Calculating heading of compass to a specific coordinate instead of to north

Question

I can't get this algorithm right. I'm trying to make a compass that points at a certain location instead of just pointing to, let's say, north. Something is wrong. I've spent a lot of time trying to figure this out, but i just can't find it. Any ideas?

- (void)locationManager:(CLLocationManager *)manager didUpdateHeading:(CLHeading *)newHeading{

double distanceEast = (location.longitude > 0 && otherLocation.longitude < 0) ? 180 - location.longitude + otherLocation.longitude - -180: otherLocation.longitude - location.longitude;

    if (distanceEast < 0) {
        distanceEast += 360;
    }

    double distanceWest = (location.longitude < 0 && otherLocation.longitude > 0) ? -180 - location.longitude - 180 - otherLocation.longitude : location.longitude - otherLocation.longitude;

    if (distanceWest < 0) {
        distanceWest += 360;
    }

    float latitudinalDifference = (otherLocation.latitude - location.latitude);
    float longitudinalDifference = fmin(distanceEast,distanceWest);

    float arcTan = atan(longitudinalDifference / latitudinalDifference);

        float oldRadian = (-manager.heading.trueHeading *M_PI /180.0f)+arcTan+M_PI;
        float newRadian = (-newHeading.trueHeading *M_PI /180.0f)+arcTan+M_PI;

        CABasicAnimation *animation;
        animation=[CABasicAnimation animationWithKeyPath:@"transform.rotation"];
        animation.fromValue = [NSNumber numberWithFloat:oldRadian];
        animation.toValue = [NSNumber numberWithFloat:newRadian];
        animation.duration = 0.5f;
        directionsArrow.layer.anchorPoint = CGPointMake(0.5, 0.5);

        [directionsArrow.layer addAnimation:animation forKey:@"rotationCompass"];
        directionsArrow.transform = CGAffineTransformMakeRotation(newRadian);
}

Answer 1

double lon = location.longitude - otherLocation.longitude;
double y = sin(lon) * cos(otherLocation.latitude);
double x = cos(location.latitude) * sin(otherLocation.latitude) - sin(location.latitude) * cos(otherLocation.latitude) * cos(lon);
double angle = atan2(y, x);

angle is the bearing between the two locations.

Answer 2

“Map Coordinates Systems” in the Location Awareness Programming Guide says “Specifically, on a Mercator map projection, a straight line drawn between any two points on the map yields a course heading that can be used in actual navigation on the surface of the Earth.” This makes me think you should convert your map coordinates to map points (MKMapPointForCoordinate) and call atan on the difference between map points. (Actually, you should probably use atan2, not atan.) Have you tried that?