Category Archives: 3D

globalToLocal() in 3D

Actionscript:
  1. [SWF(frameRate=60, backgroundColor=0x000000, width=500, height=500)]
  2. stage.quality = "medium";
  3. var frame:Sprite = Sprite(addChild(new Sprite()));
  4. with (frame.graphics) beginFill(0xCCCCCC), drawRect(-200, -200, 400, 400), endFill();
  5. frame.x = stage.stageWidth / 2;
  6. frame.y = stage.stageHeight / 2;
  7. frame.z = 100;
  8.  
  9. var canvas:Shape = Shape(frame.addChild(new Shape()));
  10. var msk:Shape = Shape(frame.addChild(new Shape()));
  11. with (msk.graphics) beginFill(0x00FF00), drawRect(-200, -200, 400, 400), endFill();
  12. canvas.mask = msk
  13.  
  14. var txt:TextField = TextField(addChild(new TextField()));
  15. txt.defaultTextFormat = new TextFormat("_sans", 12);
  16. txt.x = txt.y = 10;
  17. txt.textColor = 0xFFFFFF, txt.autoSize="left", txt.text = "Draw on the 3D plane...";
  18.  
  19. stage.addEventListener(MouseEvent.MOUSE_DOWN, onDown);
  20. stage.addEventListener(MouseEvent.MOUSE_UP, onUp);
  21. function onDown(evt:MouseEvent):void{
  22.     canvas.graphics.lineStyle(4, 0x000000);
  23.     var pnt:Point = frame.globalToLocal(new Point(mouseX, mouseY));
  24.     canvas.graphics.moveTo(pnt.x, pnt.y);
  25.     addEventListener(Event.ENTER_FRAME, onDraw);
  26. }
  27. function onUp(evt:MouseEvent):void{
  28.     removeEventListener(Event.ENTER_FRAME, onDraw);
  29. }
  30.  
  31. var t:Number = 0;
  32. addEventListener(Event.ENTER_FRAME, onLoop);
  33. function onLoop(evt:Event):void {
  34.     frame.rotationY = 35 * Math.sin(t);
  35.     frame.rotationX = 35 * Math.cos(t);
  36.     t+=0.02;
  37. }
  38.  
  39. function onDraw(evt:Event):void {
  40.         var pnt:Point = frame.globalToLocal(new Point(mouseX, mouseY));
  41.     canvas.graphics.lineTo(pnt.x, pnt.y);
  42. }

This demo shows that globalToLocal() works with 3D - saving us the trouble of doing some extra math if we want to draw on 3D display objects...

Have a look at the swf....


Was made aware of this trick by watching a video that kevinSuttle sent me via twitter. The video is an interview with Chris Nuuja (one of the flash player engineers).

