javascript 从种子点生成特定半径内的随机地理坐标
声明：本页面是StackOverFlow热门问题的中英对照翻译，遵循CC BY-SA 4.0协议，如果您需要使用它，必须同样遵循CC BY-SA许可，注明原文地址和作者信息，同时你必须将它归于原作者（不是我）：StackOverFlow
原文地址: http://stackoverflow.com/questions/31192451/
Warning: these are provided under cc-by-sa 4.0 license. You are free to use/share it, But you must attribute it to the original authors (not me):
StackOverFlow
提示：将鼠标放在中文语句上可以显示对应的英文。显示中英文
时间：2020-10-28 13:25:24 来源:igfitidea点击:
Generate random geo coordinates within specific radius from seed point
提问by brandonscript
I'm using the following function to generate random geo coordinates within a specified radius from a seed point:
我正在使用以下函数从种子点生成指定半径内的随机地理坐标：
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:
我使用 2000 米半径和以下种子点在循环中执行此操作数次：
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:
我希望所有这些结果都在 2000m 以内；相反，我看到的值超过 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.
鉴于我（无耻地！）从其他地方剽窃了这个解决方案（尽管我见过几个类似的实现），我似乎无法弄清楚数学哪里出了问题。
(Also, in case you want it, this is how I'm calculating the distance. Pretty sure this is correct.)
（另外，如果你想要的话，这就是我计算距离的方式。很确定这是正确的。）
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));
}
回答by webworker01
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:
问题似乎源于这样一个事实，即根据您使用的中心点，这只是一个不准确的计算。特别是这一行：
var xp = x / Math.cos(y0);
Removing this line and changing longitude to
删除这条线并将经度更改为
'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.
似乎将所有点都保留在指定半径内，尽管没有这条线，在某些情况下，点似乎不会完全填满东西。
Anyway, I found someone experiencing a similar issue herewith 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.
无论如何，我发现有人在这里遇到了类似的问题，并将其他人的 Matlab 代码作为可能的解决方案。如果您想使用不同的公式，则取决于您需要随机点的均匀分布。
Here is a google maps visualization of what's going on with your provided formula:
这是您提供的公式发生的事情的谷歌地图可视化：
<!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>