Category Archives: Vector

BitmapData Frame Texture

Actionscript:
  1. [SWF(width = 800, height = 600)]
  2. var circle:Shape = new Shape();
  3. var radius:Number = 4;
  4. var diameter:Number = radius * 2;
  5. var diam4:Number = diameter * 4;
  6. with(circle.graphics) beginFill(0x000000), drawCircle(diameter,diameter,radius);
  7. circle.filters = [new BlurFilter(5, 5, 2)];
  8.  
  9. var currFrame:Frame;
  10.  
  11. // populate the linked list
  12. generateAnimation();
  13.  
  14. var animationNum:int = 8000;
  15. var animation:Vector.<Frame> = new Vector.<Frame>();
  16. var locs:Vector.<Point> = new Vector.<Point>();
  17. // populate locs and animation
  18. while(animation.length <animationNum){
  19.        currFrame = currFrame.next;
  20.        animation.push(currFrame);
  21.        locs.push(new Point(Math.random() * stage.stageWidth - radius,
  22.                            Math.random() * (stage.stageHeight+diam4) - diam4));
  23. }
  24.  
  25. var rect:Rectangle = animation[0].bitmap.rect;
  26. var bottom:Number = stage.stageHeight + rect.height;
  27. var top:Number = -rect.height;
  28.  
  29. var canvas:BitmapData = new
  30. BitmapData(stage.stageWidth,stage.stageHeight,false, 0x000000);
  31. addChild(new Bitmap(canvas));
  32.  
  33. addEventListener(Event.ENTER_FRAME, onLoop);
  34. function onLoop(evt:Event):void {
  35.        // clear the canvas
  36.        canvas.fillRect(canvas.rect, 0x222222);
  37.        // draw the current frame
  38.        for (var i:int = 0; i<animationNum; i++){
  39.                var ani:Frame = animation[i];
  40.                var pnt:Point = locs[i];
  41.                canvas.copyPixels(ani.bitmap, rect, pnt, null, null, true);
  42.                // get the next frame of the animation
  43.                pnt.y += 1;
  44.                if (pnt.y> bottom){
  45.                    pnt.y = top;
  46.                }
  47.                animation[i] = ani.next;
  48.        }
  49.  
  50. }
  51.  
  52. // generate and capture 40 bitmaps by altering the colorTransform of
  53.  
  54. function generateAnimation():void{
  55.        var channel:uint = 0;
  56.        var ct:ColorTransform = new ColorTransform();
  57.        var increase:Boolean = true;
  58.        var firstFrame:Frame;
  59.        var pFrame:Frame;
  60.        for (var i:int = 0; i<40; i++){
  61.                if (increase){
  62.                   channel += 10.25;
  63.                   if (channel> 200){
  64.                          increase = false;
  65.                   }
  66.                }else{
  67.                   channel -= 10;
  68.                }
  69.                ct.color = channel <<16 | channel <<8 | channel;
  70.                circle.transform.colorTransform = ct;
  71.                
  72.                // populate linked list
  73.                currFrame = capture(circle);
  74.                if (pFrame){
  75.                   pFrame.next = currFrame;
  76.                }
  77.                if (i == 0){
  78.                   firstFrame = currFrame;
  79.                }
  80.                pFrame = currFrame;
  81.        }
  82.        // close the list
  83.        currFrame.next = firstFrame;
  84.        currFrame = firstFrame;
  85. }
  86.  
  87. // create the Frame instance and draw the circle to it
  88. // preserving the colorTransform information
  89. function capture(target:Shape):Frame{
  90.        var frame:Frame = new Frame();
  91.        frame.bitmap = new BitmapData(target.width*2, target.height*2, true, 0x000000000);
  92.        frame.bitmap.draw(target, target.transform.matrix, target.transform.colorTransform);
  93.        return frame;
  94. }

This is a variation on the last post. It captures 40 small bitmaps of a blurred circle fading in and out and then draws 8000 of them to the stage.


Have a look at the swf...

