Object.extend(Math, 
{
	degToRad : function(x) 
	{
		return (x*this.PI) / 180;
	},
	
	radToDeg : function(x) 
	{
		return (x*180) / this.PI;
	},
	
	factorial : function(n) 
	{
		if (n<1)
		{
			return 0; 
		}
		
		var retVal = 1;
		for (var i=1; i<=n; i++)
		{
			retVal *= i;
		}
		
		return retVal;
	},
	
	permutations : function(n,k)
	{
		if (n==0 || k==0)
		{
			return 1;
		}
		
		return (Math.factorial(n) / Math.factorial(n-k));
	},
	
	combinations : function(n,r)
	{
		if (n==0 || r==0)
		{
			return 1;
		}
		
		return (Math.factorial(n) / (Math.factorial(n-r) * Math.factorial(r)));
	},
	
	bernstein : function(t,n,i)
	{
		return (Math.combinations(n,i) * Math.pow(t,i) * Math.pow(1-t,n-1));
	}
});

Math.Curves = {};
Math.Curves.Line = Class.create();
Math.Curves.Line.prototype =
{
	initialize : function(start, end)
	{
		this.start = start;
		this.end = end;
		this.dimensions = start.length;

		for(var i = 0; i < start.length; i++) {
			start[i] = Number(start[i]);
		}

		for(var i = 0; i < end.length; i++) {
			end[i] = Number(end[i]);
		}
		
		return this;
	},
	
	getValue : function(n)
	{
		var retVal = new Array(this.dimensions);
		for(var i=0;i<this.dimensions;i++)
		{
			retVal[i] = ((this.end[i] - this.start[i]) * n) + this.start[i];
		}
		return retVal;
	}
}

Math.Curves.Bezier = Class.create();
Math.Curves.Bezier.prototype =
{
	initialize : function(points)
	{
		this.p = points;
		return this;
	},
	
	getValue : function(step)
	{
		if(step >= 1) return this.p[this.p.length-1];	// if step>=1 we must be at the end of the curve
		if(step <= 0) return this.p[0];					// if step<=0 we must be at the start of the curve
		var retVal = new Array(this.p[0].length);
		for(var k=0;j<this.p[0].length;k++) { retVal[k]=0; }
		for(var j=0;j<this.p[0].length;j++) {
			var C=0; var D=0;
			for(var i=0;i<this.p.length;i++) {
				C += this.p[i][j] * this.p[this.p.length-1][0]
					* Math.bernstein(step,this.p.length,i);
			}
			for(var l=0;l<this.p.length;l++) {
				D += this.p[this.p.length-1][0] * Math.bernstein(step,this.p.length,l);
			}
			retVal[j] = C/D;
		}
		return retVal;
	}
}

Math.Curves.CatmullRom = Class.create();
Math.Curves.CatmullRom.prototype =
{
	initialize : function(points, c)
	{
		if(!c) this.c = 0.7;
		else this.c = c;
		this.p = points;

		return this;
	},
	
	getValue : function(step)
	{
		var percent = step * (this.p.length-1);
		var node = Math.floor(percent);
		var progress = percent - node;

		var i0 = node-1; if(i0 < 0) i0 = 0;
		var i = node;
		var i1 = node+1; if(i1 >= this.p.length) i1 = this.p.length-1;
		var i2 = node+2; if(i2 >= this.p.length) i2 = this.p.length-1;

		var u = progress;
		var u2 = progress*progress;
		var u3 = progress*progress*progress;

		var retVal = new Array(this.p[0].length);
		for(var k=0;k<this.p[0].length;k++) {
			var x1 = ( -this.c * this.p[i0][k] ) + ( (2 - this.c) * this.p[i][k] ) + ( (this.c-2) * this.p[i1][k] ) + ( this.c * this.p[i2][k] );
			var x2 = ( 2 * this.c * this.p[i0][k] ) + ( (this.c-3) * this.p[i][k] ) + ( (3 - 2 * this.c) * this.p[i1][k] ) + ( -this.c * this.p[i2][k] );
			var x3 = ( -this.c * this.p[i0][k] ) + ( this.c * this.p[i1][k] );
			var x4 = this.p[i][k];

