calculateGeodesicLineIntersection static method

LatLng? calculateGeodesicLineIntersection(LatLng start1, LatLng end1, LatLng start2, LatLng end2,)

Calculates the intersection point of two geodesic lines defined by their starting and ending points.

start1 - The LatLng coordinates of the starting point of the first line.

end1 - The LatLng coordinates of the ending point of the first line.

start2 - The LatLng coordinates of the starting point of the second line.

end2 - The LatLng coordinates of the ending point of the second line.

Returns the intersection point as a LatLng object, or null if no intersection is found.

Implementation

static LatLng? calculateGeodesicLineIntersection(
    LatLng start1, LatLng end1, LatLng start2, LatLng end2) {
  const double earthRadius = 6371000; // Earth's radius in meters

  final Distance distance = const Distance();
  final num bearing13 = initialBearing(start1, end1);
  final num bearing23 = initialBearing(start2, end2);
  final num lat1 = (start1.latitude).toRadians();
  final num lon1 = (start1.longitude).toRadians();
  final num lat2 = (start2.latitude).toRadians();
  final num lon2 = (start2.longitude).toRadians();
  final num lat3 = (end2.latitude).toRadians();

  final num dLon = lon2 - lon1;

  final num dist12 = distance(start1, start2);
  if (dist12 == 0) {
    return null; // The two starting points are the same.
  }

  final num alpha1 = bearing13;
  final num alpha2 = bearing23;
  final num alpha3 = acos(cos(dist12 / earthRadius) /
      (cos(lat1) * cos(lat2) * sin(alpha1) * sin(alpha2) * sin(dLon)));
  final num dist13 = earthRadius * alpha3;
  final num bearingA = asin(sin(alpha1) * sin(dist13 / earthRadius));
  final num bearingB = asin(sin(alpha2) * sin(dist13 / earthRadius));

  final num alpha4 = acos(-cos(dist13 / earthRadius) /
      (cos(lat1) * cos(lat3) * sin(bearingA) * sin(bearingB)));
  final num dist14 = earthRadius * alpha4;

  if (dist14.isNaN) {
    return null; // No intersection found.
  }

  final num lat4 = atan2(
      sin(lat1) * cos(dist14 / earthRadius) * sin(bearingA),
      cos(lat1) * sin(dist14 / earthRadius) * sin(bearingA) * cos(bearing13) -
          sin(lat1) *
              cos(dist14 / earthRadius) *
              cos(bearingA) *
              sin(bearing13) +
          cos(lat1) *
              cos(dist14 / earthRadius) *
              cos(bearingA) *
              cos(bearing13));

  final num lon4 = lon1 +
      atan2(
          sin(bearing13) * sin(dist14 / earthRadius) * sin(bearingA),
          cos(dist14 / earthRadius) -
              sin(lat1) * sin(lat4) -
              cos(lat1) * cos(lat4) * cos(bearingA));
  return LatLng((lat4).toDegrees(), (lon4).toDegrees());
}