Recently saw some great links making use of Global Illumination/Ambient Occlusion… these ones are from wonderfl posted by keim at Si :
This first example is based on something called AO bench.
one
two
three
and there is something called MiniLight which has been ported to Flex.
Actionscript:
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var verts:Vector.<Number> = new Vector.<Number>();
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var pVerts:Vector.<Number> = new Vector.<Number>();
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var uvts:Vector.<Number> = new Vector.<Number>();
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var hs:Number = 2.3;
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var step:Number = 0.04;
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var tVerts:Vector.<Number> = new Vector.<Number>();
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var rVerts:Vector.<Number> = new Vector.<Number>();
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var matrix:Matrix3D = new Matrix3D();
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matrix.identity();
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matrix.appendRotation(45,Vector3D.Y_AXIS);
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matrix.appendRotation(45,Vector3D.X_AXIS);
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var inc:int = 0;
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var i:Number, j:Number, k:Number;
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i = hs;
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while( i> -hs){
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j = hs;
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while(j> -hs){
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k = hs;
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while(k> -hs){
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tVerts[inc] = -i;
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inc++
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tVerts[inc] = -j;
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inc++
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tVerts[inc] = -k;
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inc++
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k -= step;
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}
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j -= step;
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}
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i -= step;
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}
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matrix.transformVectors(tVerts, rVerts);
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var vinc:int = 0;
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inc = 0
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var R:Number = 1.5;
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var r:Number = .5;
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for (i= -hs; i<hs; i+=step){
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for (j = -hs; j<hs; j+=step){
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for (k = -hs; k<hs; k+=step){
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var vx:Number = rVerts[inc] ;
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inc++
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var vy:Number = rVerts[inc] ;
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inc++
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var vz:Number= rVerts[inc] ;
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inc++
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var s:Number = Math.pow(vx * vx + vy * vy + vz * vz + R*R - r * r, 2) - 4 * (R * R)*(vx * vx + vy * vy);
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if (s <0 && s> -.5){
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verts[vinc] = (i * 50);
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vinc++
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verts[vinc] = (j * 50);
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vinc++
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verts[vinc] = (k * 50);
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vinc++
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inc += int((hs - k) / step) * 3;
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k = hs;
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}
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}
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}
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}
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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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render();
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function render():void{
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matrix.identity();
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matrix.appendTranslation(200, 200, 0);
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Utils3D.projectVectors(matrix, verts, pVerts, uvts);
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canvas.lock();
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canvas.fillRect(canvas.rect, 0x000000);
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var inc:int = 2;
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var c:int = 0;
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var r:Rectangle = new Rectangle();
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r.width = r.height = 2;
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for (var i:int = 0; i<pVerts.length; i+=2){
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r.x = pVerts[i];
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r.y = pVerts[i + 1];
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c = Math.max(0,100 - verts[inc]);
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canvas.fillRect(r, c <<16 | c <<8 | c);
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inc += 3;
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}
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canvas.unlock();
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}
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.
Actionscript:
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var matrix:Matrix3D = new Matrix3D();
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var verts:Vector.<Number> = new Vector.<Number>();
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var pVerts:Vector.<Number> = new Vector.<Number>();
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var uvts:Vector.<Number> = new Vector.<Number>();
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var sqrt2:Number = Math.sqrt(2)
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var pi:Number = Math.PI;
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var pi23:Number= 2 * Math.PI / 3;
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var step:Number= pi / 50;
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for (var u:Number = -pi; u<pi; u+=step) {
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for (var v:Number = -pi; v<pi; v+=step) {
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// from here http://local.wasp.uwa.edu.au/~pbourke/geometry/hexatorus/
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var px = Math.sin(u) / Math.abs(sqrt2+ Math.cos(v))
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var py = Math.sin(u+pi23) / Math.abs(sqrt2 +Math.cos(v + pi23))
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var pz = Math.cos(u-pi23) / Math.abs(sqrt2 +Math.cos(v - pi23))
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verts.push(px * 50);
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verts.push(py * 50);
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verts.push(pz * 50);
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}
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}
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var brush:BitmapData=new BitmapData(3,2,true,0x41FFFFFF);
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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 dx:Number=0;
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var dy:Number=0;
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addEventListener(Event.ENTER_FRAME, onLoop);
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function onLoop(evt:Event):void {
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dx += (mouseX - dx)/4;
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dy += (mouseY - dy)/4;
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matrix.identity();
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matrix.appendRotation(dy,Vector3D.X_AXIS);
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matrix.appendRotation(dx,Vector3D.Y_AXIS);
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matrix.appendTranslation(200, 200, 0);
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Utils3D.projectVectors(matrix, verts, pVerts, uvts);
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canvas.lock();
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canvas.fillRect(canvas.rect, 0x000000);
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var p = new Point();
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for (var i:int = 0; i<pVerts.length; i+=2) {
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p.x = pVerts[i];
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p.y = pVerts[i+1];
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canvas.copyPixels(brush, brush.rect, p, null, null, true);
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}
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canvas.unlock();
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}
More 3D shapes inspired by (taken from) Paul Bourke's website. I figured I should probably add a parametric 3D surface to this set of posts - so I chose to plot the Triaxial Hexatorus. It's important to note that U and V go from -PI to PI.
I googled Triaxial Hexatorus and stumbled upon a great papervision demo that creates meshes using parametric equations - it also morphs between shapes.
I also noticed that I don't need to populate the uvts or pVerts Vectors with zeros - seems to work fine without doing that.
Actionscript:
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var matrix:Matrix3D = new Matrix3D();
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var verts:Vector.<Number> = new Vector.<Number>();
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var pVerts:Vector.<Number> = new Vector.<Number>();
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var uvts:Vector.<Number> = new Vector.<Number>();
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for (var i:Number = -10; i<10; i+=.04) {
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for (var j:Number = -5; j<8; j+=.04) {
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for (var k:Number = -10; k<10; k+=.04) {
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var s:Number = i * i * j + j * k * k;
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if (s <10 && s> 9.95) {
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verts.push(i * 20);
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verts.push(j * 20);
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verts.push(k * 20);
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pVerts.push(0),pVerts.push(0);
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uvts.push(0),uvts.push(0),uvts.push(0);
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}
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}
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}
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}
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var brush:BitmapData=new BitmapData(3,2,true,0x41FFFFFF);
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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 dx:Number=0;
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var dy:Number=0;
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addEventListener(Event.ENTER_FRAME, onLoop);
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function onLoop(evt:Event):void {
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dx += (mouseX - dx)/4;
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dy += (mouseY - dy)/4;
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matrix.identity();
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matrix.appendRotation(dy,Vector3D.X_AXIS);
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matrix.appendRotation(dx,Vector3D.Y_AXIS);
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matrix.appendTranslation(200, 200, 0);
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Utils3D.projectVectors(matrix, verts, pVerts, uvts);
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canvas.lock();
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canvas.fillRect(canvas.rect, 0x000000);
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var p = new Point();
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for (var i:int = 0; i<pVerts.length; i+=2) {
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p.x = pVerts[i];
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p.y = pVerts[i+1];
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canvas.copyPixels(brush, brush.rect, p, null, null, true);
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}
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canvas.unlock();
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}
Yet another variation on the post from the last two days. This one plots something resembling a wormhole - I was randomly tweaking the equation for a sphere and stumbled upon this...