Also posted in DisplayObject, Graphics, misc, motion | Tagged , , | 3 Comments

3D Key Controls

Actionscript:
  1. [SWF(backgroundColor=0x000000, width=500, height=500)]
  2. var hsw:Number = stage.stageWidth / 2;
  3. var hsh:Number = stage.stageHeight / 2;
  4. var pointNum:int = 300;
  5. var points3D:Vector.<Number> = new Vector.<Number>();
  6. var points2D:Vector.<Number> = new Vector.<Number>();
  7. var uvts:Vector.<Number> = new Vector.<Number>();
  8. var sorted:Array = [];
  9. var pnt:Point = new Point();
  10. var m:Matrix3D = new Matrix3D();
  11. var v:Vector3D = new Vector3D();
  12. for (var i:int = 0; i<pointNum; i++){
  13.     v.x = 300;
  14.     v.y = v.z = 0;
  15.     m.identity();
  16.     m.appendRotation(Math.random()*360, Vector3D.X_AXIS);
  17.     m.appendRotation(Math.random()*360, Vector3D.Y_AXIS);
  18.     m.appendRotation(Math.random()*360, Vector3D.Z_AXIS);
  19.     v = m.transformVector(v);
  20.     points3D.push(v.x, v.y, v.z);
  21.     points2D.push(0,0);
  22.     uvts.push(0,0,0);
  23.     sorted.push(new Vector3D());
  24. }
  25. points3D.fixed = true;
  26. points2D.fixed = true;
  27. uvts.fixed = true;
  28. var p:PerspectiveProjection = new PerspectiveProjection();
  29. var proj:Matrix3D = p.toMatrix3D();
  30. var rx:Number = 0, ry:Number = 0;
  31. addEventListener(Event.ENTER_FRAME, onLoop);
  32. function onLoop(evt:Event):void {
  33.     var i:int, j:int;
  34.     m.identity();
  35.     if (key[Keyboard.RIGHT]){
  36.         rx+=3
  37.     }else
  38.     if (key[Keyboard.LEFT]){
  39.         rx-=3
  40.     }else
  41.     if (key[Keyboard.UP]){
  42.         ry-=3
  43.     }else
  44.     if (key[Keyboard.DOWN]){
  45.         ry+=3
  46.     }
  47.     m.appendRotation(rx, Vector3D.Y_AXIS);
  48.     m.appendRotation(ry, Vector3D.X_AXIS);
  49.     m.appendTranslation(0, 0, 1000);
  50.     m.append(proj);
  51.     Utils3D.projectVectors(m, points3D, points2D, uvts);
  52.     for (i = 0, j = 0; i<points2D.length; i+=2, j++){
  53.         sorted[j].x = points2D[i] + hsw;
  54.         sorted[j].y = points2D[i + 1] + hsh;
  55.         sorted[j].z = uvts[j * 3 + 2];
  56.     }
  57.     sorted.sortOn("z", Array.NUMERIC);
  58.     graphics.clear();
  59.     graphics.lineStyle(2, 0x000000, 0.1);
  60.     for(i = 0; i<sorted.length; i++){
  61.         var zpos:Number = sorted[i].z * 12000;
  62.         var c:int = zpos * 14;
  63.         c = (c> 255) ? 255 : c;
  64.         graphics.beginFill(100<<16 | 100 <<8 |c);
  65.         graphics.drawCircle(sorted[i].x, sorted[i].y,zpos);
  66.         graphics.endFill();
  67.     }
  68. }
  69.  
  70. // permanently applies the matrix to the points3D vector
  71. function applyTransform():void{
  72.     m.identity();
  73.     m.appendRotation(rx, Vector3D.Y_AXIS);
  74.     m.appendRotation(ry, Vector3D.X_AXIS);
  75.     var temp:Vector.<Number> = new Vector.<Number>();
  76.     m.transformVectors(points3D, temp);
  77.     points3D = temp;
  78.     points3D.fixed = true;
  79.     rx = 0, ry = 0;
  80. }
  81.  
  82. // basic key setup
  83. var key:Object = new Object();
  84. stage.addEventListener(KeyboardEvent.KEY_DOWN, onKeyPressed);
  85. stage.addEventListener(KeyboardEvent.KEY_UP, onKeyReleased);
  86. function onKeyPressed(evt:KeyboardEvent):void {
  87.     key[evt.keyCode] = true;
  88.     key.keyCode = evt.keyCode;
  89. }
  90. function onKeyReleased(evt:KeyboardEvent):void {
  91.   applyTransform();
  92.   key[evt.keyCode] = false;
  93. }

In response to Thomas Francis's question, this snippet takes the Simple z-sorting snippet and shows how one might go about adding some basic key controls to it. It works by permanently applying x and y rotation transformations to the set of 3D points every time a key is released.

Check out the swf...

If you need to be able to rotate on both the x and y axis at the same time - and just need more flexibility... one way to do it would be to use quaternions - which may be tricky - but there are plenty of examples out there in java, processing and C/C++ just waiting to be ported (been on the todo list for some time actually).

Haven't been posting every day because I've been out of the country and away from my computer... have a backlog of snippets that need to be cleaned up and put in the pipeline...

Also posted in Graphics, Vector, keys | Tagged , , | 3 Comments

Simple z-sorting

Actionscript:
  1. [SWF(backgroundColor=0x444444, width=500, height=500)]
  2. var hsw:Number = stage.stageWidth / 2;
  3. var hsh:Number = stage.stageHeight / 2;
  4.  
  5. var pointNum:int = 200;
  6. var points3D:Vector.<Number> = new Vector.<Number>();
  7. var points2D:Vector.<Number> = new Vector.<Number>();
  8. var uvts:Vector.<Number> = new Vector.<Number>();
  9. var sorted:Array = [];
  10.  
  11. var pnt:Point = new Point();
  12. var m:Matrix3D = new Matrix3D();
  13. var v:Vector3D = new Vector3D();
  14. for (var i:int = 0; i<pointNum; i++){
  15.     v.x = Math.random()*400-200;
  16.     m.identity();
  17.     m.appendRotation(Math.random()*360, Vector3D.X_AXIS);
  18.     m.appendRotation(Math.random()*360, Vector3D.Y_AXIS);
  19.     m.appendRotation(Math.random()*360, Vector3D.Z_AXIS);
  20.     v = m.transformVector(v);
  21.     points3D.push(v.x, v.y, v.z);
  22.     points2D.push(0,0);
  23.     uvts.push(0,0,0);
  24.     sorted.push(new Vector3D());
  25. }
  26. points3D.fixed = true;
  27. points2D.fixed = true;
  28. uvts.fixed = true;
  29.  
  30. var p:PerspectiveProjection = new PerspectiveProjection();
  31. var proj:Matrix3D = p.toMatrix3D();
  32.  
  33. var dx:Number = 0, dy:Number = 0;
  34. addEventListener(Event.ENTER_FRAME, onLoop);
  35. function onLoop(evt:Event):void {
  36.     var i:int, j:int;
  37.     dx += (mouseX - dx) / 4;
  38.     dy += (mouseY - dy) / 4;
  39.     m.identity();
  40.     m.appendRotation(dx, Vector3D.Y_AXIS);
  41.     m.appendRotation(dy, Vector3D.X_AXIS);
  42.     m.appendTranslation(0, 0, 1000);
  43.     m.append(proj);
  44.    
  45.     Utils3D.projectVectors(m, points3D, points2D, uvts);
  46.    
  47.     for (i = 0, j = 0; i<points2D.length; i+=2, j++){
  48.         sorted[j].x = points2D[i] + hsw;
  49.         sorted[j].y = points2D[i + 1] + hsh;
  50.         sorted[j].z = uvts[j * 3 + 2];
  51.     }
  52.     sorted.sortOn("z", Array.NUMERIC);
  53.    
  54.     graphics.clear();
  55.     for(i = 0; i<sorted.length; i++){
  56.         var zpos:Number = sorted[i].z * 12000;
  57.         var c:int = zpos * 14;
  58.         graphics.beginFill(c <<16 | c <<8 | c);
  59.         graphics.drawCircle(sorted[i].x, sorted[i].y,zpos);
  60.         graphics.endFill();
  61.     }
  62. }

Here is an easy way to do z-sorting on a cluster of circles.


Have a look at the swf over at wonderfl...

Also posted in Graphics, Vector, sortOn | Tagged , , | 5 Comments

Gradient Bezier 3D

Actionscript:
  1. [SWF(backgroundColor=0x333333, width=800, height=600)];
  2. x = stage.stageWidth / 2;
  3. y = stage.stageHeight / 2;
  4. var verts:Vector.<Number>  = new Vector.<Number>();
  5. var tVerts:Vector.<Number> = new Vector.<Number>();
  6. var pVerts:Vector.<Number> = new Vector.<Number>();
  7. var uvts:Vector.<Number> = new Vector.<Number>();
  8.  
  9. var igraph:Vector.<IGraphicsData> = new Vector.<IGraphicsData>();
  10.  
  11. var tVect:Vector3D = new Vector3D();
  12. var m:Matrix3D = new Matrix3D();
  13. for (var i:int = 0; i<200; i++){
  14.     for (var j:int = 0; j<3; j++){
  15.         tVect.x = Math.random() * 0.15;
  16.         m.identity();
  17.         m.appendRotation(Math.random()*360, Vector3D.X_AXIS);
  18.         m.appendRotation(Math.random()*360, Vector3D.Y_AXIS);
  19.         m.appendRotation(Math.random()*360, Vector3D.Z_AXIS);
  20.         tVect = m.transformVector(tVect);
  21.         verts.push(tVect.x, tVect.y, tVect.z);
  22.     }
  23.    
  24.     var stroke:GraphicsStroke = new GraphicsStroke();
  25.    
  26.     var col:int = [0xFFFFFF, 0x000000, 0xFFCC00, 0xFF0000][int(Math.random() * 4)];
  27.    
  28.     stroke.thickness = 2+(Math.random()*Math.random())*8;
  29.     var mg:Matrix = new Matrix();
  30.     mg.createGradientBox(350+Math.random()*20-10, 350+Math.random()*20-10, 0, -270+i/2,-240+i/2);
  31.     stroke.fill = new GraphicsGradientFill(GradientType.RADIAL, [0xFFFFFF,0x444444], [1, 1], [30, 255], mg);
  32.  
  33.     var bez:GraphicsPath = new GraphicsPath();
  34.     bez.commands = Vector.<int>([1, 3]);
  35.     igraph.push(stroke);
  36.     igraph.push(bez);
  37. }
  38.  
  39. var perspective:PerspectiveProjection = new PerspectiveProjection();
  40. perspective.fieldOfView = 45;
  41. var trans:Matrix3D = new Matrix3D();
  42. var proj:Matrix3D = perspective.toMatrix3D();
  43. var dx:Number = 0, dy:Number = 0;
  44.  
  45. addEventListener(Event.ENTER_FRAME, onLoop);
  46. function onLoop(evt:Event):void {
  47.     dx += (mouseX - dx) / 4;
  48.     dy += (mouseY - dy) / 4;
  49.        
  50.     trans.identity();
  51.     trans.appendRotation(dy, Vector3D.X_AXIS);
  52.     trans.appendRotation(dx, Vector3D.Y_AXIS);
  53.     trans.appendTranslation(0,0,0.5);
  54.     trans.transformVectors(verts, tVerts);
  55.     Utils3D.projectVectors(proj, tVerts, pVerts, uvts);
  56.    
  57.     var inc:int = 0;
  58.     for (var i:int = 1; i<igraph.length; i+=2){
  59.         GraphicsPath(igraph[i]).data = pVerts.slice(inc, inc + 6);
  60.         inc += 6;
  61.     }
  62.      
  63.     graphics.clear();
  64.     graphics.drawGraphicsData(igraph);
  65. }

A variation on yesterdays post - this makes use of GraphicsGradientFill to add some depth...

Check out the swf...

