added rhumb line distance algorithm to navigation module

Author: showmyth

DIRECTORY.md

@@ -262,6 +262,7 @@
   * Navigation
     * [Bearing](https://github.com/TheAlgorithms/Rust/blob/master/src/navigation/bearing.rs)
     * [Haversine](https://github.com/TheAlgorithms/Rust/blob/master/src/navigation/haversine.rs)
+    * [Rhumbline](https://github.com/TheAlgorithms/Rust/blob/master/src/navigation/rhumbline.rs)
   * Number Theory
     * [Compute Totient](https://github.com/TheAlgorithms/Rust/blob/master/src/number_theory/compute_totient.rs)
     * [Euler Totient](https://github.com/TheAlgorithms/Rust/blob/master/src/number_theory/euler_totient.rs)

src/navigation/mod.rs

@@ -1,5 +1,8 @@
 mod bearing;
 mod haversine;
-
+mod rhumbline;
 pub use self::bearing::bearing;
 pub use self::haversine::haversine;
+pub use self::rhumbline::rhumb_bearing;
+pub use self::rhumbline::rhumb_destination;
+pub use self::rhumbline::rhumb_dist;

src/navigation/rhumbline.rs

@@ -0,0 +1,85 @@
+use std::f64::consts::PI;
+
+const EARTH_RADIUS: f64 = 6371000.0;
+
+pub fn rhumb_dist(lat1: f64, long1: f64, lat2: f64, long2: f64) -> f64 {
+    let phi1 = lat1 * PI / 180.00;
+    let phi2 = lat2 * PI / 180.00;
+    let del_phi = phi2 - phi1;
+    let mut del_lambda = (long2 - long1) * PI / 180.00;
+
+    if del_lambda > PI {
+        del_lambda -= 2.00 * PI;
+    } else if del_lambda < -PI {
+        del_lambda += 2.00 * PI;
+    }
+
+    let del_psi = ((phi2 / 2.00 + PI / 4.00).tan() / (phi1 / 2.00 + PI / 4.00).tan()).ln();
+    let q = match del_psi.abs() > 1e-12 {
+        true => del_phi / del_psi,
+        false => phi1.cos(),
+    };
+
+    (del_phi.powf(2.00) + (q * del_lambda).powf(2.00)).sqrt() * EARTH_RADIUS
+}
+
+pub fn rhumb_bearing(lat1: f64, long1: f64, lat2: f64, long2: f64) -> f64 {
+    let phi1 = lat1 * PI / 180.00;
+    let phi2 = lat2 * PI / 180.00;
+    let mut del_lambda = (long2 - long1) * PI / 180.00;
+
+    if del_lambda > PI {
+        del_lambda -= 2.00 * PI;
+    } else if del_lambda < -PI {
+        del_lambda += 2.00 * PI;
+    }
+
+    let del_psi = ((phi2 / 2.00 + PI / 4.00).tan() / (phi1 / 2.00 + PI / 4.00).tan()).ln();
+    let bearing = del_lambda.atan2(del_psi) * 180.0 / PI;
+    (bearing + 360.00) % 360.00
+}
+pub fn rhumb_destination(lat: f64, long: f64, distance: f64, bearing: f64) -> (f64, f64) {
+    let del = distance / EARTH_RADIUS;
+    let phi1 = lat * PI / 180.00;
+    let lambda1 = long * PI / 180.00;
+    let theta = bearing * PI / 180.00;
+
+    let del_phi = del * theta.cos();
+    let phi2 = (phi1 + del_phi).clamp(-PI / 2.0, PI / 2.0);
+
+    let del_psi = ((phi2 / 2.00 + PI / 4.00).tan() / (phi1 / 2.0 + PI / 4.0).tan()).ln();
+    let q = match del_psi.abs() > 1e-12 {
+        true => del_phi / del_psi,
+        false => phi1.cos(),
+    };
+
+    let del_lambda = del * theta.sin() / q;
+    let lambda2 = lambda1 + del_lambda;
+
+    (phi2 * 180.00 / PI, lambda2 * 180.00 / PI)
+}
+
+//TESTS
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn test_rhumb_distance() {
+        let distance = rhumb_dist(28.5416, 77.2006, 28.5457, 77.1928);
+        assert!(distance > 700.00 && distance < 1000.0);
+    }
+
+    #[test]
+    fn test_rhumb_bearing() {
+        let bearing = rhumb_bearing(28.5416, 77.2006, 28.5457, 77.1928);
+        assert!((bearing - 300.0).abs() < 5.0);
+    }
+
+    #[test]
+    fn test_rhumb_destination_point() {
+        let (lat, lng) = rhumb_destination(28.5457, 77.1928, 1000.00, 305.0);
+        assert!((lat - 28.550).abs() < 0.010);
+        assert!((lng - 77.1851).abs() < 0.010);
+    }
+}