Category Archives: 3D

Kusner-Schmitt (Tetrahedral Implicit Surface)

By Zevan | May 11, 2009
CLICK HERE TO COPY
Actionscript:
  1. var matrix:Matrix3D = new Matrix3D();
  2. var verts:Vector.<Number> = new Vector.<Number>();
  3. var pVerts:Vector.<Number> = new Vector.<Number>();
  4. var uvts:Vector.<Number> = new Vector.<Number>();
  5. for (var i:Number = -2; i<2; i+=.02) {
  6.     for (var j:Number = -2; j<2; j+=.02) {
  7.         for (var k:Number = -2; k<2; k+=.02) {
  8.             var s:Number = (i * i + 3) * (j * j + 3) * (k * k + 3) - 32 * (i *j *k + 1);
  9.             if (s<0&&s>-.2) {
  10.                 verts.push(i * 100);
  11.                 verts.push(j * 100);
  12.                 verts.push(k * 100);
  13.                 pVerts.push(0),pVerts.push(0);
  14.                 uvts.push(0),uvts.push(0),uvts.push(0);
  15.             }
  16.         }
  17.     }
  18. }
  19. var brush:BitmapData=new BitmapData(3,2,true,0x41FFFFFF);
  20. var canvas:BitmapData=new BitmapData(400,400,false,0x000000);
  21. addChild(new Bitmap(canvas));
  22. var dx:Number=0;
  23. var dy:Number=0;
  24. addEventListener(Event.ENTER_FRAME, onLoop);
  25. function onLoop(evt:Event):void {
  26.     dx += (mouseX - dx)/4;
  27.     dy += (mouseY - dy)/4;
  28.     matrix.identity();
  29.     matrix.appendRotation(dy,Vector3D.X_AXIS);
  30.     matrix.appendRotation(dx,Vector3D.Y_AXIS);
  31.     matrix.appendTranslation(200, 200, 0);
  32.     Utils3D.projectVectors(matrix, verts, pVerts, uvts);
  33.     canvas.lock();
  34.     canvas.fillRect(canvas.rect, 0x000000);
  35.     var p = new Point();
  36.     for (var i:int = 0; i<pVerts.length; i+=2) {
  37.         p.x = pVerts[i];
  38.         p.y = pVerts[i+1];
  39.         canvas.copyPixels(brush, brush.rect, p, null, null, true);
  40.     }
  41.     canvas.unlock();
  42. }

The same as yesterdays with a different plot from Paul Bourke's website.

Also posted in BitmapData, Vector, graphics algorithms | Tagged , | Leave a comment

Implicit 3D Plot

By Zevan | May 10, 2009
CLICK HERE TO COPY
Actionscript:
  1. var matrix:Matrix3D = new Matrix3D();
  2. var verts:Vector.<Number> = new Vector.<Number>();
  3. var pVerts:Vector.<Number> = new Vector.<Number>();
  4. var uvts:Vector.<Number> = new Vector.<Number>();
  5. for (var i:Number = -2; i<2; i+=.04) {
  6.     for (var j:Number = -2; j<2; j+=.04) {
  7.         for (var k:Number = -2; k<2; k+=.04) {
  8.             // blobby, from here www.iiit.net/techreports/ImplicitTR.pdf
  9. var s:Number=i*i+j*j+k*k+Math.sin(4*i)-Math.cos(4*j)+Math.sin(4*k)-1;
  10.             if (s<0&&s>-.2) {
  11.                 verts.push(i * 60);
  12.                 verts.push(j * 60);
  13.                 verts.push(k * 60);
  14.                 pVerts.push(0),pVerts.push(0);
  15.                 uvts.push(0),uvts.push(0),uvts.push(0);
  16.             }
  17.         }
  18.     }
  19. }
  20. var brush:BitmapData=new BitmapData(3,2,true,0x41FFFFFF);
  21. var canvas:BitmapData=new BitmapData(400,400,false,0x000000);
  22. addChild(new Bitmap(canvas));
  23. var dx:Number=0;
  24. var dy:Number=0;
  25. addEventListener(Event.ENTER_FRAME, onLoop);
  26. function onLoop(evt:Event):void {
  27.     dx += (mouseX - dx)/4;
  28.     dy += (mouseY - dy)/4;
  29.     matrix.identity();
  30.     matrix.appendRotation(dy,Vector3D.X_AXIS);
  31.     matrix.appendRotation(dx,Vector3D.Y_AXIS);
  32.     matrix.appendTranslation(200, 200, 0);
  33.     Utils3D.projectVectors(matrix, verts, pVerts, uvts);
  34.     canvas.lock();
  35.     canvas.fillRect(canvas.rect, 0x000000);
  36.     var p = new Point();
  37.     for (var i:int = 0; i<pVerts.length; i+=2) {
  38.         p.x = pVerts[i];
  39.         p.y = pVerts[i+1];
  40.         canvas.copyPixels(brush, brush.rect, p, null, null, true);
  41.     }
  42.     canvas.unlock();
  43. }

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:

Also posted in BitmapData, Math, Vector, graphics algorithms, pixel manipulation, strings | Tagged , | Leave a comment