			retVal[k] = x1*u3 + x2*u2 + x3*u + x4;
		}
		return retVal;
	}
}

Math.Curves.Arc = Class.create();
Math.Curves.Arc.prototype =
{
	initialize : function(start, end, ccw)
	{
		var center = Math.points.midpoint(start, end);
		var sides = Math.points.translate(Math.points.invert(center), start);
		var rad = Math.sqrt(Math.pow(sides[0], 2) + Math.pow(sides[1], 2));
		var theta = Math.radToDeg(Math.atan(sides[1]/sides[0]));
		if( sides[0] < 0 ) {
			theta -= 90;
		} else {
			theta += 90;
		}
		return new Math.Curves.CenteredArc(this, center, rad, theta, theta+(ccw?-180:180));
	}
}

Math.Curves.CenteredArc = Class.create();
Math.Curves.CenteredArc.prototype =
{
	initialize : function(center, radius, start, end)
	{
		this.center = center;
		this.radius = radius;
		this.start = start || 0;
		this.end = end;
	
		return this;
	},
	
	getValue : function(n)
	{
		var retVal = new Array(2);
		var theta = Math.degToRad(this.start+((this.end-this.start)*n));

		retVal[0] = this.center[0] + this.radius*Math.sin(theta);
		retVal[1] = this.center[1] - this.radius*Math.cos(theta);

		return retVal;
	}
}

Math.Curves.Circle = Class.create();
Math.Curves.Circle.prototype =
{
	initialize : function(center, radius)
	{
		return new Math.Curves.CenteredArc(this, center, radius, 0, 360);
	}
}

Math.Curves.Path = Class.create();
Math.Curves.Path.prototype = 
{
	initialize : function()
	{
		this.curves = [];
		this.weights = [];
		this.ranges = [];
		this.totalWeight = 0;
		
		return this;
	},
	
	add : function(curve, weight)
	{
		if (this.weight < 0) { throw("Math.Curves.Path.add: weight cannot be less than 0"); }
		this.curves.push(curve);
		this.weights.push(weight);
		this.totalWeight += weight;
		this.computeRanges();
	},
	
	remove : function(curve)
	{
		for (var i = 0; i < this.curves.length; i++) {
			if (this.curves[i] == curve) {
				this.curves.splice(i, 1);
				this.totalWeight -= this.weights.splice(i, 1)[0];
				break;
			}
		}
		this.computeRanges();
	},
	
	removeAll : function()
	{
		this.curves = [];
		this.weights = [];
		this.totalWeight = 0;
	},
	
	getValue : function(n)
	{
		var found = false, value = 0;
		for(var i = 0; i < this.ranges.length; i++) {
			var r = this.ranges[i];
			if( n >= r[0] && n < r[1] ) {
				var subN = (n - r[0]) / r[2];
				value = this.curves[i].getValue(subN);
				found = true;
				break;
			}
		}

		if( !found ) {
			value = this.curves[this.curves.length-1].getValue(1);
		}

		for(j = 0; j < i; j++) {
			value = Math.Points.translate(value, this.curves[j].getValue(1));
		}
		return value;
	},
	
	computeRanges : function()
	{
		var start = 0;
		for(var i = 0; i < this.weights.length; i++) {
			var end = start + this.weights[i] / this.totalWeight;
			var len = end - start;
			this.ranges[i] = [start, end, len];
			start = end;
		}
	}
}

Math.Points =
{
	translate: function(a, b) 
	{
		if( a.length != b.length ) {
			throw("Math.Points.translate: points not same size (a:[" + a + "], b:[" + b + "])");
		}
		var c = new Array(a.length);
		for(var i = 0; i < a.length; i++) {
			c[i] = a[i] + b[i];
		}
		return c;
	},

	midpoint: function(a, b) 
	{
		if( a.length != b.length ) {
			throw("Math.Points.midpoint: points not same size (a:[" + a + "], b:[" + b + "])");
		}
		var c = new Array(a.length);
		for(var i = 0; i < a.length; i++) {
			c[i] = (a[i] + b[i]) / 2;
		}
		return c;
	},

	invert: function(a) 
	{
		var b = new Array(a.length);
		for(var i = 0; i < a.length; i++) { b[i] = -a[i]; }
		return b;
	},

	distance: function(a, b) 
	{
		return Math.sqrt(Math.pow(b[0]-a[0], 2) + Math.pow(b[1]-a[1], 2));
	}	
}