Also posted in Graphics, bezier | Tagged , , | Leave a comment

3D Bezier

Actionscript:
  1. [SWF(backgroundColor=0x000000, width=800, height=600)];
  2. x = stage.stageWidth / 2;
  3. y = stage.stageHeight / 2;
  4. var verts:Vector.<Number>  = new Vector.<Number>();
  5. var tVerts:Vector.<Number> = new Vector.<Number>();
  6. var pVerts:Vector.<Number> = new Vector.<Number>();
  7. var uvts:Vector.<Number> = new Vector.<Number>();
  8.  
  9. var igraph:Vector.<IGraphicsData> = new Vector.<IGraphicsData>();
  10.  
  11. var tVect:Vector3D = new Vector3D();
  12. var m:Matrix3D = new Matrix3D();
  13. for (var i:int = 0; i<300; i++){
  14.     for (var j:int = 0; j<3; j++){
  15.         tVect.x = Math.random() * 0.15;
  16.         m.identity();
  17.         m.appendRotation(Math.random()*360, Vector3D.X_AXIS);
  18.         m.appendRotation(Math.random()*360, Vector3D.Y_AXIS);
  19.         m.appendRotation(Math.random()*360, Vector3D.Z_AXIS);
  20.         tVect = m.transformVector(tVect);
  21.         verts.push(tVect.x, tVect.y, tVect.z);
  22.     }
  23.    
  24.      
  25.     var stroke:IGraphicsData = new GraphicsStroke();
  26.    
  27.     var col:int = [0xFFFFFF, 0x000000, 0xFFCC00, 0xFF0000][int(Math.random() * 4)];
  28.     with (stroke) thickness = (Math.random()*Math.random())*10, fill = new GraphicsSolidFill(col);
  29.  
  30.     var bez:GraphicsPath = new GraphicsPath();
  31.     bez.commands = Vector.<int>([1, 3]);
  32.     igraph.push(stroke);
  33.     igraph.push(bez);
  34. }
  35.  
  36. var perspective:PerspectiveProjection = new PerspectiveProjection();
  37. perspective.fieldOfView = 45;
  38. var trans:Matrix3D = new Matrix3D();
  39. var proj:Matrix3D = perspective.toMatrix3D();
  40. var dx:Number = 0, dy:Number = 0;
  41.  
  42. addEventListener(Event.ENTER_FRAME, onLoop);
  43. function onLoop(evt:Event):void {
  44.     dx += (mouseX - dx) / 4;
  45.     dy += (mouseY - dy) / 4;
  46.        
  47.     trans.identity();
  48.     trans.appendRotation(dy, Vector3D.X_AXIS);
  49.     trans.appendRotation(dx, Vector3D.Y_AXIS);
  50.     trans.appendTranslation(0,0,0.5);
  51.     trans.transformVectors(verts, tVerts);
  52.     Utils3D.projectVectors(proj, tVerts, pVerts, uvts);
  53.    
  54.     var inc:int = 0;
  55.     for (var i:int = 1; i<igraph.length; i+=2){
  56.         GraphicsPath(igraph[i]).data = pVerts.slice(inc, inc + 6);
  57.         inc += 6;
  58.     }
  59.      
  60.     graphics.clear();
  61.     graphics.drawGraphicsData(igraph);
  62. }

After a few hours of trying to get a super optimized fp10 z-sorting demo happening, I gave up (for now) and decided to just let loose with something easy. The result is this 3D Bezier example...


Check out the swf...

Also posted in Graphics, bezier | Tagged , , , | 3 Comments

Gumdrop Torus

Actionscript:
  1. var matrix:Matrix3D = new Matrix3D();
  2.  
  3. var verts:Vector.<Number> = new Vector.<Number>();
  4. var pVerts:Vector.<Number> = new Vector.<Number>();
  5. var uvts:Vector.<Number> = new Vector.<Number>();
  6.  
  7. for (var i:Number = -2; i<2; i+=.04){
  8.     for (var j:Number = -2; j<2; j+=.04){
  9.         for (var k:Number = -2; k<2; k+=.04){
  10. // equation from: http://local.wasp.uwa.edu.au/~pbourke/geometry/gumdrop/
  11.             var yz:Number = j * j + k * k;
  12.              var s:Number = 4 * (Math.pow(i,4) + Math.pow(yz,2))
  13.              + 17 * i * i *(yz) - 20 * (yz + i * i) + 17;
  14.             if (s <0 && s> -0.5){
  15.                 verts.push(i * 60);
  16.                 verts.push(j * 60);
  17.                 verts.push(k * 60);
  18.                 pVerts.push(0), pVerts.push(0);
  19.                 uvts.push(0), uvts.push(0), uvts.push(0);
  20.              }
  21.         }
  22.     }
  23. }
  24.  
  25. var tVerts:Vector.<Number> = new Vector.<Number>();
  26. matrix.appendRotation(90, Vector3D.X_AXIS);
  27. matrix.appendRotation(45, Vector3D.Y_AXIS);
  28. matrix.appendScale(1.7, 1.7, 1.7);
  29. matrix.transformVectors(verts, tVerts);
  30.  
  31. var p:Point = new Point();
  32. var brush:BitmapData=new BitmapData(3,3,true,0x41FFFFFF);
  33. var canvas:BitmapData = new BitmapData(500,500,false, 0x000000);
  34. addChild(new Bitmap(canvas));
  35. var dx:Number=0;
  36. var dy:Number=0;
  37. addEventListener(Event.ENTER_FRAME, onLoop);
  38. function onLoop(evt:Event):void {
  39.     dx += (mouseX - dx)/4;
  40.     dy += (mouseY - dy)/4;
  41.     matrix.identity();
  42.     matrix.appendRotation(dy,Vector3D.X_AXIS);
  43.     matrix.appendRotation(dx,Vector3D.Y_AXIS);
  44.     matrix.appendTranslation(250, 250, 0);
  45.     Utils3D.projectVectors(matrix, tVerts, pVerts, uvts);
  46.     canvas.lock();
  47.     canvas.fillRect(canvas.rect, 0x000000);
  48.     var inc:int = 0;
  49.     for (var i:int = 0; i<pVerts.length; i+=2){
  50.      
  51.         p.x = pVerts[i];
  52.         p.y = pVerts[i+1];
  53.         canvas.copyPixels(brush, brush.rect, p, null, null, true);
  54.     }
  55.     canvas.unlock();
  56. }

