Added GPS to UTM coordinate conversions

Author: artzha

math/conversion.h

@@ -0,0 +1,54 @@
+#include <math.h>
+#include <tuple>
+
+std::tuple<double, double, int> gpsToUTM(double lat, double lon) {
+    // Constants for UTM conversion
+    constexpr double a = 6378137.0;           // WGS-84 major axis
+    constexpr double f = 1 / 298.257223563;   // WGS-84 flattening
+    constexpr double k0 = 0.9996;             // UTM scale factor
+    constexpr double e = sqrt(f * (2 - f));   // Eccentricity
+    constexpr double e2 = e * e;
+
+    // UTM Zone
+    int zone = static_cast<int>((lon + 180) / 6) + 1;
+
+    // Convert latitude and longitude to radians
+    double lat_rad = lat * M_PI / 180.0;
+    double lon_rad = lon * M_PI / 180.0;
+
+    // Central meridian of the UTM zone
+    double lon_origin = (zone - 1) * 6 - 180 + 3;
+    double lon_origin_rad = lon_origin * M_PI / 180.0;
+
+    // Calculations for UTM coordinates
+    double N = a / sqrt(1 - e2 * sin(lat_rad) * sin(lat_rad));
+    double T = tan(lat_rad) * tan(lat_rad);
+    double C = e2 / (1 - e2) * cos(lat_rad) * cos(lat_rad);
+    double A = cos(lat_rad) * (lon_rad - lon_origin_rad);
+
+    double M = a * ((1 - e2 / 4 - 3 * e2 * e2 / 64 - 5 * e2 * e2 * e2 / 256) * lat_rad
+                    - (3 * e2 / 8 + 3 * e2 * e2 / 32 + 45 * e2 * e2 * e2 / 1024) * sin(2 * lat_rad)
+                    + (15 * e2 * e2 / 256 + 45 * e2 * e2 * e2 / 1024) * sin(4 * lat_rad)
+                    - (35 * e2 * e2 * e2 / 3072) * sin(6 * lat_rad));
+
+    double easting = k0 * N * (A + (1 - T + C) * A * A * A / 6
+                    + (5 - 18 * T + T * T + 72 * C - 58 * e2) * A * A * A * A * A / 120) + 500000.0;
+
+    double northing = k0 * (M + N * tan(lat_rad) * (A * A / 2
+                    + (5 - T + 9 * C + 4 * C * C) * A * A * A * A / 24
+                    + (61 - 58 * T + T * T + 600 * C - 330 * e2) * A * A * A * A * A * A / 720));
+
+    // Correct for southern hemisphere
+    if (lat < 0) {
+        northing += 10000000.0;
+    }
+
+    return std::make_tuple(easting, northing, zone);
+}
+
+std::tuple<double, double> gpsToGlobalCoord(double lat0, double lon0, double lat1, double lon1) {
+    // Convert latitude and longitude to utm coordinates
+    const auto& [e0, n0, zone0] = gpsToUTM(lat0, lon0);
+    const auto& [e1, n1, zone1] = gpsToUTM(lat1, lon1);
+    return {e1 - e0, n1 - n0};
+}