How to calculate the middle point between two points on the Earth in matlab?

Given the latitudes and longitudes of two points, how to get the middle point efficiently?

My trouble is there are millions of point pairs to calculate....

[Sad Grad Student]

could you give an example of your input and the expected output?

[James Tursa]

Middle point on a great circle arc assuming a sphere? Or something else?

How is your data stored?

Answer 1

[Mohammad Abouali]

Go to this page you will find bunch of useful formula. The one that you are looking for is called "midpoint" on that page. You have the JavaScript code, but implementation is rather easy

% lat1,lat2,lon1,lon2 should be in radian
Bx = cos(lat2) * cos(lon2-lon1);
By = cos(lat2) * sin(lon2-lon1);

latMid = atan2(sin(lat1) + sin(lat2), ...
               sqrt( (cos(lat1)+Bx)*(cos(lat1)+Bx) + By*By ) );
lonMid = lon1 + atan2(By, cos(lat1) + Bx);

[Ted Shultz]

Here is the matlab code of the formula provided by Mohammad, but all in degrees. Often lat/lon are in degrees, so this nearly identical code my be easier to use.

function [latMid, lonMid] = midpointLatLon(lat1, lon1, lat2, lon2)
% midpoint of two lat long cord on a sphere, all units are deg

Bx = cosd(lat2) * cosd(lon2-lon1);
By = cosd(lat2) * sind(lon2-lon1);

latMid = atan2d(sind(lat1) + sind(lat2), ...
               sqrt( (cosd(lat1)+Bx)*(cosd(lat1)+Bx) + By*By ) );
lonMid = lon1 + atan2d(By, cosd(lat1) + Bx);

Answer 2

[Ted Shultz]

There is a built in function in the matlab mapping toolbox that does what I think you are looking for: meanm

Mean location of geographic coordinates

Syntax

[latmean,lonmean] = meanm(lat,lon)

[latmean,lonmean] = meanm(lat,lon,units)

[latmean,lonmean] = meanm(lat,lon,ellipsoid)