Also posted in BitmapData, Data Structures | 1 Comment

Three Color Triangle

Actionscript:
  1. /*
  2. *       Petri Leskinen, Finland
  3. *       25 October 2009
  4. *       pixelero.wordpress.com
  5. *
  6. *       Actionscript 3.0, Flash CS3, Flash Player 10
  7. *
  8. *       threeColorTriangle
  9. *       draws a triangle with a gradient fill of three colors for each vertex
  10. *       using graphics.drawTriangles and a BitmapData of size 2x2
  11. */
  12. function threeColorTriangle(
  13.       point0:Point, color0:uint,
  14.       point1:Point, color1:uint,
  15.       point2:Point, color2:uint):void {
  16.  
  17.       //      create a  bitmap of size 2x2 pixels
  18.       var bmd:BitmapData = new BitmapData(2,2,true);
  19.       //      copy colors to bitmap
  20.       //      the fourth color is average of color1 and color2
  21.       bmd.setVector(bmd.rect,
  22.               Vector.<uint>([color0,color1,color2,
  23.                                          (color1+color2)>>1
  24.                                          ]));
  25.  
  26.       //      draw triangle
  27.       this.graphics.beginBitmapFill(bmd,null,false,true /* =smooth */ );
  28.       this.graphics.drawTriangles(
  29.               // x,y -coordinates
  30.               Vector.<Number>([
  31.                       point0.x,point0.y,
  32.                       point1.x,point1.y,
  33.                       point2.x,point2.y]),
  34.               // indices
  35.               Vector.<int>([0,1,2]),
  36.               // texture coordinates
  37.               Vector.<Number>([0,0, 1,0, 0,1])
  38.               );
  39. }
  40.  
  41.  
  42. // demo, let's draw some of these on the stage
  43. randomize();
  44. function randomize():void {
  45.       this.graphics.clear();
  46.  
  47.       for (var i:int = 0;i<128;i++) {
  48.               //      pick some random colors
  49.               var color0:uint = 0xFFFFFFFF;
  50.               var color1:uint = 0xFFFFFF*Math.random() | 0xFF000000;
  51.               var color2:uint = 0xFFFFFF*Math.random() | 0xFF000000;
  52.  
  53.               //      random points
  54. var point0:Point = new Point(Math.random()*stage.stageWidth,
  55.             Math.random()*stage.stageHeight);
  56. var point1:Point = new Point(point0.x+200*(Math.random()-Math.random()),
  57.             point0.y+200*(Math.random()-Math.random()));
  58. var point2:Point = new Point(point0.x+200*(Math.random()-Math.random()),
  59.             point0.y+200*(Math.random()-Math.random()));
  60.  
  61.         threeColorTriangle(point0, color0, point1, color1, point2,  color2);
  62.       }
  63. }

This snippet is by Petri Leskinen (pixelero). It draws a triangle with a gradient fill of three colors for each vertex using Graphics.drawTriangles and a BitmapData of size 2x2. This is the simplest case, it can easily be extended to four colors or maybe to use a larger 3x3, 4x4 etc... bitmap.

Here's a still...

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

Flowing Leaves (optical illusion)


Saw this optical illusion today... figured I'd make a snippet to create a few variations on the illusion...

Actionscript:
  1. [SWF( backgroundColor=0x2E7999, width=780, height = 600) ]
  2.  
  3. var leafNum:Number = 375;
  4. var spacing:Number = 12;
  5. var cols:Number = 25;
  6. var hh:Number = stage.stageHeight / 2;
  7. var hw:Number = stage.stageWidth / 2;
  8.  
  9. for (var i:Number = 0; i<leafNum; i++){
  10.     var leaf:Shape = makeLeaf();
  11.     leaf.scaleX = leaf.scaleY = 0.25;
  12.     leaf.rotation = 90;
  13.     leaf.x = 50 + (i % cols) * (leaf.width + spacing);
  14.     leaf.y = 40 + int(i / cols) * (leaf.height + spacing);
  15.     var dx:Number = leaf.x - hw;
  16.     var dy:Number = leaf.y - hh;
  17.     leaf.rotation = Math.sqrt(dx * dx + dy * dy);
  18. }
  19.  
  20. function makeLeaf():Shape{
  21.     var leaf:Shape = Shape(addChild(new Shape()));
  22.     leaf.graphics.beginFill(0x9DC4D4);
  23.     scaleYcircle(leaf.graphics, 50, .65, false);
  24.     leaf.graphics.endFill();
  25.     leaf.graphics.lineStyle(2, 0x003366, 1, false, "none", CapsStyle.SQUARE, JointStyle.MITER);
  26.     scaleYcircle(leaf.graphics, 50, .65);
  27.     leaf.graphics.lineStyle(2, 0xFFFFFF, 1, false, "none", CapsStyle.SQUARE, JointStyle.MITER);
  28.     scaleYcircle(leaf.graphics, -50, .65);
  29.     return leaf;
  30. }
  31.  
  32.  
  33. // original circle function by senocular (www.senocular.com) from here http://www.actionscript.org/forums/showthread.php3?s=&threadid=30328
  34. // circle that can be scaled on the y axis
  35. function scaleYcircle(g:Graphics, r:Number, s:Number = 1, isHalf:Boolean=true):void {
  36.      
  37.     var c1:Number = r * (Math.SQRT2 - 1);
  38.     var c2:Number = r * Math.SQRT2 / 2;
  39.     var rs:Number = r * s, c1s:Number = c1 * s, c2s:Number = c2 * s;
  40.     var x_r:Number =  -r, y_r:Number = -rs, x_c2:Number =  -c2;
  41.     var y_c2:Number =  -c2s, x_c1:Number =  -c1, y_c1:Number =  -c1s
  42.     g.moveTo(r, 0), g.curveTo(r, c1s, c2, c2s);
  43.     g.curveTo(c1, rs, 0, rs), g.curveTo(x_c1,rs, x_c2, c2s);
  44.     g.curveTo(x_r, c1s, x_r, 0);
  45.     if (!isHalf){
  46.      g.curveTo(x_r,y_c1,x_c2,y_c2);
  47.      g.curveTo(x_c1,y_r,0,y_r), g.curveTo(c1,y_r,c2,y_c2);
  48.      g.curveTo(r,y_c1,r,0);
  49.     }
  50. }

Also posted in Graphics, Math, misc, motion, pixel manipulation | Tagged , , , | 5 Comments

drawTriangles() Cubes

Actionscript:
  1. private function addCube(xp:Number, yp:Number, zp:Number, w:Number, h:Number, leng:Number):void{
  2.             var hw:Number = w * 0.5;
  3.             var hh:Number = h * 0.5;
  4.             var hl:Number = leng * 0.5;
  5.             var xA:Number = xp - hw;
  6.             var xB:Number = hw + xp;
  7.             var yA:Number = yp - hh;
  8.             var yB:Number = hh + yp;
  9.             var zA:Number = zp - hl;
  10.             var zB:Number = hl + zp;
  11.             _verts.push(xA, yA, zA,
  12.                         xB, yA, zA,
  13.                         xA, yB, zA,
  14.                         xB, yB, zA,
  15.                         xA, yA, zB,
  16.                         xB, yA, zB,
  17.                         xA, yB, zB,
  18.                         xB, yB, zB);
  19.            
  20.             var index:int = _boxIndex * 8;
  21.             var i0:int = index, i1:int = index + 1, i2:int = index + 2;
  22.             var i3:int = index + 3,  i4:int = index + 4, i5:int = index + 5;
  23.             var i6:int = index + 6, i7:int = index + 7;
  24.             _indices.push(i0, i1, i2,
  25.                           i1, i3, i2,
  26.                           i6, i7, i4,
  27.                           i7, i5, i4,
  28.                           i1, i5, i3,
  29.                           i7, i3, i5,
  30.                           i4, i5, i0,
  31.                           i1, i0, i5,
  32.                           i2, i6, i0,
  33.                           i0, i6, i4,
  34.                           i2, i3, i6,
  35.                           i3, i7, i6);
  36.                          
  37.             _faces.push(new Face(), new Face(), new Face(),
  38.                         new Face(),  new Face(), new Face(),
  39.                         new Face(), new Face(), new Face(),
  40.                         new Face(), new Face(), new Face());
  41.             _uvts.push(Math.random(), Math.random(), 0,
  42.                        Math.random(), Math.random(), 0,
  43.                        Math.random(), Math.random(), 0,
  44.                        Math.random(), Math.random(), 0,
  45.                        Math.random(), Math.random(), 0,
  46.                        Math.random(), Math.random(), 0,
  47.                        Math.random(), Math.random(), 0,
  48.                        Math.random(), Math.random(), 0);
  49.             _boxIndex++;
  50.         }

Lately I've been posting large code snippets... so today I'm highlighting part of a larger snippet - The above code is the heart of a small experiment I created this morning. It sets up a cube for use with drawTraingles().

The rest of the code can be read here:
Cubes3D.as

Have a look at the swf here...


I also put it on wonderfl...