Felt like revisiting implicit surface plotting today...

Have a look at the swf over at wonderfl.net

Also posted in BitmapData, Math | Tagged , , | Leave a comment

Parallax fp10

Actionscript:
  1. [SWF(backgroundColor=0x000000, width = 800, height = 600)]
  2.  
  3. // this is a trick to keep the 3D texture quality up...
  4. // try setting it right off the bat and you'll notice that the
  5. // Shapes look pixilated
  6. setTimeout(function():void{ stage.quality="low"}, 500);
  7.  
  8. var matrix:Matrix = new Matrix();
  9. matrix.createGradientBox(600, 600, 0, -450, -450);
  10.  
  11. var boxNum:int = 30;
  12. var boxes:Array = [];
  13. for (var i:int = 0; i<boxNum; i++) boxes[i] = makeBox();
  14.  
  15. var dx:Number = 0, dy:Number = 0;
  16. onLoop();
  17. addEventListener(Event.ENTER_FRAME, onLoop);
  18.  
  19. function onLoop(evt:Event=null):void {
  20.     dx += (mouseX - dx) / 4;
  21.     dy += (mouseY - dy) / 4;
  22.     for (var i:int = 0; i<boxNum; i++){
  23.         var box:Shape = boxes[i];
  24.         box.z = 400 - i * 20;
  25.         box.x = dx;
  26.         box.y = dy;
  27.         box.rotation = i + getTimer() / 10;
  28.     }
  29. }
  30.  
  31. function makeBox():Shape{
  32.     var box:Shape = Shape(addChild(new Shape()));
  33.     box.x = stage.stageWidth/2;
  34.     box.y = stage.stageHeight/2;
  35.     box.z = 1;
  36.     with (box.graphics){
  37.          beginGradientFill(GradientType.RADIAL, [0xFFFFFF, 0x333333], [1,1], [0, 255], matrix, SpreadMethod.PAD);
  38.         drawRect(-100, -100, 200, 200);
  39.         drawRect(-70, -70, 140, 140);
  40.     }
  41.     return box;
  42. }

This snippet draws 30 gradient box shapes, gives them different z values and then moves them based on the mouse. This technique is good if you just want a few layers of parallax motion - I got carried away and you'll notice that if you add more boxes it begins to slow down pretty quick.


Have a look at the swf....



I first used this technique for this small interactive drawing...

Something interesting I noticed about fp10 3D DisplayObjects is that if you set the stage.quality to low right off the bat, the display objects look pixelated... but if you wait a few milliseconds, you end up with less pixelation and you still get a speed boost from the low quality - I think it must have something to do with the way the 3D textures are handled by the player...

Tomorrow I think I'll post a version of this that uses IGraphicsData and Utils.projectVectors()... should be a huge speed boost...

