Gradient Tooth

var canvas:BitmapData=new BitmapData(400,400,false,0x000000);
addChild(new Bitmap(canvas));

var a:Number=-1.21;
var r:Rectangle=new Rectangle(0,0,3,5);
var halfWidth:Number=canvas.width/2;
var halfHeight:Number=canvas.height/2;

render();

function render():void{
	for (var x:Number = -2; x<=2; x+=.01) {
		for (var y:Number = -2; y<=2; y+=.02) {
	
			// equation from : http://en.wikipedia.org/wiki/Bicuspid_curve
			//(x^2 - a^2) * (x - a)^2 + (y^2 - a^2) * (y^2 - a^2) = 0
	
			// unpoptimized:
			// var e:Number = (x*x - a*a) * (x-a)*(x-a) + (y*y-a*a) * (y*y-a*a);  
			// optimized:
			var x_a:Number=x-a;
			// factoring: x^2 - a^2 = (x + a) * (x - a)
			var y2_a2:Number =  (y + a) * (y - a);
			var e:Number = (x + a) * x_a * x_a *  x_a +  y2_a2 * y2_a2;
			 
				r.x=halfWidth+y*50;
				r.y=halfHeight-x*100;
				var col:Number = e * 50;
				if (col < 10){
					col = Math.abs(col) + 70;
				    canvas.fillRect(r, col << 16 | col << 8 | col );
				}
		}
	}
}

This is a variation on a post from a little while back…. it plots a modified Bicuspid that resembles a tooth: