Implicit 3D Plot

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) {
			// blobby, from here www.iiit.net/techreports/ImplicitTR.pdf
var s:Number=i*i+j*j+k*k+Math.sin(4*i)-Math.cos(4*j)+Math.sin(4*k)-1;
			if (s<0&&s>-.2) {
				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 brush:BitmapData=new BitmapData(3,2,true,0x41FFFFFF);
var canvas:BitmapData=new BitmapData(400,400,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(200, 200, 0);
	Utils3D.projectVectors(matrix, verts, pVerts, uvts);
	canvas.lock();
	canvas.fillRect(canvas.rect, 0x000000);
	var p = new Point();
	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();
}

I was looking at some equations for implicit 3D surfaces in this pdf about raytracing… anyway, I realized I could just modify the Utils3D.projectVectors() code (that I wrote a little while ago) to easily render any of the implicit equations mentioned in the pdf. I also did some experimentation with fake lighting and distance rendering which I may post in the future.

(check out the swf on wonderfl.net)

Here are some stills of the above snippet: