Answer by cffk for PHP Select a random lon/lat within a certain radius

The following Matlab code samples points uniformly on the ellipsoid within a specifieddistance of a center point.

function [lat, lon] = geosample(lat0, lon0, r0, n)% [lat, lon] = geosample(lat0, lon0, r0, n)%% Return n points on the WGS84 ellipsoid within a distance r0 of% (lat0,lon0) and uniformly distributed on the surface.  The returned% lat and lon are n x 1 vectors.%% Requires Matlab package%  http://www.mathworks.com/matlabcentral/fileexchange/39108  todo = true(n,1); lat = zeros(n,1); lon = lat;  while any(todo)    n1 = sum(todo);    r = r0 * max(rand(n1,2), [], 2);  % r = r0*sqrt(U) using cheap sqrt    azi = 180 * (2 * rand(n1,1) - 1); % sample azi uniformly    [lat(todo), lon(todo), ~, ~, m, ~, ~, sig] = ...        geodreckon(lat0, lon0, r, azi);    % Only count points with sig <= 180 (otherwise it's not a shortest    % path).  Also because of the curvature of the ellipsoid, large r    % are sampled too frequently, by a factor r/m.  This following    % accounts for this...    todo(todo) = ~(sig <= 180 & r .* rand(n1,1) <= m);  endend

This code samples uniformly within a circle on the azimuthal equidistantprojection centered at lat0, lon0. The radial, resp. azimuthal,scale for this projection is 1, resp. r/m. Hence the arealdistortion is r/m and this is accounted for by accepting such pointswith a probability m/r.

This code also accounts for the situation where r0 is about half thecircumference of the earth and avoids double sampling nearly antipodalpoints.