Also posted in 3D, Graphics, matrix, motion | Tagged , , | 6 Comments

Distance Spring

Actionscript:
  1. [SWF(backgroundColor=0x222222, width=500, height=500)]
  2. var hsw:Number = stage.stageWidth / 2;
  3. var hsh:Number = stage.stageHeight / 2;
  4. var pointNum:int = 800
  5. var points3D:Vector.<Number> = new Vector.<Number>();
  6. var points3Dout: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. var pnt:Point = new Point();
  11. var m:Matrix3D = new Matrix3D();
  12. var v:Vector3D = new Vector3D();
  13. for (var i:int = 0; i<pointNum; i++){
  14.     v.y = i * 0.7 - 300
  15.     var t =Math.random()*6.28;
  16.     v.x = 200 * Math.cos(i * 2 * Math.PI / 180);
  17.     v.z = 200 * Math.sin(i * 2 * Math.PI / 180);
  18.     v = m.transformVector(v);
  19.     points3D.push(v.x, v.y, v.z);
  20.     points2D.push(0,0);
  21.     uvts.push(0,0,0);
  22.     sorted.push(new Vector3D());
  23. }
  24. points3D.fixed = true;
  25. points2D.fixed = true;
  26. uvts.fixed = true;
  27. var p:PerspectiveProjection = new PerspectiveProjection();
  28. var proj:Matrix3D = p.toMatrix3D();
  29. var dx:Number = 0, dy:Number = 0;
  30. addEventListener(Event.ENTER_FRAME, onLoop);
  31. function onLoop(evt:Event):void {
  32.     var i:int, j:int;
  33.     dx += (mouseX - dx) / 4;
  34.     dy += (mouseY - dy) / 4;
  35.     m.identity();
  36.     m.appendRotation(getTimer() / 4, Vector3D.Y_AXIS);
  37.     m.transformVectors(points3D, points3Dout);
  38.    
  39.     m.identity();
  40.     m.appendRotation(dx, Vector3D.Z_AXIS);
  41.     m.appendRotation(dy, Vector3D.X_AXIS);
  42.     m.appendTranslation(0, 0, 1000);
  43.     m.append(proj);
  44.     Utils3D.projectVectors(m, points3Dout, points2D, uvts);
  45.     for (i = 0, j = 0; i<points2D.length; i+=2, j++){
  46.         sorted[j].x = points2D[i] + hsw;
  47.         sorted[j].y = points2D[i + 1] + hsh;
  48.         sorted[j].z = uvts[j * 3 + 2];
  49.     }
  50.     sorted.sortOn("z", Array.NUMERIC);
  51.     graphics.clear();
  52.     for(i = 0; i<sorted.length; i++){
  53.         var zpos:Number = sorted[i].z * 10000;
  54.         var c:int = zpos * 14;
  55.         graphics.beginFill(c <<16 | c <<8 | c);
  56.         graphics.drawCircle(sorted[i].x, sorted[i].y, zpos);
  57.         graphics.endFill();
  58.     }
  59. }

A variation on some recent posts... this snippet draws a rotating spring made up of 800 particles...

Have a look at the swf...


