Question

2

Generate random geo coordinates within specific radius from seed point

rated 0 times [ 6] [ 4] / answers: 1 / hits: 19622 / 9 Years ago, thu, july 2, 2015, 12:00:00

I'm using the following function to generate random geo coordinates within a specified radius from a seed point:

function randomGeo(center, radius) {

    var y0 = center.latitude;

    var x0 = center.longitude;

    var rd = radius / 111300;



    var u = Math.random();

    var v = Math.random();



    var w = rd * Math.sqrt(u);

    var t = 2 * Math.PI * v;

    var x = w * Math.cos(t);

    var y = w * Math.sin(t);



    var xp = x / Math.cos(y0);



    return {

        'latitude': y + y0,

        'longitude': xp + x0

    };

}

I do this in a loop, several times, using a 2000m radius and the following seed point:

location: { // Oxford

    latitude: 51.73213,

    longitude: -1.20631

}

I'd expect all of these results to be within 2000m; instead, I'm seeing values upwards of 10000m:

[ { latitude: 51.73256540025445, longitude: -1.3358092771716716 },   // 3838.75070783092

  { latitude: 51.7214165686511, longitude: -1.1644147572878725 },    // 3652.1890457730474

  { latitude: 51.71721400063117, longitude: -1.2082082568884593 },   // 8196.861603477768

  { latitude: 51.73583824510363, longitude: -1.0940424351649711 },   // 5104.820455873758

  { latitude: 51.74017571473442, longitude: -1.3150742602532257 },   // 4112.3279147866215

  { latitude: 51.73496163915278, longitude: -1.0379454413532996 },   // 9920.01459343298

  { latitude: 51.73582333121239, longitude: -1.0939302282840453 },   // 11652.160906253064

  { latitude: 51.72145745285658, longitude: -1.2491630482776055 },   // 7599.550622138115

  { latitude: 51.73036335927129, longitude: -1.3516902043395063 },   // 8348.276271205428

  { latitude: 51.748104753808924, longitude: -1.2669212014250266 },  // 8880.760669882042

  { latitude: 51.72010719621805, longitude: -1.327161328951446 },    // 8182.466715589904

  { latitude: 51.725727610071125, longitude: -1.0691503599266818 } ] // 2026.3687763449955

Given that I (shamelessly!) plagiarized this solution from elsewhere (albeit I've seen several similar implementations), I can't seem to figure out where the math is going wrong.

(Also, in case you want it, this is how I'm calculating the distance. Pretty sure this is correct.)

function distance(lat1, lon1, lat2, lon2) {

    var R = 6371000;

    var a = 0.5 - Math.cos((lat2 - lat1) * Math.PI / 180) / 2 + Math.cos(lat1 * Math.PI / 180) * Math.cos(lat2 * Math.PI / 180) * (1 - Math.cos((lon2 - lon1) * Math.PI / 180)) / 2;

    return R * 2 * Math.asin(Math.sqrt(a));

}

Answers

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samir

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1 Year ago

answered 9 Years ago braydon · Accepted Answer

The problem seems to stem from the fact that this is just an inaccurate calculation depending on which center point you are using. Particularly this line:

var xp = x / Math.cos(y0);

Removing this line and changing longitude to

'longitude': x + x0

Seems to keep all of the points within the specified radius, although without this line it seems the points will not completely fill out east to west in some cases.

Anyway, I found someone experiencing a similar issue here with someone elses Matlab code as a possible solution. Depends on how uniformly spread out you need the random points if you wanted to work with a different formula.

Here is a google maps visualization of what's going on with your provided formula:

<!doctype html>

<html>

<head>

    <script type=text/javascript src=//maps.google.com/maps/api/js?sensor=false></script>

    <script type=text/javascript src=//ajax.googleapis.com/ajax/libs/jquery/2.1.4/jquery.min.js></script>



    <script>

    var distanceLimit = 2000; //in meters

    var numberRandomPoints = 200;

    var mapZoomLevel = 11;

    var locationindex = 0;

    var locations = [

        {'name': 'Oxford, England', 'latitude': 51.73213, 'longitude': -1.20631},

        {'name': 'Quito, Ecuador', 'latitude': -0.2333, 'longitude': -78.5167},

        {'name': 'Ushuaia, Argentina', 'latitude': -54.8000, 'longitude': -68.3000},

        {'name': 'McMurdo Station, Antartica', 'latitude': -77.847281, 'longitude': 166.667942},

        {'name': 'Norilsk, Siberia', 'latitude': 69.3333, 'longitude': 88.2167},

        {'name': 'Greenwich, England', 'latitude': 51.4800, 'longitude': 0.0000},

        {'name': 'Suva, Fiji', 'latitude': -18.1416, 'longitude': 178.4419},

        {'name': 'Tokyo, Japan', 'latitude': 35.6833, 'longitude': 139.6833},

        {'name': 'Mumbai, India', 'latitude': 18.9750, 'longitude': 72.8258},

        {'name': 'New York, USA', 'latitude': 40.7127, 'longitude': -74.0059},

        {'name': 'Moscow, Russia', 'latitude': 55.7500, 'longitude': 37.6167},

        {'name': 'Cape Town, South Africa', 'latitude': -33.9253, 'longitude': 18.4239},

        {'name': 'Cairo, Egypt', 'latitude': 30.0500, 'longitude': 31.2333},

        {'name': 'Sydney, Australia', 'latitude': -33.8650, 'longitude': 151.2094},

    ];

    </script>

</head>

<body>

<div id=topbar>

    <select id=location_switch>

    <script>

        for (i=0; i<locations.length; i++) {

            document.write('<option value=' + i + '>' + locations[i].name + '</option>');

        }

    </script>

    </select>

    <img src=http://google.com/mapfiles/ms/micons/ylw-pushpin.png style=height:15px;> = Center

