Code Implementation of Formula to get a MidPoint Coords between to GPS Positions not working correctly

Question

Good day, I'm fairly new to Objective C Dev and am enquiring to an implementation of the midpoint formula located here http://www.movable-type.co.uk/scripts/latlong.html.

Formula:

Bx = cos(lat2).cos(Δlong)

By = cos(lat2).sin(Δlong)

latm = atan2(sin(lat1) + sin(lat2), √((cos(lat1)+Bx)² + By²))

lonm = lon1 + atan2(By, cos(lat1)+Bx)

My Implementation of this formula in Objective C is.

 - (CLLocationCoordinate2D) getMidPointCoords
 {
    double dLon = (self.toCoordinate.longitude - self.fromCoordinate.longitude) * (M_PI/180);
    double Bx = cos(self.toCoordinate.latitude)*cos(dLon);
    double By = cos(self.toCoordinate.latitude)*sin(dLon);
    double latM = atan2(sin(self.fromCoordinate.latitude)+sin(self.toCoordinate.latitude), sqrt( (cos(self.fromCoordinate.latitude)+Bx)*(cos(self.fromCoordinate.latitude)+Bx) + By*By) );
    double lonM = self.fromCoordinate.longitude + atan2(By, cos(self.fromCoordinate.latitude) + Bx);

    CLLocationCoordinate2D midPoint;
    midPoint.latitude = latM;
    midPoint.longitude = lonM;
 }

When I debug this code though it is clearly returning the incorrect coordinates. So essentially my Question is "Is this because of the fact that I am using doubles?" or is my implementation of this formula simply flauwed?

Thank you in advance to any assistance, or insight provided.

So which variable is computed incorrectly? Did you compute the results with a calculator and compared step-by-step? — Martin R

Unknown Unknown · Accepted Answer · 2012-07-30T12:49:28

The trigonometric functions you are using (sin, cos, atan2) require their parameter to be in radians, not degrees.

For example, in this line:

double Bx = cos(self.toCoordinate.latitude)*cos(dLon);

the cos(self.toCoordinate.latitude) is wrong because self.toCoordinate.latitude is in degrees but cos requires radians.

Everywhere that you call a trigonometric function, first convert the parameter from degrees to radians (multiply degrees by (M_PI/180.0)).

In addition, in this line:

double lonM = self.fromCoordinate.longitude + atan2(...

the self.fromCoordinate.longitude also needs to be converted to radians because the rest of the expression is also in radians.

Finally, at the end latM and lonM will have the midpoint but in radians (not degrees).

So when setting midPoint.latitude and midPoint.longitude, you have to convert latM and lonM from radians back to degrees by multiplying them by (180.0/M_PI).

Code Implementation of Formula to get a MidPoint Coords between to GPS Positions not working correctly

1 Answers