/*
  Cubic Bezier Drawing v1.1
  Oct. 29, 2002
  (c) 2002 Robert Penner
  
  MovieClip methods to draw cubic beziers (four control points)
  using recursive quadratic approximation with adjustable tolerance.
  
	MovieClip.drawBezier()
	MovieClip.drawBezierPts()
	MovieClip.curveToCubic()
	MovieClip.curveToCubicPts()
  
  Dependencies: _xpen and _ypen movie clip properties (drawing_api_core_extensions.as)
  
  Discussed in Chapter 10 of 
  Robert Penner's Programming Macromedia Flash MX
  
  http://www.robertpenner.com/profmx
  http://www.amazon.com/exec/obidos/ASIN/0072223561/robertpennerc-20
*/

if (typeof _level0._xpen == "undefined") trace ("Error: _xpen and _ypen not defined (drawing_api_core_extensions.as)");

/* 
==========================
Cubic Bezier Drawing v0.9
==========================
recursive quadratic approximation 
with adjustable tolerance

May 20, 2002

Robert Penner
www.robertpenner.com

	MovieClip.drawBezier()
	MovieClip.drawBezierPts()
	MovieClip.curveToCubic()
	MovieClip.curveToCubicPts()

*/


Math.intersect2Lines = function (p1, p2, p3, p4) {
	var x1 = p1.x; var y1 = p1.y;
	var x4 = p4.x; var y4 = p4.y;

	var dx1 = p2.x - x1;
	var dx2 = p3.x - x4;
	if (!(dx1 || dx2)) return NaN;
	
	var m1 = (p2.y - y1) / dx1;
	var m2 = (p3.y - y4) / dx2;
	
	if (!dx1) {
		// infinity
		return { x:x1,
		         y:m2 * (x1 - x4) + y4 };

	} else if (!dx2) {
		// infinity
		return { x:x4,
		         y:m1 * (x4 - x1) + y1 };
	}
	var xInt = (-m2 * x4 + y4 + m1 * x1 - y1) / (m1 - m2);
	var yInt = m1 * (xInt - x1) + y1;
	return { x:xInt, y:yInt };
};

Math.midLine = function (a, b) {
	return { x:(a.x + b.x)/2, y:(a.y + b.y)/2 };
};

Math.bezierSplit = function (p0, p1, p2, p3) {
	var m = Math.midLine;
	var p01 = m (p0, p1);
	var p12 = m (p1, p2);
	var p23 = m (p2, p3);
	var p02 = m (p01, p12);
	var p13 = m (p12, p23);
	var p03 = m (p02, p13);
	return {
		b0:{a:p0,  b:p01, c:p02, d:p03},
		b1:{a:p03, b:p13, c:p23, d:p3 }  
	};
};

var MCP = MovieClip.prototype;

MCP.$cBez = function (a, b, c, d, k) {
	// find intersection between bezier arms
	var s = Math.intersect2Lines (a, b, c, d);
	// find distance between the midpoints
	var dx = (a.x + d.x + s.x * 4 - (b.x + c.x) * 3) * .125;
	var dy = (a.y + d.y + s.y * 4 - (b.y + c.y) * 3) * .125;
	// split curve if the quadratic isn't close enough
	if (dx*dx + dy*dy > k) {
		var halves = Math.bezierSplit (a, b, c, d);
		var b0 = halves.b0; var b1 = halves.b1;
		// recursive call to subdivide curve
		this.$cBez (a,     b0.b, b0.c, b0.d, k);
		this.$cBez (b1.a,  b1.b, b1.c, d,    k);
	} else {
		// end recursion by drawing quadratic bezier
		this.curveTo (s.x, s.y, d.x, d.y);
	}
};

MCP.drawBezierPts = function (p1, p2, p3, p4, tolerance) {
	if (tolerance == undefined) tolerance = 5;
	this.moveTo (p1.x, p1.y);
	this.$cBez (p1, p2, p3, p4, tolerance*tolerance);
};

MCP.drawBezier = function (x1, y1, x2, y2, x3, y3, x4, y4, tolerance) {
	this.drawBezierPts ({x:x1, y:y1},
						{x:x2, y:y2},
						{x:x3, y:y3},
						{x:x4, y:y4},
						tolerance);
};

MCP.curveToCubic = function (x1, y1, x2, y2, x3, y3, tolerance) {
	if (tolerance == undefined) tolerance = 5;
	this.$cBez (
		{x:this._xpen, y:this._ypen},
		{x:x1, y:y1},
		{x:x2, y:y2},
		{x:x3, y:y3},
		tolerance*tolerance );
};

MCP.curveToCubicPts = function (p1, p2, p3, tolerance) {
	if (tolerance == undefined) tolerance = 5;
	this.$cBez (
		{x:this._xpen, y:this._ypen},
		p1, p2, p3, tolerance*tolerance );
};

delete MCP;