Generate random coordinates around a location

Question

I'd like to have a function that accepts a geo location (Latitude, Longitude) and generates random sets of coordinates around it but also takes these parameters as a part of the calculation:

• Number Of Random Coordinates To Make
• Radius to generate in
• Min distance between the random coordinates in meters
• The root coordinates to generate the locations around it.

Example of how the generation would be:

What's a good approach to achieve this?

Answer 1

Generate random coordinates around a location

function generateRandomPoint($centre, $radius) {     $radius_earth = 3959; //miles      //Pick random distance within $distance;     $distance = lcg_value()*$radius;      //Convert degrees to radians.     $centre_rads = array_map( 'deg2rad', $centre );      //First suppose our point is the north pole.     //Find a random point $distance miles away     $lat_rads = (pi()/2) -  $distance/$radius_earth;     $lng_rads = lcg_value()*2*pi();       //($lat_rads,$lng_rads) is a point on the circle which is     //$distance miles from the north pole. Convert to Cartesian     $x1 = cos( $lat_rads ) * sin( $lng_rads );     $y1 = cos( $lat_rads ) * cos( $lng_rads );     $z1 = sin( $lat_rads );       //Rotate that sphere so that the north pole is now at $centre.      //Rotate in x axis by $rot = (pi()/2) - $centre_rads[0];     $rot = (pi()/2) - $centre_rads[0];     $x2 = $x1;     $y2 = $y1 * cos( $rot ) + $z1 * sin( $rot );     $z2 = -$y1 * sin( $rot ) + $z1 * cos( $rot );      //Rotate in z axis by $rot = $centre_rads[1]     $rot = $centre_rads[1];     $x3 = $x2 * cos( $rot ) + $y2 * sin( $rot );     $y3 = -$x2 * sin( $rot ) + $y2 * cos( $rot );     $z3 = $z2;       //Finally convert this point to polar co-ords     $lng_rads = atan2( $x3, $y3 );     $lat_rads = asin( $z3 );      return array_map( 'rad2deg', array( $lat_rads, $lng_rads ) ); } 

Usage

generateRandomPoint(array(3.1528, 101.7038), 4); 

Answer 2

A brute force method should be good enough.

for each point to generate "n"   find a random angle   get the x and y from the angle * a random radius up to max radius   for each point already generated "p"      calculate the distance between "n" and "p"   if "n" satisfies the min distance      add new point "n" 

In PHP, generating a new point is easy

$angle = deg2rad(mt_rand(0, 359)); $pointRadius = mt_rand(0, $radius); $point = array(    'x' => sin($angle) * $pointRadius,    'y' => cos($angle) * $pointRadius ); 

Then calculating the distance between two points

$distance = sqrt(pow($n['x'] - $p['x'], 2) + pow($n['y'] - $p['y'], 2)); 

** Edit **

For the sake of clarifying what others have said, and after doing some further research (I'm not a mathematician, but the comments did make me wonder), here the most simple definition of a gaussian distribution :

If you were in 1 dimension, then $pointRadius = $x * mt_rand(0, $radius); would be OK since there is no distinction between $radius and $x when $x has a gaussian distribution.

In 2 or more dimensions, however, if the coordinates ($x,$y,...) have gaussian distributions then the radius $radius does not have a gaussian distribution.

In fact the distribution of $radius^2 in 2 dimensions [or k dimensions] is what is called the "chi-squared distribution with 2 [or k] degrees of freedom", provided the ($x,$y,...) are independent and have zero means and equal variances.

Therefore, to have a normal distribution, you'd have to change the line of the generated radius to

$pointRadius = sqrt(mt_rand(0, $radius*$radius)); 

as others have suggested.