random.php

<?php
 */
 function generate_random_point( $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', [ $lat_rads, $lng_rads ] );
 }