diff --git a/README.md b/README.md
index df184b7e2..cf330e0f1 100644
--- a/README.md
+++ b/README.md
@@ -27,7 +27,6 @@
 ## フォルダ構成
 
 - アプリケーション：
-  - [`nusamai`](./nusamai/) — アプリケーションバックエンドおよびコマンドライン版の実装
 - 基盤・ユーティリティ：
   - [`nusamai-geometry`](./nusamai-geometry/) — ジオメトリ型
   - [`nusamai-projection`](./nusamai-projection/) — 投影法変換
diff --git a/nusamai-geometry/src/compact/linestring.rs b/nusamai-geometry/src/compact/linestring.rs
index e08cd6691..90b92218b 100644
--- a/nusamai-geometry/src/compact/linestring.rs
+++ b/nusamai-geometry/src/compact/linestring.rs
@@ -1,9 +1,9 @@
 use crate::{Coord, Coord2d};
-use std::borrow::Cow;
+use std::{borrow::Cow, hash::Hash};
 
 /// Computer-friendly LineString
 #[cfg_attr(feature = "serde", derive(serde::Serialize, serde::Deserialize))]
-#[derive(Debug, Clone, Default, PartialEq)]
+#[derive(Debug, Clone, Default)]
 pub struct LineString<'a, T: Coord> {
     /// Coordinates of all points
     ///
@@ -14,6 +14,34 @@ pub struct LineString<'a, T: Coord> {
 pub type LineString2<'a, C = f64> = LineString<'a, [C; 2]>;
 pub type LineString3<'a, C = f64> = LineString<'a, [C; 3]>;
 
+impl PartialEq for LineString2<'_, f64> {
+    fn eq(&self, other: &Self) -> bool {
+        self.coords == other.coords
+    }
+}
+
+impl PartialEq for LineString3<'_, f64> {
+    fn eq(&self, other: &Self) -> bool {
+        self.coords == other.coords
+    }
+}
+
+impl Hash for LineString2<'_, f64> {
+    fn hash<H: std::hash::Hasher>(&self, state: &mut H) {
+        self.coords
+            .iter()
+            .for_each(|c| c.iter().for_each(|a| a.to_bits().hash(state)));
+    }
+}
+
+impl Hash for LineString3<'_, f64> {
+    fn hash<H: std::hash::Hasher>(&self, state: &mut H) {
+        self.coords
+            .iter()
+            .for_each(|c| c.iter().for_each(|a| a.to_bits().hash(state)));
+    }
+}
+
 impl<'a, T: Coord> LineString<'a, T> {
     /// Creates an empty LineString.
     pub fn new() -> Self {
diff --git a/nusamai-geometry/src/compact/polygon.rs b/nusamai-geometry/src/compact/polygon.rs
index 71facf9ca..fbaeb5a1a 100644
--- a/nusamai-geometry/src/compact/polygon.rs
+++ b/nusamai-geometry/src/compact/polygon.rs
@@ -1,4 +1,4 @@
-use std::borrow::Cow;
+use std::{borrow::Cow, hash::Hash};
 
 use crate::Coord2d;
 
@@ -6,7 +6,7 @@ use super::{linestring::LineString, Coord};
 
 /// Computer-friendly Polygon
 #[cfg_attr(feature = "serde", derive(serde::Serialize, serde::Deserialize))]
-#[derive(Debug, Clone, Default, PartialEq)]
+#[derive(Debug, Clone, Default)]
 pub struct Polygon<'a, T: Coord> {
     /// Coordinates
     coords: Cow<'a, [T]>,
@@ -18,6 +18,41 @@ pub struct Polygon<'a, T: Coord> {
 pub type Polygon3<'a, C = f64> = Polygon<'a, [C; 3]>;
 pub type Polygon2<'a, C = f64> = Polygon<'a, [C; 2]>;
 
+impl PartialEq for Polygon3<'_, f64> {
+    fn eq(&self, other: &Self) -> bool {
+        self.exterior() == other.exterior()
+            && self.interiors().zip(other.interiors()).all(|(a, b)| a == b)
+    }
+}
+
+impl PartialEq for Polygon2<'_, f64> {
+    fn eq(&self, other: &Self) -> bool {
+        self.exterior() == other.exterior()
+            && self.interiors().zip(other.interiors()).all(|(a, b)| a == b)
+    }
+}
+
+impl Hash for Polygon2<'_, f64> {
+    fn hash<H: std::hash::Hasher>(&self, state: &mut H) {
+        self.exterior().hash(state);
+        for interior in self.interiors() {
+            interior.hash(state);
+        }
+    }
+}
+
+impl Hash for Polygon3<'_, f64> {
+    fn hash<H: std::hash::Hasher>(&self, state: &mut H) {
+        self.exterior().hash(state);
+        for interior in self.interiors() {
+            interior.hash(state);
+        }
+    }
+}
+
+impl Eq for Polygon3<'_, f64> {}
+impl Eq for Polygon2<'_, f64> {}
+
 impl<'a, T: Coord> Polygon<'a, T> {
     /// Creates an empty Polygon.
     pub fn new() -> Self {
@@ -98,7 +133,7 @@ impl<'a, T: Coord> Polygon<'a, T> {
     }
 
     /// Create a new Polygon by applying the given transformation to all coordinates.
-    pub fn transform<T2: Coord>(&self, f: impl Fn(&T) -> T2) -> Polygon<T2> {
+    pub fn transform<T2: Coord>(self, f: impl Fn(&T) -> T2) -> Polygon<'a, T2> {
         Polygon {
             coords: self.coords.iter().map(f).collect(),
             hole_indices: self.hole_indices.clone(),