feat: Add UTM coordinates #38

ref:

lib/utils/location_formats.dart

@@ -1,3 +1,169 @@
+import 'dart:math' as math;
+
+enum CoordinateDisplayFormat { decimal, dms, utm }
+
+String formatCoordinates(
+  double latitude,
+  double longitude,
+  CoordinateDisplayFormat format,
+) {
+  switch (format) {
+    case CoordinateDisplayFormat.decimal:
+      return '${latitude.toStringAsFixed(5)}, ${longitude.toStringAsFixed(5)}';
+    case CoordinateDisplayFormat.dms:
+      return '${formatDmsCoordinate(latitude, true)} ${formatDmsCoordinate(longitude, false)}';
+    case CoordinateDisplayFormat.utm:
+      return formatUtm(latitude, longitude);
+  }
+}
+
+String formatDmsCoordinate(double degrees, bool isLatitude) {
+  final direction = isLatitude
+      ? (degrees >= 0 ? 'N' : 'S')
+      : (degrees >= 0 ? 'E' : 'W');
+
+  final absolute = degrees.abs();
+  final deg = absolute.floor();
+  final minDecimal = (absolute - deg) * 60;
+  final min = minDecimal.floor();
+  final sec = (minDecimal - min) * 60;
+
+  return '$deg°${min.toString().padLeft(2, '0')}\'${sec.toStringAsFixed(2).padLeft(5, '0')}"$direction';
+}
+
+String formatUtm(double latitude, double longitude) {
+  if (latitude < -80 || latitude > 84) {
+    return formatCoordinates(
+      latitude,
+      longitude,
+      CoordinateDisplayFormat.decimal,
+    );
+  }
+
+  final zone = _utmZone(latitude, longitude);
+  final band = _utmLatitudeBand(latitude);
+  final latRad = _degreesToRadians(latitude);
+  final lonRad = _degreesToRadians(longitude);
+  final centralMeridianRad = _degreesToRadians((zone - 1) * 6 - 180 + 3);
+
+  const semiMajorAxis = 6378137.0;
+  const flattening = 1 / 298.257223563;
+  const scaleFactor = 0.9996;
+  final eccentricitySquared = flattening * (2 - flattening);
+  final secondEccentricitySquared =
+      eccentricitySquared / (1 - eccentricitySquared);
+
+  final sinLat = math.sin(latRad);
+  final cosLat = math.cos(latRad);
+  final tanLat = math.tan(latRad);
+  final n = semiMajorAxis /
+      math.sqrt(1 - eccentricitySquared * sinLat * sinLat);
+  final t = tanLat * tanLat;
+  final c = secondEccentricitySquared * cosLat * cosLat;
+  final a = cosLat * (lonRad - centralMeridianRad);
+
+  final meridianArc = semiMajorAxis *
+      ((1 -
+                  eccentricitySquared / 4 -
+                  3 * eccentricitySquared * eccentricitySquared / 64 -
+                  5 *
+                      eccentricitySquared *
+                      eccentricitySquared *
+                      eccentricitySquared /
+                      256) *
+              latRad -
+          (3 * eccentricitySquared / 8 +
+                  3 * eccentricitySquared * eccentricitySquared / 32 +
+                  45 *
+                      eccentricitySquared *
+                      eccentricitySquared *
+                      eccentricitySquared /
+                      1024) *
+              math.sin(2 * latRad) +
+          (15 * eccentricitySquared * eccentricitySquared / 256 +
+                  45 *
+                      eccentricitySquared *
+                      eccentricitySquared *
+                      eccentricitySquared /
+                      1024) *
+              math.sin(4 * latRad) -
+          (35 *
+                  eccentricitySquared *
+                  eccentricitySquared *
+                  eccentricitySquared /
+                  3072) *
+              math.sin(6 * latRad));
+
+  final easting = scaleFactor *
+          n *
+          (a +
+              (1 - t + c) * a * a * a / 6 +
+              (5 - 18 * t + t * t + 72 * c - 58 * secondEccentricitySquared) *
+                  a *
+                  a *
+                  a *
+                  a *
+                  a /
+                  120) +
+      500000;
+  var northing = scaleFactor *
+      (meridianArc +
+          n *
+              tanLat *
+              (a * a / 2 +
+                  (5 - t + 9 * c + 4 * c * c) * a * a * a * a / 24 +
+                  (61 -
+                          58 * t +
+                          t * t +
+                          600 * c -
+                          330 * secondEccentricitySquared) *
+                      a *
+                      a *
+                      a *
+                      a *
+                      a *
+                      a /
+                      720));
+  if (latitude < 0) {
+    northing += 10000000;
+  }
+
+  return '$zone$band ${easting.round()}E ${northing.round()}N';
+}
+
+int _utmZone(double latitude, double longitude) {
+  var zone = ((longitude + 180) / 6).floor() + 1;
+  if (longitude == 180) {
+    zone = 60;
+  }
+  if (latitude >= 56 &&
+      latitude < 64 &&
+      longitude >= 3 &&
+      longitude < 12) {
+    zone = 32;
+  }
+  if (latitude >= 72 && latitude < 84) {
+    if (longitude >= 0 && longitude < 9) {
+      zone = 31;
+    } else if (longitude >= 9 && longitude < 21) {
+      zone = 33;
+    } else if (longitude >= 21 && longitude < 33) {
+      zone = 35;
+    } else if (longitude >= 33 && longitude < 42) {
+      zone = 37;
+    }
+  }
+  return zone.clamp(1, 60);
+}
+
+String _utmLatitudeBand(double latitude) {
+  const bands = 'CDEFGHJKLMNPQRSTUVWX';
+  final index = ((latitude + 80) / 8).floor().clamp(0, bands.length - 1);
+  return bands[index];
+}
+
+double _degreesToRadians(double degrees) => degrees * math.pi / 180;
+
 String formatPlusCode(double lat, double lon) {
   const base = '23456789CFGHJMPQRVWX';