From ffbc851a321315995832dce4dd88c39754f21f98 Mon Sep 17 00:00:00 2001
From: Priyanshu Singh <123263608+dev-priyanshu15@users.noreply.github.com>
Date: Sun, 13 Oct 2024 07:02:42 +0530
Subject: [PATCH] Create vincenty.rs

---
 src/geometry/vincenty.rs | 88 ++++++++++++++++++++++++++++++++++++++++
 1 file changed, 88 insertions(+)
 create mode 100644 src/geometry/vincenty.rs

diff --git a/src/geometry/vincenty.rs b/src/geometry/vincenty.rs
new file mode 100644
index 00000000000..d459ff65759
--- /dev/null
+++ b/src/geometry/vincenty.rs
@@ -0,0 +1,88 @@
+// Constants for WGS84 Earth ellipsoid model
+const WGS84_A: f64 = 6378137.0;  // Semi-major axis in meters
+const WGS84_B: f64 = 6356752.314245;  // Semi-minor axis in meters
+const WGS84_F: f64 = 1.0 / 298.257223563;  // Flattening
+
+/// Calculate the geodesic distance between two points on Earth using the Vincenty formula
+///
+/// # Arguments
+/// * `lat1` - Latitude of the first point in degrees
+/// * `lon1` - Longitude of the first point in degrees
+/// * `lat2` - Latitude of the second point in degrees
+/// * `lon2` - Longitude of the second point in degrees
+///
+/// # Returns
+/// The distance in meters
+pub fn vincenty(lat1: f64, lon1: f64, lat2: f64, lon2: f64) -> f64 {
+    // Convert latitudes to radians and adjust for the ellipsoid's flattening
+    let reduced_lat1 = (1.0 - WGS84_F) * lat1.to_radians().tan();
+    let reduced_lat2 = (1.0 - WGS84_F) * lat2.to_radians().tan();
+    let delta_longitude = (lon2 - lon1).to_radians();
+
+    // Trigonometric precomputations
+    let sin_lat1 = reduced_lat1.sin();
+    let cos_lat1 = reduced_lat1.cos();
+    let sin_lat2 = reduced_lat2.sin();
+    let cos_lat2 = reduced_lat2.cos();
+
+    let mut lambda = delta_longitude;
+    let mut lambda_prev;
+    let mut iterations = 100;
+
+    let mut sin_sigma;
+    let mut cos_sigma;
+    let mut cos_sq_alpha;
+    let mut cos2_sigma_m;
+    let mut sigma = 0.0;
+
+    // Iterate until convergence or the limit is reached
+    while iterations > 0 {
+        lambda_prev = lambda;
+
+        let sin_lambda = lambda.sin();
+        let cos_lambda = lambda.cos();
+
+        sin_sigma = ((cos_lat2 * sin_lambda).powi(2) + 
+                    (cos_lat1 * sin_lat2 - sin_lat1 * cos_lat2 * cos_lambda).powi(2)).sqrt();
+        if sin_sigma == 0.0 {
+            return 0.0; // Points are coincident
+        }
+
+        cos_sigma = sin_lat1 * sin_lat2 + cos_lat1 * cos_lat2 * cos_lambda;
+        sigma = sin_sigma.atan2(cos_sigma);
+
+        let sin_alpha = cos_lat1 * cos_lat2 * sin_lambda / sin_sigma;
+        cos_sq_alpha = 1.0 - sin_alpha.powi(2);
+
+        cos2_sigma_m = if cos_sq_alpha == 0.0 {
+            0.0 // Equatorial line
+        } else {
+            cos_sigma - 2.0 * sin_lat1 * sin_lat2 / cos_sq_alpha
+        };
+
+        let c = WGS84_F / 16.0 * cos_sq_alpha * (4.0 + WGS84_F * (4.0 - 3.0 * cos_sq_alpha));
+        lambda = delta_longitude + (1.0 - c) * WGS84_F * sin_alpha * (sigma + c * sin_sigma * 
+                (cos2_sigma_m + c * cos_sigma * (-1.0 + 2.0 * cos2_sigma_m.powi(2))));
+
+        if (lambda - lambda_prev).abs() < 1e-12 {
+            break;  // Convergence reached
+        }
+        iterations -= 1;
+    }
+
+    if iterations == 0 {
+        return f64::NAN; // Formula failed to converge
+    }
+
+    // Final calculations for the distance
+    let u_sq = cos_sq_alpha * (WGS84_A.powi(2) - WGS84_B.powi(2)) / WGS84_B.powi(2);
+    let a = 1.0 + u_sq / 16384.0 * (4096.0 + u_sq * (-768.0 + u_sq * (320.0 - 175.0 * u_sq)));
+    let b = u_sq / 1024.0 * (256.0 + u_sq * (-128.0 + u_sq * (74.0 - 47.0 * u_sq)));
+
+    let delta_sigma = b * sin_sigma * (cos2_sigma_m + b / 4.0 * (cos_sigma * (-1.0 + 2.0 * cos2_sigma_m.powi(2)) - 
+                     b / 6.0 * cos2_sigma_m * (-3.0 + 4.0 * sin_sigma.powi(2)) * (-3.0 + 4.0 * cos2_sigma_m.powi(2))));
+
+    let distance = WGS84_B * a * (sigma - delta_sigma);
+
+    distance // distance in meters
+}