Rotate an image to direct to a well know point using compass heading

Question

As a proof of concept, I want to create an application that retrieve the current coordinates, calculate the direction towards an another point and, using compass, rotate an arrow image to direct to that point in space.

I know how to retrieve current coordinate and to rotate the image through CGAffineTransformMakeRotation, but I haven't find a formula to calculate the correct angle.

Any hints?

Answer 1

First you need to calculate a bearing. This page gives a neat formula for doing that:

http://www.movable-type.co.uk/scripts/latlong.html

Then, you can do some simple arithmetic to find the difference between that bearing and the heading the iPhone is pointed towards. Rotate your image by that difference.

Answer 2

Bearing is:

double bearingUsingStartCoordinate(CLLocation *start, CLLocation *end)
{
    double tc1;
    tc1 = 0.0;

    //dlat = lat2 - lat1
    //CLLocationDegrees dlat = end.coordinate.latitude - start.coordinate.latitude; 

    //dlon = lon2 - lon1
    CLLocationDegrees dlon = end.coordinate.longitude - start.coordinate.longitude;

    //y = sin(lon2-lon1)*cos(lat2)
    double y = sin(d2r(dlon)) * cos(d2r(end.coordinate.latitude));

    //x = cos(lat1)*sin(lat2)-sin(lat1)*cos(lat2)*cos(lon2-lon1)
    double x = cos(d2r(start.coordinate.latitude))*sin(d2r(end.coordinate.latitude)) - sin(d2r(start.coordinate.latitude))*cos(d2r(end.coordinate.latitude))*cos(d2r(dlon)); 

    if (y > 0)
    {
        if (x > 0)
            tc1 = r2d(atan(y/x));

        if (x < 0)
            tc1 = 180 - r2d(atan(-y/x));

        if (x == 0)
            tc1 = 90;

    } else if (y < 0)
    {
        if (x > 0)
            tc1 = r2d(-atan(-y/x));

        if (x < 0)
            tc1 = r2d(atan(y/x)) - 180;

        if (x == 0)
            tc1 = 270;

    } else if (y == 0)
    {
        if (x > 0)
            tc1 = 0;

        if (x < 0)
            tc1 = 180;

        if (x == 0)
            tc1 = nan(0);
    }
    if (tc1 < 0)
        tc1 +=360.0;
        return tc1;
}

And for those looking for the distance between two points:

double haversine_km(double lat1, double long1, double lat2, double long2)
{
    double dlong = d2r(long2 - long1);
    double dlat = d2r(lat2 - lat1);
    double a = pow(sin(dlat/2.0), 2) + cos(d2r(lat1)) * cos(d2r(lat2)) * pow(sin(dlong/2.0), 2);
    double c = 2 * atan2(sqrt(a), sqrt(1-a));
    double d = 6367 * c;

    return d;
}

double haversine_mi(double lat1, double long1, double lat2, double long2)
{
    double dlong = d2r(long2 - long1);
    double dlat = d2r(lat2 - lat1);
    double a = pow(sin(dlat/2.0), 2) + cos(d2r(lat1)) * cos(d2r(lat2)) * pow(sin(dlong/2.0), 2);
    double c = 2 * atan2(sqrt(a), sqrt(1-a));
    double d = 3956 * c; 

    return d;
}