Add formulas used in navigation (TheAlgorithms#464)

Author: lucioreyli

src/lib.rs

@@ -9,6 +9,7 @@ pub mod dynamic_programming;
 pub mod general;
 pub mod graph;
 pub mod math;
+pub mod navigation;
 pub mod searching;
 pub mod sorting;
 pub mod string;

src/navigation/bearing.rs

@@ -0,0 +1,40 @@
+use std::f64::consts::PI;
+
+pub fn bearing(lat1: f64, lng1: f64, lat2: f64, lng2: f64) -> f64 {
+    let lat1 = lat1 * PI / 180.0;
+    let lng1 = lng1 * PI / 180.0;
+
+    let lat2 = lat2 * PI / 180.0;
+    let lng2 = lng2 * PI / 180.0;
+
+    let delta_longitude = lng2 - lng1;
+
+    let y = delta_longitude.sin() * lat2.cos();
+    let x = lat1.cos() * lat2.sin() - lat1.sin() * lat2.cos() * delta_longitude.cos();
+
+    let mut brng = y.atan2(x);
+    brng = brng.to_degrees();
+
+    (brng + 360.0) % 360.0
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn testing() {
+        assert_eq!(
+            format!(
+                "{:.0}º",
+                bearing(
+                    -27.2020447088982,
+                    -49.631891179172555,
+                    -3.106362,
+                    -60.025826,
+                )
+            ),
+            "336º"
+        );
+    }
+}

src/navigation/haversine.rs

@@ -0,0 +1,35 @@
+use std::f64::consts::PI;
+
+const EARTH_RADIUS: f64 = 6371000.00;
+
+pub fn haversine(lat1: f64, lng1: f64, lat2: f64, lng2: f64) -> f64 {
+    let delta_dist_lat = (lat2 - lat1) * PI / 180.0;
+    let delta_dist_lng = (lng2 - lng1) * PI / 180.0;
+
+    let cos1 = lat1 * PI / 180.0;
+    let cos2 = lat2 * PI / 180.0;
+
+    let delta_lat = (delta_dist_lat / 2.0).sin().powf(2.0);
+    let delta_lng = (delta_dist_lng / 2.0).sin().powf(2.0);
+
+    let a = delta_lat + delta_lng * cos1.cos() * cos2.cos();
+    let result = 2.0 * a.asin().sqrt();
+
+    result * EARTH_RADIUS
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn testing() {
+        assert_eq!(
+            format!(
+                "{:.2}km",
+                haversine(52.375603, 4.903206, 52.366059, 4.926692) / 1000.0
+            ),
+            "1.92km"
+        );
+    }
+}

src/navigation/mod.rs

@@ -0,0 +1,5 @@
+mod bearing;
+mod haversine;
+
+pub use self::bearing::bearing;
+pub use self::haversine::haversine;