// forked from makc3d's A circle through three points (trail version)
// forked from makc3d's A circle through three points
package
{
    import flash.display.*;
    import flash.geom.*;
     
    /** 
    * Catmull-Rom spline through N points.
    * @author makc
    * @license WTFPLv2, http://sam.zoy.org/wtfpl/
    */ 
    public class CatmullRom extends Sprite
    {
        public var b:Bitmap, ct:ColorTransform, s:Shape;

public var ps:Array = [];
		public var vs:Array = [];

public function CatmullRom ()  
        {
            b = new Bitmap (new BitmapData (465, 465, true, 0xFFFFFF));
            addChild (b);ct = new ColorTransform (1,1,1,0.95);
            s = new Shape;addChild (s);

var N:int = 3 + 10 * Math.random ();
			for (var i:int = 0; i < N; i++) {
				ps.push (new Point (465 * Math.random (), 465 * Math.random ()));
				vs.push (new Point (5 * (Math.random () - Math.random ()), 5 * (Math.random () - Math.random ())));
			}

addEventListener ("enterFrame", loop);
        }

public function loop (e:*):void 
        {
			var i:int;

// move points around randomly
			for (i = 0; i < ps.length; i++) {
				var p:Point = ps [i];
				var v:Point = vs [i];
				p.x += v.x; p.y += v.y;
				if ((p.x < 0) || (p.x > 465)) { p.x = Math.max (0, Math.min (465, p.x)); v.x *= -1; }
				if ((p.y < 0) || (p.y > 465)) { p.y = Math.max (0, Math.min (465, p.y)); v.y *= -1; }
			}

// prepare graphics
            s.graphics.clear ();

// draw spline
            for (i = 0; i < ps.length; i++) {
				var p0:Point = ps [(i -1 + ps.length) % ps.length];
				var p1:Point = ps [i];
				var p2:Point = ps [(i +1 + ps.length) % ps.length];
				var p3:Point = ps [(i +2 + ps.length) % ps.length];

s.graphics.lineStyle (0, 0x7FFF);
				s.graphics.beginFill (0, 0);
				s.graphics.moveTo (p1.x, p1.y);
				for (var j:int = 1; j < 101; j++) {
					var q:Point = spline (p0, p1, p2, p3, 0.01 * j);
					s.graphics.lineTo (q.x, q.y);
				}
				s.graphics.lineStyle ();
				s.graphics.endFill ();
			}

b.bitmapData.draw (s);
            b.bitmapData.colorTransform (b.bitmapData.rect, ct)

// draw points 
            s.graphics.beginFill (0xFF0000);
			for (i = 0; i < ps.length; i++) {
				s.graphics.drawCircle (ps [i].x, ps [i].y, 3.5);
			}
        }

/* 
        * Calculates 2D cubic Catmull-Rom spline.
        * @see http://www.mvps.org/directx/articles/catmull/ 
        */ 
        public function spline (p0:Point, p1:Point, p2:Point, p3:Point, t:Number):Point 
        {
            return new Point (
				0.5 * ((          2*p1.x) +
					t * (( -p0.x           +p2.x) +
					t * ((2*p0.x -5*p1.x +4*p2.x -p3.x) +
					t * (  -p0.x +3*p1.x -3*p2.x +p3.x)))),
				0.5 * ((          2*p1.y) +
					t * (( -p0.y           +p2.y) +
					t * ((2*p0.y -5*p1.y +4*p2.y -p3.y) +
					t * (  -p0.y +3*p1.y -3*p2.y +p3.y))))
			);
        }

}

Catmull-Rom spline through N points