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

Fake Light w/ UV & Quads

Actionscript:
  1. [SWF(width = 500, height=500, backgroundColor = 0x000000)]
  2. x = stage.stageWidth / 2;
  3. y = stage.stageHeight / 2;
  4. var quadNum:int = 2200;
  5. // standard Vectors for using drawTriangles
  6. var verts:Vector.<Number> = new Vector.<Number>();
  7. var pVerts:Vector.<Number>;
  8. var uvts:Vector.<Number> = new Vector.<Number>();
  9. var indices:Vector.<int> = new Vector.<int>();
  10. // needed for z-sorting
  11. var sortedIndices:Vector.<int>;
  12. var faces:Array = [];
  13. // we'll use this for tranforming points
  14. // and as the transformation matrix for our render
  15. var m:Matrix3D = new Matrix3D();
  16. // plot a quad
  17. var quad:Vector.<Number>;
  18. quad = Vector.<Number>([-10, -10, 0,
  19.                         10, -10, 0,
  20.                         -10, 10, 0,
  21.                         10, 10, 0]);
  22. // temp vect for any transformed quads
  23. var transQuad:Vector.<Number> = new Vector.<Number>();
  24. var i:int;
  25. var inc:int = 0;
  26. for (i = 0; i<quadNum; i++){
  27.     m.identity();
  28.     var s:Number = (int(Math.random()*50) == 1) ? 2 + Math.random()*2 : .1 + Math.random() * 2;
  29.     m.appendScale(s, s, 1);
  30.     m.appendRotation(90, Vector3D.Y_AXIS);
  31.     var mult:Number = 100 + Math.random()*200;
  32.     m.appendTranslation(mult, 0, 0);
  33.     m.appendRotation(Math.random()*360, Vector3D.X_AXIS);
  34.     m.appendRotation(Math.random()*360, Vector3D.Y_AXIS);
  35.     m.appendRotation(Math.random()*360, Vector3D.Z_AXIS);
  36.     m.transformVectors(quad, transQuad);
  37.     verts = verts.concat(transQuad);
  38.     faces.push(new Vector3D());
  39.     faces.push(new Vector3D());
  40.     var i4:int = i * 4;
  41.     indices.push(0 + i4, 1 + i4, 2 + i4,
  42.                  1 + i4, 3 + i4, 2 + i4);
  43.     mult /= 300;
  44.     uvts.push(mult,mult,0,
  45.               mult+.1,mult,0,
  46.               mult,mult - .1,0,
  47.               mult + .1,mult + .1,0);
  48. }
  49. sortedIndices = new Vector.<int>(indices.length, true);
  50. // create texture
  51. var tex:BitmapData = new BitmapData(400,400,false, 0x000000);
  52. var grad:Shape = new Shape();
  53. var mat:Matrix = new Matrix();
  54. mat.createGradientBox(400,400,0,0,0);
  55. with (grad.graphics){
  56.     beginGradientFill(GradientType.LINEAR, [0xFFFFFF,0x002244], [1, 1], [100, 255], mat);
  57.     drawRect(0,0,400,400);
  58. }
  59. tex.draw(grad);
  60. // create background
  61. mat.createGradientBox(1600,1200,0,-550, 0);
  62. with (grad.graphics){
  63.     beginGradientFill(GradientType.RADIAL, [0x000000, 0x001133], [1, 1], [0, 255], mat);
  64.     drawRect(0,0,500,500);
  65. }
  66. grad.x = -stage.stageWidth/2
  67. grad.y = -stage.stageHeight/2;
  68. addChild(grad);
  69. // triangles will be drawn to this
  70. var render:Shape = Shape(addChild(new Shape()));
  71. // fix all vector lengths
  72. verts.fixed = true, uvts.fixed = true, indices.fixed = true
  73. pVerts = new Vector.<Number>(verts.length/3 * 2, true);
  74. // we need these if we want perspective
  75. var persp:PerspectiveProjection = new PerspectiveProjection();
  76. persp.fieldOfView = 45;
  77. // projection matrix
  78. var proj:Matrix3D = persp.toMatrix3D();
  79. var dx:Number = 0, dy:Number = 0;
  80. addEventListener(Event.ENTER_FRAME, onLoop);
  81. function onLoop(evt:Event):void {
  82.     dx += (mouseX - dx) / 4;
  83.     dy += (mouseY - dy) / 4;
  84.     m.identity();
  85.     m.appendRotation(dy, Vector3D.X_AXIS);
  86.     m.appendRotation(dx, Vector3D.Y_AXIS);
  87.     m.appendTranslation(0,0,800);
  88.     m.append(proj);
  89.     Utils3D.projectVectors(m, verts, pVerts, uvts);
  90.     var face:Vector3D;
  91.     inc = 0;
  92.     for (var i:int = 0; i<indices.length; i+=3){
  93.         face = faces[inc];
  94.         face.x = indices[i];
  95.         face.y = indices[int(i + 1)];
  96.         face.z = indices[int(i + 2)];
  97.         var i3:int = i * 3;
  98.         face.w = (uvts[int(face.x*3 + 2)] + uvts[int(face.y*3 + 2)] + uvts[int(face.z*3 + 2)]) * 0.333333;
  99.         inc++;
  100.     }
  101.     faces.sortOn("w", Array.NUMERIC);
  102.     inc = 0;
  103.     for each (face in faces){
  104.         sortedIndices[inc++] = face.x;
  105.         sortedIndices[inc++] = face.y;
  106.         sortedIndices[inc++] = face.z;
  107.     }
  108.     render.graphics.clear();
  109.     render.graphics.beginBitmapFill(tex, null, false, false);
  110.     render.graphics.drawTriangles(pVerts, sortedIndices, uvts, TriangleCulling.NEGATIVE);
  111. }

Expanding again on the z-sorting demos from the last few days - this snippet uses UV coords and a gradient to create something that vaguely resembles a light. Unlike the previous demos, the 3D cluster in this snippet is made up of quads - requiring a slight adjustment to the depth calculation.


Have a look at the swf...

I also posted the code over at wonderfl.net...

