod coords {
-	use glam::{Vec2, vec2};
-	use crate::types::Ray;
-	use super::Tube;
+	use glam::{Mat2, Vec2, vec2};
+	use crate::riemann::Metric;
+	use crate::types::{Location, Ray};
+	use super::{Rect, Tube};
 
-	pub trait Mapper<T> {
+	pub trait MapperInner<T> {
 		fn inner_to_global(self, v: T) -> T;
 		fn global_to_inner(self, v: T) -> T;
 	}
 
-	impl Mapper<Vec2> for Tube {
+	pub trait MapperOuter<T> {
+		fn outer_to_global(self, v: T) -> T;
+		fn global_to_outer(self, v: T) -> T;
+	}
+
+	impl MapperInner<Vec2> for Tube {
 		fn inner_to_global(self, pos: Vec2) -> Vec2 {
 			vec2(pos.x, self.y(pos.y))
 		}
@@ -244,7 +236,7 @@ mod coords {
 		}
 	}
 
-	impl Mapper<Ray> for Tube {
+	impl MapperInner<Ray> for Tube {
 		fn inner_to_global(self, ray: Ray) -> Ray {
 			Ray {
 				pos: self.inner_to_global(ray.pos),
@@ -259,4 +251,49 @@ mod coords {
 			}
 		}
 	}
+
+	impl Tube {
+		fn flat_to_global(&self, at: Vec2) -> Mat2 {
+			Mat2::from(self.sqrt_at(at).inverse())
+		}
+
+		fn global_to_flat(&self, at: Vec2) -> Mat2 {
+			Mat2::from(self.sqrt_at(at))
+		}
+	}
+
+	impl MapperInner<Location> for Tube {
+		fn inner_to_global(self, loc: Location) -> Location {
+			todo!()
+		}
+
+		// NB: не работает для частей Outer с |y| < external_halflength. Но они и не нужны.
+		fn global_to_inner(self, loc: Location) -> Location {
+			Location {
+				pos: vec2(loc.pos.x, self.v(loc.pos.y)), // в плоской СК для Inner или её продолжении на Outer
+				rot: self.global_to_flat(loc.pos) * loc.rot,
+			}
+		}
+	}
+
+	impl MapperOuter<Location> for Tube {
+		fn outer_to_global(self, loc: Location) -> Location {
+			todo!()
+		}
+
+		// NB: имеет разрыв в области Inner на y = 0.
+		fn global_to_outer(self, loc: Location) -> Location {
+			let inner = Rect { size: vec2(self.inner_radius, self.internal_halflength) };
+			if inner.is_inside(loc.pos) {
+				let Vec2 { x: u, y } = loc.pos; // в основной СК
+				let v = self.v(y) + y.signum() * (self.external_halflength - self.internal_halflength);
+				Location {
+					pos: vec2(u, v), // в плоском продолжении СК Outer на область Inner
+					rot: self.global_to_flat(loc.pos) * loc.rot,
+				}
+			} else {
+				loc
+			}
+		}
+	}
 }