Also posted in motion | Tagged , , | 1 Comment

Spring PerspectiveProjection

Actionscript:
  1. var pointNum:int = 3000;
  2. x = stage.stageWidth / 2;
  3. y = stage.stageHeight / 2;
  4.  
  5. var verts:Vector.<Number>  = new Vector.<Number>();
  6. var tVerts:Vector.<Number> = new Vector.<Number>();
  7. var pVerts:Vector.<Number> = new Vector.<Number>();
  8. var uv:Vector.<Number> = new Vector.<Number>();
  9. var cmds:Vector.<int> = new Vector.<int>();
  10.  
  11. var index:int = 0;
  12. var half:Number = pointNum / 20000;
  13. for (var i:int = 0; i<pointNum; i+=3){
  14.     verts[i] = 0.08 * Math.cos(i * Math.PI / 180);
  15.     verts[i+1] = 0.08 * Math.sin(i * Math.PI / 180);
  16.     verts[i+2] =  i / 10000 - half;
  17.     cmds[index++] = 2;
  18. }
  19. cmds[0] = 1;
  20.  
  21. var proj:PerspectiveProjection = new PerspectiveProjection();
  22. proj.fieldOfView = 45;
  23. var projMat:Matrix3D = proj.toMatrix3D();
  24. var m:Matrix3D = new Matrix3D();
  25. var dx:Number = 0, dy:Number = 0;
  26. addEventListener(Event.ENTER_FRAME, onLoop);
  27. function onLoop(evt:Event):void {
  28.        m.identity();
  29.        dx += (mouseX - dx) / 4;
  30.        dy += (mouseY - dy) / 4;
  31.        m.appendRotation(dy,Vector3D.X_AXIS);
  32.        m.appendRotation(dx,Vector3D.Y_AXIS);
  33.        m.appendTranslation(0,0,0.5);
  34.        m.transformVectors(verts, tVerts);
  35.        Utils3D.projectVectors(projMat, tVerts, pVerts, uv);
  36.        graphics.clear();
  37.        graphics.lineStyle(3,0x000000);
  38.        graphics.drawPath(cmds, pVerts);
  39. }

This snippet draws a spring shape in 3D with perspective. This is the first snippet where I've made use of the PerspectiveProjection class. So if your wondering how to add perspective to your Utils3D.projectVectors code... this is one way to do it...


Have a look at the swf...

Also posted in Graphics, Video, matrix | Tagged , , | 1 Comment

Quick Pixel Sphere

Actionscript:
  1. var pointNum:int = 20000;
  2. var radius:int = 150;
  3.  
  4. var canvas:BitmapData = new BitmapData(400,400,false, 0x000000);
  5. addChild(new Bitmap(canvas));
  6. var verts:Vector.<Number>  = new Vector.<Number>();
  7. var pVerts:Vector.<Number> = new Vector.<Number>();
  8. var uv:Vector.<Number> = new Vector.<Number>();
  9.  
  10. for (var i:int = 0; i<pointNum; i+=3){
  11.     var xp:Number = Math.random() * 400 - 200;
  12.     var yp:Number = Math.random() * 400 - 200;
  13.     var zp:Number = Math.random() * 400 - 200;
  14.     var dist:Number = Math.sqrt(xp * xp + yp * yp + zp * zp);
  15.     // normalize and scale x,y,z
  16.     verts[i] = xp / dist * radius;
  17.     verts[i+1] = yp / dist * radius;
  18.     verts[i+2] = zp / dist * radius;
  19. }
  20.  
  21. var m:Matrix3D = new Matrix3D();
  22. var dx:Number = 0, dy:Number = 0;
  23. addEventListener(Event.ENTER_FRAME, onLoop);
  24. function onLoop(evt:Event):void {
  25.        m.identity();
  26.        dx += (mouseX - dx) / 4;
  27.        dy += (mouseY - dy) / 4;
  28.        m.appendRotation(dx, Vector3D.X_AXIS);
  29.        m.appendRotation(dy, Vector3D.Y_AXIS);
  30.        m.appendTranslation(200,200,0);
  31.        Utils3D.projectVectors(m, verts, pVerts, uv);
  32.        canvas.fillRect(canvas.rect, 0x000000);
  33.        for (var i:int = 0; i<pVerts.length; i+=2){
  34.          canvas.setPixel(pVerts[i], pVerts[i + 1], 0xFFFFFF);
  35.        }
  36. }

This snippet shows a quick way to randomly place a bunch of xyz coordinates on the surface of a sphere. I saw this trick in an OpenGL book a few years back - dug around my books but couldn't find it... If I find it I'll update this post.

The trick is achieved by normalizing the vector defined by each 3D coordinate...


Have a look at the swf...