Also posted in 3D, Graphics, matrix, misc, sortOn | Tagged , , , | 2 Comments

More z-sorting

Actionscript:
  1. [SWF(width = 500, height=500, backgroundColor = 0x333333)]
  2. x = stage.stageWidth / 2;
  3. y = stage.stageHeight / 2;
  4.  
  5.  
  6. var polyNum:int = 3000;
  7. // standard Vectors for using drawTriangles
  8. var verts:Vector.<Number> = new Vector.<Number>();
  9. var pVerts:Vector.<Number>;
  10. var uvts:Vector.<Number> = new Vector.<Number>();
  11. var indices:Vector.<int> = new Vector.<int>();
  12. // needed for z-sorting
  13. var sortedIndices:Vector.<int>;
  14. var faces:Array = [];
  15.  
  16. // we'll use this for tranforming points
  17. // and as the transormation matrix for our render
  18. var m:Matrix3D = new Matrix3D();
  19.  
  20. // plot a poly
  21. var poly:Vector.<Number>;
  22. poly = Vector.<Number>([ 0, 0, 0,
  23.                         10, 0, 0,
  24.                         0,10, 0]);
  25.  
  26. // temp vect for any transformed polygons
  27. var transPoly:Vector.<Number> = new Vector.<Number>();
  28.  
  29. var i:int;
  30. var inc:int = 0;
  31. for (i = 0; i<polyNum; i++){
  32.     m.identity();
  33.     var s:Number = (int(Math.random()*50) == 1) ? 4 + Math.random()*2 : 1 + Math.random() * 2;
  34.     m.appendScale(s, s, 1);
  35.     m.appendRotation(Math.random()*360, Vector3D.X_AXIS);
  36.     m.appendRotation(Math.random()*360, Vector3D.Y_AXIS);
  37.     m.appendRotation(Math.random()*360, Vector3D.Z_AXIS);
  38.     m.appendTranslation(200,0,0);
  39.                          
  40.     m.appendRotation(Math.random()*360, Vector3D.X_AXIS);
  41.     m.appendRotation(Math.random()*360, Vector3D.Y_AXIS);
  42.     m.appendRotation(Math.random()*360, Vector3D.Z_AXIS);
  43.    
  44.     m.transformVectors(poly, transPoly);
  45.    
  46.     verts = verts.concat(transPoly);
  47.     faces.push(new Vector3D());
  48.     indices.push(inc++, inc++, inc++);
  49.     uvts.push(Math.random(), Math.random(), 0, Math.random(), Math.random(), 0, Math.random(), Math.random(), 0);
  50. }
  51.  
  52. sortedIndices = new Vector.<int>(indices.length, true);
  53.  
  54. // create texture
  55. var tex:BitmapData = new BitmapData(400,400,false, 0x000000);
  56. var grad:Shape = new Shape();
  57. var mat:Matrix = new Matrix();
  58. mat.createGradientBox(400,400,0,0,0);
  59. with (grad.graphics){
  60.     beginGradientFill(GradientType.LINEAR, [0x000000, 0xAA0000, 0xFFFF00], [1, 1, 1], [20, 200, 255], mat);
  61.     drawRect(0,0,400,400);
  62. }
  63. tex.draw(grad);
  64.  
  65. // create background
  66. mat.createGradientBox(1600,1000,0,-550, -100);
  67. with (grad.graphics){
  68.     beginGradientFill(GradientType.RADIAL, [0x333333, 0xffffff], [1, 1], [0, 255], mat);
  69.     drawRect(0,0,500,500);
  70. }
  71. grad.x = -stage.stageWidth/2
  72. grad.y = -stage.stageHeight/2;
  73. addChild(grad);
  74.  
  75. // triangles will be drawn to this
  76. var render:Shape = Shape(addChild(new Shape()));
  77.  
  78. // fix all vector lengths
  79. verts.fixed = true, uvts.fixed = true, indices.fixed = true
  80. pVerts = new Vector.<Number>(verts.length/3 * 2, true);
  81.  
  82. // we need these if we want perspective
  83. var persp:PerspectiveProjection = new PerspectiveProjection();
  84. persp.fieldOfView = 45;
  85. // projection matrix
  86. var proj:Matrix3D = persp.toMatrix3D();
  87.  
  88. var dx:Number = 0, dy:Number = 0;
  89. addEventListener(Event.ENTER_FRAME, onLoop);
  90. function onLoop(evt:Event):void {
  91.     dx += (mouseX - dx) / 4;
  92.     dy += (mouseY - dy) / 4;
  93.     m.identity();
  94.     m.appendRotation(dy, Vector3D.X_AXIS);
  95.     m.appendRotation(dx, Vector3D.Y_AXIS);
  96.     // push everything back so its not to close
  97.     m.appendTranslation(0,0,800);
  98.     // append the projection matrix at the end
  99.     m.append(proj);
  100.    
  101.     Utils3D.projectVectors(m, verts, pVerts, uvts);
  102.    
  103.     var face:Vector3D;
  104.     inc = 0;
  105.     for (var i:int = 0; i<indices.length; i+=3){
  106.         face = faces[inc];
  107.         face.x = indices[i];
  108.         // it may look odd, but casting to an int
  109.         // when doing operations inside array sytnax
  110.         // adds a big speed boost
  111.         face.y = indices[int(i + 1)];
  112.         face.z = indices[int(i + 2)];
  113.         var i3:int = i * 3;
  114.         // get the average z position (t value) and store it in the Vector3D w property
  115.         // depending on your model, you may not need to do an average of all 3 values
  116.         face.w = (uvts[int(i3 + 2)] + uvts[int(i3 + 5)] + uvts[int(i3 + 8)]) * 0.333333;
  117.         inc++;
  118.     }
  119.      
  120.     // sort on w, so far this beats all other sorting methods for speed,
  121.     // faster than Vector.sort(), faster than any custom sort method I could find
  122.     faces.sortOn("w", Array.NUMERIC);
  123.  
  124.     // re-order indices so that faces are drawn in the correct order (back to front);
  125.     inc = 0;
  126.     for each (face in faces){
  127.         sortedIndices[inc++] = face.x;
  128.         sortedIndices[inc++] = face.y;
  129.         sortedIndices[inc++] = face.z;
  130.     }
  131.    
  132.     render.graphics.clear();
  133.     render.graphics.beginBitmapFill(tex, null, false, false);
  134.     render.graphics.drawTriangles(pVerts, sortedIndices, uvts, TriangleCulling.NONE);
  135. }

This is a slightly more advanced version of the z-sorting demo from yesterday. Here 3000 polygons are randomly arranged in a sphere formation...


Have a look at the swf...

Also posted in 3D, Graphics, matrix, misc | Tagged , , , , | 6 Comments

drawTriangles() & z-sorting

Actionscript:
  1. [SWF(width = 500, height=500, backgroundColor = 0x000000)]
  2. x = stage.stageWidth / 2;
  3. y = stage.stageHeight / 2;
  4.  
  5. // standard Vectors for using drawTriangles and projectVectors
  6. var verts:Vector.<Number> = new Vector.<Number>();
  7. var pVerts:Vector.<Number>;
  8. var uvts:Vector.<Number>;
  9. var indices:Vector.<int>;
  10. // needed for z-sorting
  11. var sortedIndices:Vector.<int>;
  12. var faces:Array = [];
  13.  
  14. // we'll use this for transforming points
  15. // and as the transformation matrix for our render
  16. var m:Matrix3D = new Matrix3D();
  17.  
  18. // plot a poly
  19. var poly:Vector.<Number>;
  20. poly = Vector.<Number>([ 0, 0, 0,
  21.                         10, 0, 0,
  22.                         0,10, 0]);
  23.  
  24. verts = verts.concat(poly);
  25. faces.push(new Vector3D());
  26.  
  27. // add two more polygons by transorming the poly Vector
  28. // and concatenating it to the verts Vector
  29. // Vector3D instances are added to the faces
  30. // Array for z-sorting
  31.  
  32. // temp vect for any transformed polygons
  33. var transPoly:Vector.<Number> = new Vector.<Number>();
  34.  
  35. m.appendRotation(10, Vector3D.Z_AXIS);
  36. m.appendTranslation(0,-2,5);
  37. m.transformVectors(poly, transPoly);
  38.  
  39. verts = verts.concat(transPoly);
  40. faces.push(new Vector3D());
  41.  
  42. m.appendRotation(10, Vector3D.Z_AXIS);
  43. m.appendTranslation(0,-2,5);
  44. m.transformVectors(poly, transPoly);
  45. verts = verts.concat(transPoly);
  46. faces.push(new Vector3D());
  47.  
  48. // hard coded indices
  49. indices = Vector.<int>([0, 1, 2, 3, 4, 5, 6, 7, 8]);
  50. sortedIndices = new Vector.<int>(indices.length, true);
  51.  
  52. // create texture
  53. var tex:BitmapData = new BitmapData(100,100,false, 0x000000);
  54. tex.fillRect(new Rectangle(0,0,50,50), 0xFF0000);
  55. tex.fillRect(new Rectangle(50,0,50,50), 0x0000FF);
  56. tex.fillRect(new Rectangle(0,50,50,50), 0x00FF00);
  57.  
  58. // hard coded uvts
  59. uvts = Vector.<Number>([0,0,0, .5,0,0, 0,.5,0,
  60.                         .53, 0, 0, 1, 0, 0, .53, .5, 0,
  61.                          0,.6,.5, 0,.6,0, 0,1, 0]);
  62.                        
  63. // fix all vector lengths
  64. verts.fixed = true, uvts.fixed = true, indices.fixed = true
  65. pVerts = new Vector.<Number>(verts.length/3 * 2, true);
  66.  
  67. // we need these if we want perspective
  68. var persp:PerspectiveProjection = new PerspectiveProjection();
  69. // projection matrix
  70. var proj:Matrix3D = persp.toMatrix3D();
  71.  
  72. addEventListener(Event.ENTER_FRAME, onLoop);
  73. function onLoop(evt:Event):void {
  74.     m.identity();
  75.     m.appendRotation(mouseY * 2, Vector3D.X_AXIS);
  76.     m.appendRotation(mouseX * 2, Vector3D.Y_AXIS);
  77.     // push everything back so its not too close
  78.     m.appendTranslation(0,0,40);
  79.     // append the projection matrix at the end
  80.     m.append(proj);
  81.    
  82.     Utils3D.projectVectors(m, verts, pVerts, uvts);
  83.    
  84.     var face:Vector3D;
  85.     var inc:int = 0;
  86.     for (var i:int = 0; i<indices.length; i+=3){
  87.         face = faces[inc];
  88.         face.x = indices[i];
  89.         // it may look odd, but casting to an int
  90.         // when doing operations inside array sytnax
  91.         // adds a big speed boost
  92.         face.y = indices[int(i + 1)];
  93.         face.z = indices[int(i + 2)];
  94.         var i3:int = i * 3;
  95.         // get the average z position (t value) and store it in the Vector3D w property
  96.         // depending on your model, you may not need to do an average of all 3 values
  97.                 // (t is the distance from the eye to the texture)
  98.         face.w = (uvts[int(i3 + 2)] + uvts[int(i3 + 5)] + uvts[int(i3 + 8)]) * 0.333333;
  99.         inc++;
  100.     }
  101.    
  102.     // sort on w, so far this beats all other sorting methods for speed,
  103.     // faster than Vector.sort(), faster than any custom sort method I could find
  104.     faces.sortOn("w", Array.NUMERIC);
  105.    
  106.     // re-order indices so that faces are drawn in the correct order (back to front);
  107.     inc = 0;
  108.     for each (face in faces){
  109.         sortedIndices[inc++] = face.x;
  110.         sortedIndices[inc++] = face.y;
  111.         sortedIndices[inc++] = face.z;
  112.     }
  113.    
  114.     graphics.clear();
  115.     graphics.beginBitmapFill(tex, null, false, false);
  116.     graphics.drawTriangles(pVerts, sortedIndices, uvts, TriangleCulling.NONE);
  117. }