3D Hypocycloid Shape

By Zevan | April 21, 2009
CLICK HERE TO COPY
Actionscript:
  1. var matrix:Matrix3D = new Matrix3D();
  2. var verts:Vector.<Number> = new Vector.<Number>();
  3. var pVerts:Vector.<Number> = new Vector.<Number>();
  4. var uvts:Vector.<Number> = new Vector.<Number>();
  5. const TWO_PI:Number=Math.PI * 2;
  6. var step:Number=.05;
  7.  
  8. var brush:BitmapData = new BitmapData(3, 2, true, 0x41FFFFFF);
  9. var n:Number=8;
  10. var xp:Number=0,yp:Number=0,a:Number=12,t:Number=0;
  11. for (var i:Number = 0; i<TWO_PI; i+=step) {
  12.     for (var j:Number = 0; j<TWO_PI; j+=step) {
  13.         // unoptimized for readability
  14.     var cosi:Number = a/n * ((n - 1) * Math.cos(i) + Math.cos(Math.abs((n - 1) * i)));
  15.     var sini:Number = a/n * ((n - 1) * Math.sin(i) - Math.sin(Math.abs((n - 1) * i)));
  16.     var cosj:Number = a/n * ((n - 1) * Math.cos(j) + Math.cos(Math.abs((n - 1) * j)));
  17.     var sinj:Number = a/n * ((n - 1) * Math.sin(j) - Math.sin(Math.abs((n - 1) * j)));
  18.         verts.push(cosi * cosj);
  19.         verts.push(sini * cosj);
  20.         verts.push(a * sinj);
  21.         pVerts.push(0),pVerts.push(0);
  22.         uvts.push(0),uvts.push(0),uvts.push(0);
  23.     }
  24. }
  25. var canvas:BitmapData=new BitmapData(400,400,false,0x000000);
  26. addChild(new Bitmap(canvas));
  27. var dx:Number=0;
  28. var dy:Number=0;
  29. addEventListener(Event.ENTER_FRAME, onLoop);
  30. function onLoop(evt:Event):void {
  31.     dx += (mouseX - dx)/4;
  32.     dy += (mouseY - dy)/4;
  33.     matrix.identity();
  34.     matrix.appendRotation(dy,Vector3D.X_AXIS);
  35.     matrix.appendRotation(dx,Vector3D.Y_AXIS);
  36.     matrix.appendTranslation(200, 200, 0);
  37.     Utils3D.projectVectors(matrix, verts, pVerts, uvts);
  38.     canvas.lock();
  39.     canvas.fillRect(canvas.rect, 0x000000);
  40.     var p = new Point();
  41.     for (var i:int = 0; i<pVerts.length; i+=2) {
  42.         p.x = pVerts[i];
  43.         p.y = pVerts[i + 1];
  44.         canvas.copyPixels(brush, brush.rect, p, null, null, true);
  45.     }
  46.     canvas.unlock();
  47. }

Taking the Hypocycloid stuff from yesterday into 3D...

Also posted in BitmapData, Math | Tagged , | 6 Comments

Utils3D.projectVectors() & 100,000 pixels

By Zevan | April 12, 2009
CLICK HERE TO COPY
Actionscript:
  1. var matrix:Matrix3D = new Matrix3D();
  2.  
  3. const PARTICLE_NUM:int = 100000;
  4. var verts:Vector.<Number> = new Vector.<Number>();
  5. var pVerts:Vector.<Number> = new Vector.<Number>();
  6. var uvts:Vector.<Number> = new Vector.<Number>();
  7.  
  8. for (var i:int = 0; i<PARTICLE_NUM; i++){
  9.     verts.push(Math.random()*250 - 125);
  10.     verts.push(Math.random()*250 - 125);
  11.     verts.push(Math.random()*250 - 125);
  12.    
  13.     pVerts.push(0), pVerts.push(0);
  14.     uvts.push(0), uvts.push(0), uvts.push(0);
  15. }
  16.  
  17. var canvas:BitmapData = new BitmapData(400,400,false, 0x000000);
  18. addChild(new Bitmap(canvas));
  19. var dx:Number=0;
  20. var dy:Number=0;
  21.  
  22. addEventListener(Event.ENTER_FRAME, onLoop);
  23. function onLoop(evt:Event):void {
  24.  
  25.     dx += (mouseX - dx)/4;
  26.     dy += (mouseY - dy)/4;
  27.    
  28.     matrix.identity();
  29.     matrix.appendRotation(dy,Vector3D.X_AXIS);
  30.     matrix.appendRotation(dx,Vector3D.Y_AXIS);
  31.     matrix.appendTranslation(200, 200, 0);
  32.    
  33.     Utils3D.projectVectors(matrix, verts, pVerts, uvts);
  34.    
  35.     canvas.lock();
  36.     canvas.fillRect(canvas.rect, 0x000000);
  37.         var leng:int = pVerts.length;
  38.     for (var i:int = 0; i<leng; i+=2){
  39.         canvas.setPixel( pVerts[i], pVerts[i + 1], 0xFFFFFF);
  40.     }
  41.     canvas.unlock();
  42. }

The above shows an easy way to use Utils3D.projectVectors() to move some pixels around in 3D. Since the 3D math is done behind the scenes by the flash player it runs quite fast...

Also posted in BitmapData, Vector, matrix, setPixel | Tagged , | 3 Comments