Also posted in BitmapData, Math, matrix, setPixel | Tagged , , | 4 Comments

Sphere of Squares

Actionscript:
  1. [SWF(width = 600, height = 600, backgroundColor=0x000000)]
  2. var squareNum:int  = 1000;
  3. var hw:Number = stage.stageWidth / 2;
  4. var hh:Number = stage.stageHeight / 2;
  5. // verts defines a single square
  6. var verts:Vector.<Number> = Vector.<Number>([-20, 0, 0, 20, 0, 0, 20, 0, 40, -20, 0, 40, -20, 0, 0]);
  7. var cmds:Vector.<int> = Vector.<int>([1,2,2,2,2]);
  8. var tempVerts:Vector.<Number> = new Vector.<Number>();
  9. var newVerts:Vector.<Number> = new Vector.<Number>();
  10. var pVerts:Vector.<Number> = new Vector.<Number>(10 * squareNum);
  11. var uv:Vector.<Number> = new Vector.<Number>(15 * squareNum);
  12. var vectors:Shape = new Shape();
  13. var canvas:BitmapData = new BitmapData(stage.stageWidth,stage.stageHeight,false, 0x000000);
  14. addChild(new Bitmap(canvas));
  15. var blurred:BitmapData = new BitmapData(stage.stageWidth,stage.stageHeight,false, 0x000000);
  16. var blur:BlurFilter = new BlurFilter(20,20,1);
  17.  
  18. var m:Matrix3D = new Matrix3D();
  19.  
  20. var radius:Number = 200;
  21. // duplicate the verts array a bunch of times
  22. // each time moving the square to a random place on the
  23. // circumference of a sphere
  24. for (var i:int = 0; i<squareNum; i++){
  25.     m.identity();
  26.     var s:Number = Math.random()*.5 + .5;
  27.     m.appendScale(s, s, s);
  28.     m.appendRotation(90,Vector3D.X_AXIS);
  29.     m.appendTranslation(0, 0, radius);
  30.     m.appendRotation(Math.random()*360,Vector3D.X_AXIS);
  31.     m.appendRotation(Math.random()*360,Vector3D.Y_AXIS);
  32.     m.appendRotation(Math.random()*360,Vector3D.Z_AXIS);
  33.     m.transformVectors(verts,tempVerts);
  34.     newVerts = newVerts.concat(tempVerts);
  35.     cmds = cmds.concat(Vector.<int>([1,2,2,2,2]));
  36. }
  37. newVerts.fixed = pVerts.fixed = uv.fixed = true;
  38. var dx:Number = 0, dy:Number = 0;
  39. var pnt:Point = new Point();
  40. addEventListener(Event.ENTER_FRAME, onLoop);
  41. function onLoop(evt:Event):void {
  42.        dx += (mouseX - dx) / 4;
  43.        dy += (mouseY - dy) / 4;
  44.        m.identity();
  45.        m.appendRotation(dx,Vector3D.Z_AXIS);
  46.        m.appendRotation(dy,Vector3D.X_AXIS);
  47.        m.appendTranslation(hw,hh, 0);
  48.        Utils3D.projectVectors(m, newVerts, pVerts, uv);
  49.        with(vectors.graphics){
  50.            clear();
  51.            beginFill(0xFFFFFF);
  52.            drawCircle(hw, hh, radius+10);
  53.            beginFill(0x000000);
  54.            drawPath(cmds, pVerts, GraphicsPathWinding.NON_ZERO);
  55.        }
  56.        canvas.fillRect(canvas.rect, 0x000000);
  57.        canvas.draw(vectors);
  58.        blurred.copyPixels(canvas, canvas.rect, pnt);
  59.        blurred.applyFilter(blurred,blurred.rect, pnt, blur);
  60.        canvas.draw(blurred, null, null, BlendMode.SCREEN);
  61. }

This snippet is similar to yesterdays post but the visual result is rather different. This one does a little more Matrix3D stuff resulting in a sphere made up entirely of squares. This is obscured by the size of the squares and the fact that they overlap and cut each other up. BitmapData a BlurFilter and a BlendMode give the entire thing a slight glow...


Have a look at the swf here...

Also posted in BitmapData, Vector | Tagged , , , | 12 Comments