/**
 *  Use this class freely - 2009 blog.efnx.com
 */

package
{
    import flash.geom.Point;
   
public class GrahamScan extends Object
{
    /**
     *  The Graham scan is a method of computing the convex hull of a finite set of points
     *  in the plane with time complexity O(n log n). It is named after Ronald Graham, who
     *  published the original algorithm in 1972. The algorithm finds all vertices of
     *  the convex hull ordered along its boundary. It may also be easily modified to report
     *  all input points that lie on the boundary of their convex hull.
     */
   
    public function GrahamScan()
    {
        super();
    }
   
    /**
     *  Returns a convex hull given an unordered array of points.
     */
    public static function convexHull(data:Array):Array
    {
        return findHull( order(data) );
    }
    /**
     *  Orders an array of points counterclockwise.
     */
    public static function order(data:Array):Array
    {
        trace("GrahamScan::order()");
        // first run through all the points and find the upper left [lower left]
        var p:Point = data[0];
        var n:int   = data.length;
        for (var i:int = 1; i < n; i++)
        {
            //trace("   p:",p,"d:",data[i]);
            if(data[i].y < p.y)
            {
                //trace("   d.y < p.y / d is new p.");
                p = data[i];
            }
            else if(data[i].y == p.y && data[i].x < p.x)
            {
                //trace("   d.y == p.y, d.x < p.x / d is new p.");
                p = data[i];
            }
        }
        // next find all the cotangents of the angles made by the point P and the
        // other points
        var sorted  :Array = new Array();
        // we need arrays for positive and negative values, because Array.sort
        // will put sort the negatives backwards.
        var pos     :Array = new Array();
        var neg     :Array = new Array();
        // add points back in order
        for (i = 0; i < n; i++)
        {
            var a   :Number = data[i].x - p.x;
            var b   :Number = data[i].y - p.y;
            var cot :Number = b/a;
            if(cot < 0)
                neg.push({point:data[i], cotangent:cot});
            else
                pos.push({point:data[i], cotangent:cot});
        }
        // sort the arrays
        pos.sortOn("cotangent", Array.NUMERIC | Array.DESCENDING);
        neg.sortOn("cotangent", Array.NUMERIC | Array.DESCENDING);
        sorted = neg.concat(pos);
       
        var ordered :Array = new Array();
            ordered.push(p);
        for (i = 0; i < n; i++)
        {
            if(p == sorted[i].point)
                continue;
            ordered.push(sorted[i].point)
        }
        return ordered;
    }
    /**
     *  Given an array of points ordered counterclockwise, findHull will
     *  filter the points and return an array containing the vertices of a
     *  convex polygon that envelopes those points.
     */
    public static function findHull(data:Array):Array
    {
        trace("GrahamScan::findHull()");
        var n   :int    = data.length;
        var hull:Array  = new Array();
            hull.push(data[0]); // add the pivot
            hull.push(data[1]); // makes first vector
           
        for (var i:int = 2; i < n; i++)
        {
            while(direction(hull[hull.length - 2], hull[hull.length - 1], data[i]) >= 0)
                hull.pop();
            hull.push(data[i]);
        }
       
        return hull;
    }
    /**
     *
     */
    private static function direction(p1:Point, p2:Point, p3:Point):Number
    {
        // > 0  is right turn
        // == 0 is collinear
        // < 0  is left turn
        // we only want right turns, usually we want right turns, but
        // flash's grid is flipped on y.
        return (p2.x - p1.x) * (p3.y - p1.y) - (p2.y - p1.y) * (p3.x - p1.x);
    }
}

}