convert2DPointToSphereCoordinates function

GlobeCoordinates? convert2DPointToSphereCoordinates(Offset hoverOffset, Offset sphereCenter, double radius, double rotationY, double rotationZ,)

Converts the 2D offset to spherical coordinates.

Takes hoverOffset, sphereCenter, radius, rotationY, and rotationZ as input parameters. hoverOffset is the 2D position of the point on the screen. sphereCenter is the center of the sphere. radius is the radius of the sphere. rotationY and rotationZ are rotation angles around the Y and Z axes, respectively.

Returns a GlobeCoordinates object representing the spherical coordinates of the point. Returns null if the point is not on the sphere.

Implementation

GlobeCoordinates? convert2DPointToSphereCoordinates(Offset hoverOffset,
    Offset sphereCenter, double radius, double rotationY, double rotationZ) {
  // Convert the 2D offset back into 3D coordinates relative to the center
  double x = hoverOffset.dx - sphereCenter.dx;
  double y = hoverOffset.dy - sphereCenter.dy;
  // Assuming z can be derived from x and y considering the radius and the spherical nature
  double z = sqrt(radius * radius - x * x - y * y);

  // Convert back to the original Cartesian coordinate system before rotations were applied
  Vector3 cartesian = Vector3(z, x, -y);

  // Inverse the rotations using rotation matrices
  Matrix3 rotationMatrixY = Matrix3.rotationY(rotationY); // Inverse rotation
  Matrix3 rotationMatrixZ = Matrix3.rotationZ(rotationZ); // Inverse rotation
  Vector3 originalCartesian =
      rotationMatrixZ.multiplied(rotationMatrixY).transform(cartesian);

  // Convert Cartesian coordinates back to spherical coordinates
  double lat = asin(originalCartesian.z / radius);
  double lon;
  if (radius * cos(lat) != 0) {
    // Avoid division by zero
    lon = atan2(originalCartesian.y, originalCartesian.x);
  } else {
    lon = 0;
  }

  // Convert radians back to degrees
  double latitude = radiansToDegrees(lat);
  double longitude = radiansToDegrees(lon);
  if (latitude.isNaN || longitude.isNaN) return null;
  // Return the GlobeCoordinates object
  return GlobeCoordinates(latitude, longitude);
}