How to quickly calculate what points are within a given distance of my point

Question

I have a large number of Longitude and Latitudes and I want to quickly find out which ones are within say a 5km radius of a certain Longitude Latitude.

Instead of using a datastructure (Which would be overkill), I should be able to perform n do products very quickly. I've just done something wrong and can't seem to see what.

I have been trying to implement this in Java:

        final List<CoOrds> coOrds = Create20x20Grid();

        // Determine point X (centre of earth)
        final Vector2 X = new Vector2(0,0);

        // My CoOrd I want to check
        final double srclon = coOrds.get(0).getLongitude();
        final double srclat = coOrds.get(0).getLatitude();

        final Vector2 A = new Vector2(srclon, srclat, true);

        final double brng = 0;
        final double d = 5;
        final double R = 6371.1;
        double dist = 0;

        dist = d / R; // convert dist to angular distance in radians

        final double lat1 = Math.toRadians(srclat);
        final double lon1 = Math.toRadians(srclon);

        final double lat2 = Math.asin(Math.sin(lat1) * Math.cos(dist)+ Math.cos(lat1) * Math.sin(dist) * Math.cos(brng));
        double lon2 = lon1 + Math.atan2(Math.sin(brng) * Math.sin(dist) * Math.cos(lat1),Math.cos(dist) - Math.sin(lat1) * Math.sin(lat2));

        // normalise to -180..+180º
        lon2 = (lon2 + 3 * Math.PI) % (2 * Math.PI) - Math.PI;


        //Create another point which is the distance is d away from your point
        final Vector2 B = new Vector2(Math.toDegrees(lon2),Math.toDegrees(lat2), true);

        // Create a vector from X->A
        final Vector2 X_A = new Vector2((A.getX() - X.getX()),(A.getY() - X.getY()));
        // Create a vector from X->B
        final Vector2 X_B = new Vector2((B.getX() - X.getX()),(B.getY() - X.getY()));

        // Normalize XA
        final Vector2 nX_A = X_A.normalize();
        // Normalize XB
        final Vector2 nX_B = X_B.normalize();

        // Calculate the Dot Product
        final Double Alpha = nX_A.dot(nX_B);

        int count = 0;
        for (final CoOrds c : coOrds) {

            final Vector2 P = c.getPosition();
            final Vector2 X_P = new Vector2((P.getX() - X.getX()),(P.getY() - X.getY()));

            final Vector2 nX_P = X_P.normalize());
            final Double Beta = nX_A.dot(nX_P);

            if (Beta < Alpha) {
                System.out.println(count + " -- " + Beta + " : " + Alpha);
                count++;
            }

        }


        System.out.println("Number of CoOrds within Distance : " + count);

The new point P is correct as I've loaded it into Google Maps, but I am not entirely sure if I have the calculations correct.

I have created a custom Vector2 class, which stores the Longitude and Latitude. It also coverts them to Cartesian:

    private void convertSphericalToCartesian(final double latitude, final double longitude) {

    x = (earthRadius * Math.cos(latitude) * Math.cos(longitude)) ;
    y = (earthRadius * Math.cos(latitude) * Math.sin(longitude)) ;
}

The Dot Product:

    public double dot(final Vector2 v2) {

    return ((getX() * v2.getX()) + (getY() * v2.getY()));

}

The Normalize:

    public Vector2 normalize() {

    final double num2 = (getX() * getX()) + (getY() * getY());
    final double num = 1d / Math.sqrt(num2);

    double a = x;
    double b = y;

    a *= num;
    b *= num;

    return new Vector2(a, b);
}

Any help with this would be really appreciated

I used this website: http://www.movable-type.co.uk/scripts/latlong.html To help me calculate point B.

I used this website : http://rbrundritt.wordpress.com/2008/10/14/conversion-between-spherical-and-cartesian-coordinates-systems/ To help me transform Spherical CoOrdinates to Cartesian CoOrdinates.

Thanks

[EDIT]

The test case I am currently running is:

0-0-0

2-2-0

1-2-0

Where the above is a grid of 9 points. The point I am checking is "1". I expect it to return all the points "2". But it is returning all the points in the grid. I have manually checked the distances on Google Maps and it should only be returning the points "2".

Thanks

Answer 1

From the comments above, you're not sure if your formulae are accurate.

The first step is to figure that out.

Select a few well-known points on the globe (North Pole, South Pole, Greenwich UK, etc), and create a test case that invokes convertSphericaltoCartesian() with these coordinates. Check the results and see if they make any sense.