Calculating angle between two vectors?

Question

I'm developing an iOS app, which has to show POIs (points of interest) depending on device heading. I used CLLocationManager to get user's location and heading. I have one pair of destination's coordinates. Based on this I'm calculating which quarter is that and returning float value of deviation from south (0 degrees) in degrees. I have -/+180 degrees in the north and 0 in the south. Here is code snippet:

-(float)updateTargetLongitude:(float)lon Latitude:(float)lat{
//    //longitude = x
//    //latitude = y
      NSLog(@"current location = (%.5f, %.5f)", [[NSUserDefaults standardUserDefaults] doubleForKey:@"currentLongitude"], [[NSUserDefaults standardUserDefaults] doubleForKey:@"currentLatitude"]);
      float x = lon - [[NSUserDefaults standardUserDefaults] doubleForKey:@"currentLongitude"];
      float y = lat - [[NSUserDefaults standardUserDefaults] doubleForKey:@"currentLatitude"];
      float angle;
      NSLog(@"Searching angle from source (%.5f, %.5f) to destination (%.5f, %.5f)", locationManager.location.coordinate.longitude, locationManager.location.coordinate.latitude, lon, lat);
      if (x == 0 && y == 0) {
          NSLog(@"you're there already!");
          return -0.1;
      }
      if(x == 0 && y > 0){
          NSLog(@"look north");
          angle = 180.0;
      }
      if (x == 0 && y < 0) {
          NSLog(@"look south");
          angle = 0;
      }
      if (x > 0 && y == 0) {
          NSLog(@"look east");
          angle = 90.0;
      }
      if (x < 0 && y == 0) {
          NSLog(@"look west");
          angle = -90;
      }
      if (x > 0 && y > 0) {
          NSLog(@"first quarter");
          angle = -atan2f(y, x) - M_PI_2;
      }
      if (x < 0 && y > 0) {
          NSLog(@"second quarter");
          angle = atan2f(y, x) + M_PI_2;
      }
      if (x < 0 && y < 0) {
          NSLog(@"third quarter");
          angle = atan2f(x, y);
      }
      if (x > 0 && y < 0) {
          NSLog(@"fourth quarter");
          angle = -atan2f(x, y);
      }
      NSLog(@"returning radians angle = %.4f for (%.5f, %.5f) :: degrees = %.3f", angle, y, x, angle * 180 / M_PI);
      return angle * 180 / M_PI ;
}

Somehow I have situation, when target is in fourth quarter, but is -93 degrees from south. I'm lost and I don't have any idea how to fix that...

edit: by quarter I mean Cartesian coordinate system, where +y is north, +x is east and so on!

p.s.: I've read that iPhone compass is really bad, but if so how app like Google maps is working properly?

edit2: I made a mistake with angles. Oficially o have -90 degrees in east and 90 in west.

Answer 1

If I see it correctly, the formula

angle = atan2(x, -y) * 180.0/M_PI;

should work in all quadrants, making all the if statements unnecessary.

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atan2(y, x) returns the angle between the vector (x, y) and the positive x-axis, the return value is always between -pi and pi.

Replacing (y, x) by (x, -y) in the arguments means that the vector is rotated by 90 degrees, therefore the result of the above formula is the angle measured to the negative y-axis, which is what you wanted.

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Update (according to "edit2" in the question): If the requirement is "south = 0 deg", "east = -90 deg", "west = +90 deg" then the formula would be

angle = atan2(-x, -y) * 180.0/M_PI;