convex shell on JS

gistfile1.js

function Point(x, y) {
    this.x = x;
    this.y = y;
    return this;
}

var a = [
    new Point(0, 3)
  , new Point(1, 1)
  , new Point(1, 3)
  , new Point(2, 4)
  , new Point(3, 1)
  , new Point(3, 2)
  , new Point(4, 2)
];

function convexShell(points) {
    var n = points.length;
    if (n == 0) {
        throw new Error("Zero length array of points is not allowed");
    }
    var p = points[0];
    for(var i = 1; i < n; i++) {
        if (points[i].y > p.y) continue;
        if (points[i].y < p.y || points[i].x < p.x) {
            p = points[i];
        }
    }

    function atan(point) {
        return Math.atan2(point.y - p.y, point.x - p.x);
    }

    function dist(p1, p2) {
        return (p1.x - p2.x) * (p1.x - p2.x) + (p1.y - p2.y) * (p1.y - p2.y);
    }

    function cmp(p1, p2) {
       var d = atan(p1) - atan(p2);
       if (Math.abs(d) > 1e-8) return d;
       return dist(p1, p) - dist(p2, p);
    }

    function qsort(points, l, r) {
        var i = l, j = r;
        var m = Math.round((i + j)/2);
        var x = points[m];
        do{
            while(cmp(points[i], x) < 0) {
                ++i;
            }
            while(cmp(points[j], x) > 0) {
                --j;
            }
            if (i <= j) {
                var t = points[i];
                points[i] = points[j];
                points[j] = t;
                ++i;--j;
            }
        } while(i <= j);

        if (i < r) qsort(points, i, r);
        if (l < j) qsort(points, l, j);
    }

    qsort(points, 0, n-1);

    if (n < 3) {
        return points;
    }

    var shell = [];
    shell.push(points[0]);
    shell.push(points[1]);
    for(var i = 2; i < n; i++) {
        var sp3 = points[i];
        var sp2 = shell.pop();
        var sp1 = shell.pop();

        var x1 = sp1.x - sp2.x;
        var y1 = sp1.y - sp2.y;

        var x2 = sp3.x - sp2.x;
        var y2 = sp3.y - sp2.y;

        if (x1 * y2 - x2 * y1 < 0) {
            shell.push(sp1);
            shell.push(sp2);
            shell.push(sp3);
        } else {
            shell.push(sp1);
            shell.push(sp3);
        }
    }
    return shell;
}

for(var i = 0; i < a.length; i++) {
    console.log(a[i].x + " " + a[i].y);
}
convexShell(a);