So you want to be able to do some z-sorting with drawTriangles()? Well, its extremely unintuitive. Here is what you need to know:

1) Vector.sort() is slow
2) Array.sortOn() is quite fast
3) I couldn't get any custom sorting method to be faster than Array.sortOn
4) You can use the t value from uvts to do z-sorting (like in this demo)
5) If your going for speed, don't forget to use fixed Vectors (I often forget this step)
6) When working with Vectors cast any operations inside brackets to int() (my tests showed this is a huge speed boost up to 3x faster - franky I think it's horrible that you have to do this).

The swf is not very interesting because I wanted to keep it super simple, but here it is anyway...


Questions

I was told and have read that drawTriangles is slower than using drawGraphicsData and a GraphicsTrianglePath instance. I tested this extensively and found that drawGraphicsData was slower. I'm still not sure which is faster but am up for checking out any simple benchmarks that people have.

drawTriangles is supposed to be faster without adding t values to the uvts Vector. In my benchmark tests there was no real difference in speed. The t value is used to render more accurate textures - which would mean you could potentially use less triangles in your models. One would assume that not using a t value would be faster... but I couldn't confirm this. Again if someone has a good benchmark for this, please let me know.

Help

I had a great deal of help from a few people on Twitter, Katopz (Away3D contributor) of sleepydesign.com made me aware of the fact that Array.sortOn is the way to go... You can see some great demos over at Katopz's blog. While I didn't end up using a custom sorting method, Inspirit
pointed me to his article about custom Vector sorting methods which proved to be very enlightening. I was able to get some really great results for doing different types of sorting - just sorting 1D Vectors with FlashSort can be very fast (faster than Array.sortOn - but not helpful for sorting a 1D Vector of indices).

I also learned a good deal by looking at this code post by Psyark... I actually optimized that code to run about 2x faster (will post that on wonderfl.net at some point, it just needs to be cleaned up).

kevinSuttle sent me a link to The video

Also posted in 3D, Graphics, matrix | 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 3D, Graphics, 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 3D, Graphics, sortOn | Tagged , , | 5 Comments