使用地理数学查找半径内的所有值

Question

如何使用纬度/经度坐标找到半径 (X) 英里内的所有值（在本例中为机构）？

代码：

public class GeoGen {

    static final GeoPosition USER_POSITION = new GeoPosition(39.410868, -107.102182);

    public static void main(String[] args) {
        new Establishment("Fries Electronics", randomLocation(USER_POSITION, 40)).print();
        new Establishment("Walmart Supercenter", randomLocation(USER_POSITION, 40)).print();
        new Establishment("Target", randomLocation(USER_POSITION, 40)).print();
        new Establishment("Krogers", randomLocation(USER_POSITION, 40)).print();
        new Establishment("McDonalds", randomLocation(USER_POSITION, 40)).print();
    }

    public static GeoPosition randomLocation(GeoPosition location, double radius) {
        Random random = new Random();

        // Convert radius from miles to meters
        double meters = radius * 1609.34;

        // Convert radius from meters to degrees
        double radiusInDegrees = meters / 111000f;

        double u = random.nextDouble();
        double v = random.nextDouble();
        double w = radiusInDegrees * Math.sqrt(u);
        double t = 2 * Math.PI * v;
        double x = w * Math.cos(t);
        double y = w * Math.sin(t);

        // Adjust the x-coordinate for the shrinking of the east-west distances
        double new_x = x / Math.cos(location.latitude());

        double foundLongitude = new_x + location.longitude();
        double foundLatitude = y + location.latitude();
        return new GeoPosition(foundLongitude, foundLatitude);
    }

    public static double distanceBetween(GeoPosition a, GeoPosition b) {
        double longDif = a.longitude() - b.longitude();

        double distance = 
                Math.sin(deg2rad(a.latitude()))
                *
                Math.sin(deg2rad(b.latitude()))
                +
                Math.cos(deg2rad(a.latitude()))
                *
                Math.cos(deg2rad(b.latitude()))
                *
                Math.cos(deg2rad(longDif));
        distance = Math.acos(distance);
        distance = rad2deg(distance);
        distance = distance * 60 * 1.1515; // Convert to meters
        distance = distance * 0.8684; // Convert to miles.
        return distance;
    }

    private static double rad2deg(double rad) {
        return (rad * 180.0 / Math.PI);
    }

    private static double deg2rad(double deg) {
        return (deg * Math.PI / 180.0);
    }

}

/**
 * A class representing an establishment in the world.
 * 
 * @author Christian
 */
class Establishment {

    public static Map<GeoPosition, String> establishments = new HashMap<>();

    private final String name;
    private final GeoPosition geoPosition;

    public Establishment(String name, GeoPosition geoPosition) {
        this.name = name;
        this.geoPosition = geoPosition;
        establishments.put(geoPosition, name);
    }

    public void print() {
        System.out.print("Establishment("+name+") was created approx ");
        System.out.printf("%.2f", GeoGen.distanceBetween(geoPosition, GeoGen.USER_POSITION));
        System.out.print(" miles from specified Lat/Long \n");
    }

    public final String name() { return name; }
    public final GeoPosition position() { return geoPosition; }
}

/**
 * A class representing a geographical location using latitude/longitude.
 * 
 * @author Christian
 */
class GeoPosition {
    private final double longitude;
    private final double latitude;

    public GeoPosition(double longitude, double latitude) {
        this.longitude = longitude;
        this.latitude = latitude;
    }

    public double longitude() { return longitude; }
    public double latitude() { return latitude; }
}

运行此应用程序每次都会产生不同的结果，因为它是随机的，但这里是使用 GeoGen#distanceBetween(GeoPosition, GeoPosition) 方法的示例。

Establishment(Fries Electronics) was created approx 19.26 miles from specified Lat/Long 
Establishment(Walmart Supercenter) was created approx 9.79 miles from specified Lat/Long 
Establishment(Target) was created approx 28.83 miles from specified Lat/Long 
Establishment(Krogers) was created approx 10.61 miles from specified Lat/Long 
Establishment(McDonalds) was created approx 3.37 miles from specified Lat/Long 

但是，我想弄清楚的是如何让所有场所都在 X 英里范围内。比如这样的

GeoGen#FindEstablishmentsWithinRadius(GeoPosition, Double) returns List<Establishment>

这将返回指定 GeoPosition X 英里范围内的机构列表。

Answer 1

你已经有了计算距离的方法？只需遍历设施并检查它们是否在半径范围内。

将所有场所添加到列表中，然后您可以使用流，例如：

public List<Establishment> findEstablishmentsWithinRadius(List<Establishment> list, GeoPosition position, double radius) {
    return list.stream().filter(e -> distanceBetween(position, e.position()) <= radius).collect(Collectors.toList());
}

Answer 2

嗯，对我来说似乎相当微不足道。假设您有一个您创建的所有机构的列表，并且您已经有了一个距离函数。剩下的只是一个函数，给定一个中心和半径，迭代所有设施，计算每个设施与中心之间的距离，并收集那些落在半径以下的设施作为结果。完毕。我想这回答了你的问题。

现在，如果您正在查看性能并且此方法无法说服您（例如，您有太多的场所无法对所有场所进行线性遍历），您可能需要先使用一些近似值并预先过滤一个合理的集合，然后选择这是否足够，或者您仍想计算该子集中的距离。为此，您可能需要阅读Geohashing、Quad-Trees、R-Trees 和/或KD-trees ...或它们的一些变体:-)