    <img src=https://maps.gstatic.com/mapfiles/ms2/micons/red.png style=height:15px;> = No Longitude Adjustment

    <img src=https://maps.gstatic.com/mapfiles/ms2/micons/pink.png style=height:15px;> = With Longitude Adjustment (var xp = x / Math.cos(y0);)

</div>



<div id=map_canvas style=position:absolute; top:30px; left:0px; height:100%; height:calc(100% - 30px); width:100%;overflow:hidden;></div>



<script>

var markers = [];

var currentcircle;



//Create the default map

var mapcenter = new google.maps.LatLng(locations[locationindex].latitude, locations[locationindex].longitude);

var myOptions = {

    zoom: mapZoomLevel,

    scaleControl: true,

    center: mapcenter

};

var map = new google.maps.Map(document.getElementById('map_canvas'), myOptions);



//Draw default items

var centermarker = addCenterMarker(mapcenter, locations[locationindex].name + '<br>' + locations[locationindex].latitude + ', ' + locations[locationindex].longitude);

var mappoints = generateMapPoints(locations[locationindex], distanceLimit, numberRandomPoints);

drawRadiusCircle(map, centermarker, distanceLimit);

createRandomMapMarkers(map, mappoints);



//Create random lat/long coordinates in a specified radius around a center point

function randomGeo(center, radius) {

    var y0 = center.latitude;

    var x0 = center.longitude;

    var rd = radius / 111300; //about 111300 meters in one degree



    var u = Math.random();

    var v = Math.random();



    var w = rd * Math.sqrt(u);

    var t = 2 * Math.PI * v;

    var x = w * Math.cos(t);

    var y = w * Math.sin(t);



    //Adjust the x-coordinate for the shrinking of the east-west distances

    var xp = x / Math.cos(y0);



    var newlat = y + y0;

    var newlon = x + x0;

    var newlon2 = xp + x0;



    return {

        'latitude': newlat.toFixed(5),

        'longitude': newlon.toFixed(5),

        'longitude2': newlon2.toFixed(5),

        'distance': distance(center.latitude, center.longitude, newlat, newlon).toFixed(2),

        'distance2': distance(center.latitude, center.longitude, newlat, newlon2).toFixed(2),

    };

}



//Calc the distance between 2 coordinates as the crow flies

function distance(lat1, lon1, lat2, lon2) {

    var R = 6371000;

    var a = 0.5 - Math.cos((lat2 - lat1) * Math.PI / 180) / 2 + Math.cos(lat1 * Math.PI / 180) * Math.cos(lat2 * Math.PI / 180) * (1 - Math.cos((lon2 - lon1) * Math.PI / 180)) / 2;

    return R * 2 * Math.asin(Math.sqrt(a));

}



//Generate a number of mappoints

function generateMapPoints(centerpoint, distance, amount) {

    var mappoints = [];

    for (var i=0; i<amount; i++) {

        mappoints.push(randomGeo(centerpoint, distance));

    }

    return mappoints;

}



//Add a unique center marker

function addCenterMarker(centerposition, title) {

    

    var infowindow = new google.maps.InfoWindow({

        content: title

    });

    

    var newmarker = new google.maps.Marker({

        icon: 'http://google.com/mapfiles/ms/micons/ylw-pushpin.png',

        position: mapcenter,

        map: map,

        title: title,

        zIndex: 3

    });

    

    google.maps.event.addListenerOnce(map, 'tilesloaded', function() {

        infowindow.open(map,newmarker);

    });

    

    markers.push(newmarker);

    return newmarker;

}



//Draw a circle on the map

function drawRadiusCircle (map, marker, distance) {

    currentcircle = new google.maps.Circle({

        map: map,

        radius: distance

    });

    currentcircle.bindTo('center', marker, 'position');

}



//Create markers for the randomly generated points

function createRandomMapMarkers(map, mappoints) {

    for (var i = 0; i < mappoints.length; i++) {

        //Map points without the east/west adjustment

        var newmappoint = new google.maps.LatLng(mappoints[i].latitude, mappoints[i].longitude);

        var marker = new google.maps.Marker({

            position:newmappoint,

            map: map,

            title: mappoints[i].latitude + ', ' + mappoints[i].longitude + ' | ' + mappoints[i].distance + 'm',

            zIndex: 2

        });

        markers.push(marker);



        //Map points with the east/west adjustment

        var newmappoint = new google.maps.LatLng(mappoints[i].latitude, mappoints[i].longitude2);

        var marker = new google.maps.Marker({

            icon: 'https://maps.gstatic.com/mapfiles/ms2/micons/pink.png',

            position:newmappoint,

            map: map,

            title: mappoints[i].latitude + ', ' + mappoints[i].longitude2 + ' | ' + mappoints[i].distance2 + 'm',

            zIndex: 1

        });

        markers.push(marker);

    }

}



//Destroy all markers

function clearMarkers() {

    for (var i = 0; i < markers.length; i++) {

        markers[i].setMap(null);

    }

    markers = [];

}



$('#location_switch').change(function() {

    var newlocation = $(this).val();

    

    clearMarkers();



    mapcenter = new google.maps.LatLng(locations[newlocation].latitude, locations[newlocation].longitude);

    map.panTo(mapcenter);

    centermarker = addCenterMarker(mapcenter, locations[newlocation].name + '<br>' + locations[newlocation].latitude + ', ' + locations[newlocation].longitude);

    mappoints = generateMapPoints(locations[newlocation], distanceLimit, numberRandomPoints);



    //Draw default items

    currentcircle.setMap(null);

    drawRadiusCircle(map, centermarker, distanceLimit);

    createRandomMapMarkers(map, mappoints);

});

</script>

</body>

</html>