Actionscript:
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var canvas:BitmapData=new BitmapData(400,400,false,0x000000);
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addChild(new Bitmap(canvas));
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var a:Number=-1.21;
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var r:Rectangle=new Rectangle(0,0,3,5);
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var halfWidth:Number=canvas.width/2;
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var halfHeight:Number=canvas.height/2;
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render();
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function render():void{
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for (var x:Number = -2; x<=2; x+=.01) {
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for (var y:Number = -2; y<=2; y+=.02) {
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// equation from : http://en.wikipedia.org/wiki/Bicuspid_curve
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//(x^2 - a^2) * (x - a)^2 + (y^2 - a^2) * (y^2 - a^2) = 0
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// unpoptimized:
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// var e:Number = (x*x - a*a) * (x-a)*(x-a) + (y*y-a*a) * (y*y-a*a);
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// optimized:
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var x_a:Number=x-a;
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// factoring: x^2 - a^2 = (x + a) * (x - a)
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var y2_a2:Number = (y + a) * (y - a);
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var e:Number = (x + a) * x_a * x_a * x_a + y2_a2 * y2_a2;
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r.x=halfWidth+y*50;
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r.y=halfHeight-x*100;
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var col:Number = e * 50;
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if (col <10){
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col = Math.abs(col) + 70;
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canvas.fillRect(r, col <<16 | col <<8 | col );
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}
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}
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}
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}
This is a variation on a post from a little while back.... it plots a modified Bicuspid that resembles a tooth:
