diff --git a/Cargo.lock b/Cargo.lock
index dcdac5d..ecd1fe5 100644
--- a/Cargo.lock
+++ b/Cargo.lock
@@ -873,6 +873,17 @@ dependencies = [
  "slab",
 ]
 
+[[package]]
+name = "getrandom"
+version = "0.2.14"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "94b22e06ecb0110981051723910cbf0b5f5e09a2062dd7663334ee79a9d1286c"
+dependencies = [
+ "cfg-if 1.0.0",
+ "libc 0.2.153",
+ "wasi",
+]
+
 [[package]]
 name = "gif"
 version = "0.11.4"
@@ -908,6 +919,10 @@ name = "glam"
 version = "0.27.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "9e05e7e6723e3455f4818c7b26e855439f7546cf617ef669d1adedb8669e5cb9"
+dependencies = [
+ "approx",
+ "rand",
+]
 
 [[package]]
 name = "glob"
@@ -1634,6 +1649,12 @@ dependencies = [
  "miniz_oxide 0.3.7",
 ]
 
+[[package]]
+name = "ppv-lite86"
+version = "0.2.17"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "5b40af805b3121feab8a3c29f04d8ad262fa8e0561883e7653e024ae4479e6de"
+
 [[package]]
 name = "proc-macro-crate"
 version = "0.1.5"
@@ -1667,6 +1688,45 @@ dependencies = [
  "proc-macro2",
 ]
 
+[[package]]
+name = "rand"
+version = "0.8.5"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "34af8d1a0e25924bc5b7c43c079c942339d8f0a8b57c39049bef581b46327404"
+dependencies = [
+ "libc 0.2.153",
+ "rand_chacha",
+ "rand_core",
+]
+
+[[package]]
+name = "rand_chacha"
+version = "0.3.1"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "e6c10a63a0fa32252be49d21e7709d4d4baf8d231c2dbce1eaa8141b9b127d88"
+dependencies = [
+ "ppv-lite86",
+ "rand_core",
+]
+
+[[package]]
+name = "rand_core"
+version = "0.6.4"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "ec0be4795e2f6a28069bec0b5ff3e2ac9bafc99e6a9a7dc3547996c5c816922c"
+dependencies = [
+ "getrandom",
+]
+
+[[package]]
+name = "rand_pcg"
+version = "0.3.1"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "59cad018caf63deb318e5a4586d99a24424a364f40f1e5778c29aca23f4fc73e"
+dependencies = [
+ "rand_core",
+]
+
 [[package]]
 name = "raw-window-handle"
 version = "0.3.4"
@@ -1724,6 +1784,8 @@ dependencies = [
  "flo_draw",
  "glam",
  "itertools-num",
+ "rand",
+ "rand_pcg",
 ]
 
 [[package]]
@@ -2114,6 +2176,12 @@ dependencies = [
  "winapi-util",
 ]
 
+[[package]]
+name = "wasi"
+version = "0.11.0+wasi-snapshot-preview1"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "9c8d87e72b64a3b4db28d11ce29237c246188f4f51057d65a7eab63b7987e423"
+
 [[package]]
 name = "wayland-client"
 version = "0.28.6"
diff --git a/Cargo.toml b/Cargo.toml
index 7b8cfd7..2ad40d6 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -12,10 +12,12 @@ panic = 'abort'
 opt-level = 3
 
 [dependencies]
-glam = "0.27.0"
+glam = { version = "0.27.0", features = ["approx", "fast-math", "rand"] }
 flo_draw = "0.3.1"
 flo_canvas = "0.3.1"
 itertools-num = "0.1.3"
 
 [dev-dependencies]
 approx = "0.5.1"
+rand = "0.8.5"
+rand_pcg = "0.3.1"
diff --git a/src/bin/flat/riemann.rs b/src/bin/flat/riemann.rs
index 24b154f..a06ae24 100644
--- a/src/bin/flat/riemann.rs
+++ b/src/bin/flat/riemann.rs
@@ -1,5 +1,6 @@
 use glam::*;
 
+#[derive(Copy, Clone, Debug, PartialEq)]
 pub struct Decomp2 {
 	pub ortho: Mat2,
 	pub diag: Vec2,
@@ -13,7 +14,7 @@ impl Decomp2 {
 		}
 	}
 
-	pub(crate) fn inverse(&self) -> Self {
+	pub fn inverse(&self) -> Self {
 		Self {
 			ortho: self.ortho,
 			diag: Vec2::splat(1.0) / self.diag,
@@ -146,3 +147,49 @@ fn t2() {
 	assert_eq!(t[0].col(1)[1], 6.0);
 	assert_eq!(t[1].col(1)[1], 7.0);
 }
+
+pub mod samples {
+	use glam::{Mat2, Vec2};
+
+	use super::{Decomp2, Metric};
+
+	pub struct ScaledMetric {
+		pub scale: Vec2,
+	}
+
+	impl Metric for ScaledMetric {
+		fn sqrt_at(&self, _pos: Vec2) -> Decomp2 {
+			Decomp2 {
+				diag: self.scale,
+				ortho: Mat2::IDENTITY,
+			}
+		}
+	}
+}
+
+#[cfg(test)]
+mod tests {
+	use glam::{Mat2, mat2, vec2};
+	use rand::{Rng, SeedableRng};
+
+	use super::{Decomp2, Metric, samples};
+
+	#[test]
+	fn uniform_scaled_metric() {
+		let mut rng = rand_pcg::Pcg64Mcg::seed_from_u64(17);
+		let metric = samples::ScaledMetric { scale: vec2(3., 4.) };
+		assert_eq!(metric.sqrt_at(rng.gen()), Decomp2 { ortho: Mat2::IDENTITY, diag: vec2(3., 4.) });
+		assert_eq!(metric.at(rng.gen()), Mat2::from_cols_array(&[9., 0., 0., 16.]));
+		assert_eq!(metric.inverse_at(rng.gen()), Mat2::from_cols_array(&[1. / 9., 0., 0., 1. / 16.]));
+		assert_eq!(metric.part_derivs_at(rng.gen()), [Mat2::ZERO, Mat2::ZERO]);
+		assert_eq!(metric.vec_length_at(rng.gen(), vec2(1., 0.)), 3.);
+		assert_eq!(metric.vec_length_at(rng.gen(), vec2(0., 1.)), 4.);
+		assert_eq!(metric.vec_length_at(rng.gen(), vec2(1., 1.)), 5.);
+		assert_eq!(metric.normalize_vec_at(rng.gen(), vec2(1., 0.)), vec2(1. / 3., 0.));
+		assert_eq!(metric.normalize_vec_at(rng.gen(), vec2(0., 1.)), vec2(0., 1. / 4.));
+		assert_eq!(metric.normalize_vec_at(rng.gen(), vec2(1., 1.)), vec2(1. / 5., 1. / 5.));
+		assert_eq!(metric.globalize(rng.gen(), vec2(1., 0.)), vec2(1. / 3., 0.));
+		assert_eq!(metric.globalize(rng.gen(), vec2(0., 1.)), vec2(0., 1. / 4.));
+		assert_eq!(metric.globalize(rng.gen(), vec2(1., 1.)), vec2(1. / 3., 1. / 4.));
+	}
+}
diff --git a/src/bin/flat/tube/coords.rs b/src/bin/flat/tube/coords.rs
index de2e614..cd5ba46 100644
--- a/src/bin/flat/tube/coords.rs
+++ b/src/bin/flat/tube/coords.rs
@@ -113,13 +113,34 @@ impl FlatRegion for OuterCS {
 }
 
 #[cfg(test)]
-mod test {
+mod tests {
 	use approx::{AbsDiffEq, assert_abs_diff_eq};
-	use glam::{Mat2, vec2, Vec2};
+	use glam::{Mat2, mat2, vec2, Vec2};
 	use itertools_num::linspace;
 
+	use crate::riemann::samples;
+
 	use super::*;
 
+	#[test]
+	fn uniform_scaled_metric() {
+		struct Scaled(samples::ScaledMetric, Vec2);
+		impl FlatCoordinateSystem<Vec2> for Scaled {
+			fn flat_to_global(&self, pos: Vec2) -> Vec2 { (pos - self.1) / self.0.scale }
+			fn global_to_flat(&self, pos: Vec2) -> Vec2 { pos * self.0.scale + self.1 }
+		}
+		impl MetricCS for Scaled {
+			fn global_metric(&self) -> &impl Metric { &self.0 }
+		}
+		let cs = Scaled(samples::ScaledMetric { scale: vec2(3., 4.) }, vec2(2., 3.));
+		assert_eq!(cs.global_to_flat(vec2(7., 3.)), vec2(23., 15.));
+		assert_eq!(cs.flat_to_global(vec2(8., 7.)), vec2(2., 1.));
+		assert_eq!(cs.global_to_flat(Ray { pos: vec2(7., 3.), dir: vec2(3., 2.) }), Ray { pos: vec2(23., 15.), dir: vec2(9., 8.) });
+		assert_eq!(cs.flat_to_global(Ray { pos: vec2(23., 15.), dir: vec2(9., 8.) }), Ray { pos: vec2(7., 3.), dir: vec2(3., 2.) });
+		assert_eq!(cs.global_to_flat(Location { pos: vec2(2., 1.), rot: mat2(vec2(0., 1.), vec2(-1., 0.)) }), Location { pos: vec2(8., 7.), rot: mat2(vec2(0., 4.), vec2(-3., 0.)) });
+		assert_eq!(cs.flat_to_global(Location { pos: vec2(2., 1.), rot: mat2(vec2(0., 1.), vec2(-1., 0.)) }), Location { pos: vec2(0., -0.5), rot: mat2(vec2(0., 0.25), vec2(-1. / 3., 0.)) });
+	}
+
 	fn test_flat_region(region: &impl FlatRegion, range_global: (Vec2, Vec2), range_flat: (Vec2, Vec2)) {
 		const ε: f32 = 1e-3;
 		macro_rules! assert_eq_at {
diff --git a/src/bin/flat/tube/metric.rs b/src/bin/flat/tube/metric.rs
index 03ab641..308a8ee 100644
--- a/src/bin/flat/tube/metric.rs
+++ b/src/bin/flat/tube/metric.rs
@@ -168,7 +168,6 @@ mod test {
 			let Δ = vec2(0.0, 2.0 * (space.tube.internal_halflength + off));
 			let dir = Δ / (steps as f32);
 			let traced = space.trace_iter(Ray { pos: a, dir }).nth(steps).unwrap();
-			println!("{traced:?}");
 			assert_abs_diff_eq!(traced.pos.x, b.x, epsilon=1.0e-1);
 			assert_abs_diff_eq!(traced.pos.y, b.y, epsilon=1.0e0);
 			assert_abs_diff_eq!(traced.dir.x, dir.x, epsilon=1.0e-2);
diff --git a/src/bin/flat/types.rs b/src/bin/flat/types.rs
index 101348a..2edc6d8 100644
--- a/src/bin/flat/types.rs
+++ b/src/bin/flat/types.rs
@@ -20,7 +20,7 @@ impl std::ops::Mul<Ray> for Mat2 {
 	}
 }
 
-#[derive(Copy, Clone, Debug)]
+#[derive(Copy, Clone, Debug, PartialEq)]
 pub struct Location {
 	/// Положение в основной СК
 	pub pos: Vec2,