All of the previous answers are only partially correct. Specially in region like Australia, they always include pole and calculate a very large rectangle even for 10kms.
Specially the algorithm by Jan Philip Matuschek at http://janmatuschek.de/LatitudeLongitudeBoundingCoordinates#UsingIndex included a very large rectangle from (-37, -90, -180, 180) for almost every point in Australia. This hits a large users in database and distance have to be calculated for all of the users in almost half the country.
I found that the Drupal API Earth Algorithm by Rochester Institute of Technology works better around pole as well as elsewhere and is much easier to implement.
https://www.rit.edu/drupal/api/drupal/sites%21all%21modules%21location%21earth.inc/7.54
Use earth_latitude_range and earth_longitude_range from the above algorithm for calculating bounding rectangle
Here is the implementation is Java
/**
* Get bouding rectangle using Drupal Earth Algorithm
* @see https://www.rit.edu/drupal/api/drupal/sites%21all%21modules%21location%21earth.inc/7.54
* @param lat
* @param lng
* @param distance
* @return
*/
default BoundingRectangle getBoundingRectangleDrupalEarthAlgo(double lat, double lng, int distance) {
lng = Math.toRadians(lng);
lat = Math.toRadians(lat);
double radius = earth_radius(lat);
List<Double> retLats = earth_latitude_range(lat, radius, distance);
List<Double> retLngs = earth_longitude_range(lat, lng, radius, distance);
return new BoundingRectangle(retLats.get(0), retLats.get(1), retLngs.get(0), retLngs.get(1));
}
/**
* Calculate latitude range based on earths radius at a given point
* @param latitude
* @param longitude
* @param distance
* @return
*/
default List<Double> earth_latitude_range(double lat, double radius, double distance) {
// Estimate the min and max latitudes within distance of a given location.
double angle = distance / radius;
double minlat = lat - angle;
double maxlat = lat + angle;
double rightangle = Math.PI / 2;
// Wrapped around the south pole.
if (minlat < -rightangle) {
double overshoot = -minlat - rightangle;
minlat = -rightangle + overshoot;
if (minlat > maxlat) {
maxlat = minlat;
}
minlat = -rightangle;
}
// Wrapped around the north pole.
if (maxlat > rightangle) {
double overshoot = maxlat - rightangle;
maxlat = rightangle - overshoot;
if (maxlat < minlat) {
minlat = maxlat;
}
maxlat = rightangle;
}
List<Double> ret = new ArrayList<>();
ret.add((minlat));
ret.add((maxlat));
return ret;
}
/**
* Calculate longitude range based on earths radius at a given point
* @param lat
* @param lng
* @param earth_radius
* @param distance
* @return
*/
default List<Double> earth_longitude_range(double lat, double lng, double earth_radius, int distance) {
// Estimate the min and max longitudes within distance of a given location.
double radius = earth_radius * Math.cos(lat);
double angle;
if (radius > 0) {
angle = Math.abs(distance / radius);
angle = Math.min(angle, Math.PI);
}
else {
angle = Math.PI;
}
double minlong = lng - angle;
double maxlong = lng + angle;
if (minlong < -Math.PI) {
minlong = minlong + Math.PI * 2;
}
if (maxlong > Math.PI) {
maxlong = maxlong - Math.PI * 2;
}
List<Double> ret = new ArrayList<>();
ret.add((minlong));
ret.add((maxlong));
return ret;
}
/**
* Calculate earth radius at given latitude
* @param latitude
* @return
*/
default Double earth_radius(double latitude) {
// Estimate the Earth's radius at a given latitude.
// Default to an approximate average radius for the United States.
double lat = Math.toRadians(latitude);
double x = Math.cos(lat) / 6378137.0;
double y = Math.sin(lat) / (6378137.0 * (1 - (1 / 298.257223563)));
//Make sure earth's radius is in km , not meters
return (1 / (Math.sqrt(x * x + y * y)))/1000;
}
And use the distance calculation formula documented by google maps to calculate distance
https://developers.google.com/maps/solutions/store-locator/clothing-store-locator#outputting-data-as-xml-using-php
To search by kilometers instead of miles, replace 3959 with 6371.
For (Lat, Lng) = (37, -122) and a Markers table with columns lat and lng, the formula is:
SELECT id, ( 3959 * acos( cos( radians(37) ) * cos( radians( lat ) ) * cos( radians( lng ) - radians(-122) ) + sin( radians(37) ) * sin( radians( lat ) ) ) ) AS distance FROM markers HAVING distance < 25 ORDER BY distance LIMIT 0 , 20;
