Gumdrop Torus

var matrix:Matrix3D = new Matrix3D();
 
var verts:Vector.<Number> = new Vector.<Number>();
var pVerts:Vector.<Number> = new Vector.<Number>();
var uvts:Vector.<Number> = new Vector.<Number>();

for (var i:Number = -2; i<2; i+=.04){
	for (var j:Number = -2; j<2; j+=.04){
		for (var k:Number = -2; k<2; k+=.04){
// equation from: http://local.wasp.uwa.edu.au/~pbourke/geometry/gumdrop/
			var yz:Number = j * j + k * k;
		     var s:Number = 4 * (Math.pow(i,4) + Math.pow(yz,2)) 
			 + 17 * i * i *(yz) - 20 * (yz + i * i) + 17;
			if (s <0 && s > -0.5){
				verts.push(i * 60);
				verts.push(j * 60);
				verts.push(k * 60);
				pVerts.push(0), pVerts.push(0);
				uvts.push(0), uvts.push(0), uvts.push(0);
			 }
		}
	}
}

var tVerts:Vector.<Number> = new Vector.<Number>();
matrix.appendRotation(90, Vector3D.X_AXIS);
matrix.appendRotation(45, Vector3D.Y_AXIS);
matrix.appendScale(1.7, 1.7, 1.7);
matrix.transformVectors(verts, tVerts);

var p:Point = new Point();
var brush:BitmapData=new BitmapData(3,3,true,0x41FFFFFF);
var canvas:BitmapData = new BitmapData(500,500,false, 0x000000);
addChild(new Bitmap(canvas));
var dx:Number=0;
var dy:Number=0;
addEventListener(Event.ENTER_FRAME, onLoop);
function onLoop(evt:Event):void {
	dx += (mouseX - dx)/4;
	dy += (mouseY - dy)/4;
	matrix.identity();
	matrix.appendRotation(dy,Vector3D.X_AXIS);
	matrix.appendRotation(dx,Vector3D.Y_AXIS);
	matrix.appendTranslation(250, 250, 0);
	Utils3D.projectVectors(matrix, tVerts, pVerts, uvts);
	canvas.lock();
	canvas.fillRect(canvas.rect, 0x000000);
	var inc:int = 0;
	for (var i:int = 0; i<pVerts.length; i+=2){
	 
        p.x = pVerts[i];
        p.y = pVerts[i+1];
		canvas.copyPixels(brush, brush.rect, p, null, null, true); 
	}
	canvas.unlock();
}

Felt like revisiting implicit surface plotting today…

Have a look at the swf over at wonderfl.net