Distance Render

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

var hs:Number = 2.3;
var step:Number = 0.04;

var tVerts:Vector.<Number> = new Vector.<Number>();
var rVerts:Vector.<Number> = new Vector.<Number>();
var matrix:Matrix3D = new Matrix3D();
matrix.identity();
matrix.appendRotation(45,Vector3D.Y_AXIS);
matrix.appendRotation(45,Vector3D.X_AXIS);
var inc:int = 0;
var i:Number, j:Number, k:Number;
i = hs;
while( i > -hs){
	j = hs;
	while(j > -hs){
		k = hs;
		while(k > -hs){
			tVerts[inc] = -i;
			inc++
			tVerts[inc] = -j;
			inc++
			tVerts[inc] = -k;
			inc++
			k -= step;
		}
		j -= step;
	}
	i -= step;
}

matrix.transformVectors(tVerts, rVerts);
 
var vinc:int = 0;
inc = 0
var R:Number = 1.5;
var r:Number = .5;
for (i= -hs; i<hs; i+=step){
	for (j = -hs; j<hs; j+=step){
		for (k = -hs; k<hs; k+=step){
			var vx:Number = rVerts[inc] ;
			inc++
			var vy:Number = rVerts[inc]  ;
			inc++
			var vz:Number=  rVerts[inc] ;
			inc++
			var s:Number = Math.pow(vx  * vx  + vy * vy + vz * vz + R*R - r * r, 2) - 4 * (R * R)*(vx * vx + vy * vy); 
			if (s <0 && s > -.5){ 
				verts[vinc] = (i * 50);
				vinc++
				verts[vinc] = (j * 50);
				vinc++
				verts[vinc] = (k * 50);
				vinc++
				  inc += int((hs - k) / step) * 3;
				  k = hs;
			 }
		}
	}
}

var canvas:BitmapData = new BitmapData(400,400,false, 0x000000);
addChild(new Bitmap(canvas));
render();
function render():void{
	matrix.identity();
    matrix.appendTranslation(200, 200, 0);
	Utils3D.projectVectors(matrix, verts, pVerts, uvts);
	canvas.lock();
	canvas.fillRect(canvas.rect, 0x000000);
	var inc:int = 2;
	var c:int = 0;
	var r:Rectangle = new Rectangle();
	r.width = r.height = 2;
	for (var i:int = 0; i<pVerts.length; i+=2){
		  r.x = pVerts[i];
		  r.y = pVerts[i + 1];
		  c = Math.max(0,100 - verts[inc]);
		  canvas.fillRect(r, c << 16 | c << 8 | c);
		  inc += 3; 
	}
	canvas.unlock();
}

This snippet uses some of the techniques from the last few posts to create a distance render – this renders the implicit equation for a torus.