lng/lat を Web Mercator に変換する関数 (#32)

地理座標とWeb Mercatorを相互変換するだけの関数を用意します。

MVT形式でしか使わない予定なので、ひとまず `nusamai-mvt` 内に作りました。

Cargo.toml

@@ -1,9 +1,10 @@
 [workspace]
 
 members = [
+    "app/src-tauri",
     "nusamai-geometry",
     "nusamai-geojson",
     "nusamai-plateau",
-    "app/src-tauri"
+    "nusamai-mvt",
 ]
 resolver = "2"

nusamai-mvt/Cargo.toml

@@ -0,0 +1,6 @@
+[package]
+name = "nusamai-mvt"
+version = "0.1.0"
+edition = "2021"
+
+[dependencies]

nusamai-mvt/src/lib.rs

@@ -0,0 +1 @@
+pub mod webmercator;

nusamai-mvt/src/webmercator.rs

@@ -0,0 +1,54 @@
+use std::f64::consts::FRAC_PI_2;
+
+/// Converts geographic coordinate (lng, lat) to Web Mercator coordinate (mx, my).
+///
+/// The range of (mx, my) is [0.0, 0.0]-[1.0, 1.0] (same as Mapbox/MapLibre API, etc.)
+pub fn lnglat_to_web_mercator(lng: f64, lat: f64) -> (f64, f64) {
+    let mx = (lng + 180.0) / 360.0;
+    let my = ((90.0 + lat).to_radians() / 2.0).tan().ln().to_degrees();
+    let my = (-my + 180.0) / 360.0;
+    (mx, my)
+}
+
+/// Converts Web Mercator coordinate (mx, my) to geographic coordinate (lng, lat).
+///
+/// The range of (mx, my) is [0.0, 0.0]-[1.0, 1.0] (same as Mapbox/MapLibre API, etc.)
+pub fn web_mercator_to_lnglat(mx: f64, my: f64) -> (f64, f64) {
+    let lng = mx * 360.0 - 180.0;
+    let lat = my * 360.0 - 180.0;
+    let lat = -(2.0 * (lat.to_radians().exp()).atan() - FRAC_PI_2).to_degrees();
+    (lng, lat)
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn roundtrip() {
+        {
+            let (lng, lat) = (136.08, 37.39);
+            let (mx, my) = lnglat_to_web_mercator(lng, lat);
+            let (lng2, lat2) = web_mercator_to_lnglat(mx, my);
+            assert!((lng - lng2).abs() < 1e-13);
+            assert!((lat - lat2).abs() < 1e-13);
+        }
+        {
+            let (lng, lat) = (0.3, 0.2);
+            let (mx, my) = lnglat_to_web_mercator(lng, lat);
+            let (lng2, lat2) = web_mercator_to_lnglat(mx, my);
+            assert!((lng - lng2).abs() < 1e-13);
+            assert!((lat - lat2).abs() < 1e-13);
+        }
+    }
+
+    #[test]
+    fn null_island() {
+        // https://en.wikipedia.org/wiki/Null_Island
+        // (lng: 0, lat: 0) -> (mx: 0.5, my: 0.5)
+        let (lng, lat) = (0., 0.);
+        let (mx, my) = lnglat_to_web_mercator(lng, lat);
+        assert!((mx - 0.5).abs() < 1e-10);
+        assert!((my - 0.5).abs() < 1e-10);
+    }
+}