Finding a set of coordinates within a certain range from latitude and longitide

Question

I am working on a project in javascript involving google maps.

The goal is to figure out 16-20 coordinate points within n kilometers from a set of latitude longitude coordinates such that the 16 points if connected will form a circle around the original coordinates.

The end goal is to make it so I can figure out coordinates to plot and connect on google maps to make a circle around a given set of coordinates.

The code would go something like:

var coordinates = Array();
function findCoordinates(lat, long, range) {
}
coordinates = findCoordinates(-20, 40, 3);

Now to make the magic happen in the findCoordinates() function.

Solution 1

Basically what you're trying to do is find N points on the radius of a circle from a given point with a given radius. One simple way of doing it is splitting the 360 degrees of a circle in to N equal chunks, and finding the points at regular intervals.

The following should do roughly what you're after -

function findCoordinates(lat, long, range)
{
    // How many points do we want? (should probably be function param..)
    var numberOfPoints = 16;
    var degreesPerPoint = 360 / numberOfPoints;

    // Keep track of the angle from centre to radius
    var currentAngle = 0;

    // The points on the radius will be lat+x2, long+y2
    var x2;
    var y2;
    // Track the points we generate to return at the end
    var points = [];

    for(var i=0; i < numberOfPoints; i++)
    {
        // X2 point will be cosine of angle * radius (range)
        x2 = Math.cos(currentAngle) * range;
        // Y2 point will be sin * range
        y2 = Math.sin(currentAngle) * range;

        // Assuming here you're using points for each x,y..             
        p = new Point(lat+x2, long+y2);

        // save to our results array
        points.push(p);

        // Shift our angle around for the next point
        currentAngle += degreesPerPoint;
    }
    // Return the points we've generated
    return points;
}

The array of points you get back can then easily be used to draw the circle you wish on your google map.

If your overall goal however is just to draw a circle at a fixed radius around a point, then a far easier solution may be to use an overlay. I've found KMBox to be very easy to set up - you give it a central point, a radius and an image overlay (in your case, a transparent circle with a visible line around the edge) and it takes care of everything else, including resizing it on zoom in/out.

Solution 2

I had to find some code to calculate Great Circle distances a while back (just Google "Great Circle" if you don't know what I'm talking about) and I found this site:

http://williams.best.vwh.net/gccalc.htm

You might be able to build up your own JavaScript code to do your lat/lon range calculations using the JavaScript from that site as a reference. It sounds to me like you just need to divide up the 360 degrees of a circle into an equal number of pieces and draw a line out to an equal distance from the center at each "bearing". Once you know the lat/lon at the other end of each bearing/distance line, then connecting the dots to form a polygon is trivial.