Averaged Coordinates – How to Compute an Averaged Latitude and Longitude Coordinates

latitude longitude

How can I compute the average between several latitude and longitude spots?

Should I just compute the Arithmetic mean for both lat and lng?

Best Answer

For a simple mean, you do not want to average the longitude and latitude coordinates. This might work pretty well at lower latitudes, but at higher latitudes it will begin to give poor results and completely break down near the poles.

The method I've used for this type of thing is to convert the longitude/latitude coordinates to 3d cartesian coordinates (x,y,z). Average these (to give a cartesian vector), and then convert back again. Note that you probably do not need to normalize the vector, so the actual average process could be a simple sum.

Edit, here is my code:

The following converts cartesian coordinates to latitude/longitude (in degrees): Remove the RAD2DEG constants for radians. 

Latitude = MPUtility.RAD2DEG * Math.Atan2(z, Math.Sqrt(x * x + y * y));
Longitude = MPUtility.RAD2DEG * Math.Atan2(-y, x);

And here we calculate cartesian coordinates from latitude/longitude (specified in radians):

private void CalcCartesianCoord()
{
    _x = Math.Sin(LatitudeRadians) * Math.Cos(LongitudeRadians);
    _y = Math.Sin(LatitudeRadians) * Math.Sin(LongitudeRadians);
    _z = Math.Cos(LatitudeRadians); 
}

Both are cut & pasted from real code, hence the mix of degrees and radians. There are properties here which do some of the conversions (eg. LatitudeRadians is a property that returns a radian value).

Note that optimization is possible: the duplicate sine calculations, for instance. Also the trig calculations might be cacheable if you call them a lot.

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