Category Archives: Math

Triangular Numbers

By Zevan | October 20, 2009
CLICK HERE TO COPY
Actionscript:
  1. [SWF(width = 500, height = 500)]
  2.  
  3. var txt:TextField = TextField(addChild(new TextField()));
  4. txt.defaultTextFormat = new TextFormat("_sans", 4);
  5. txt.width = stage.stageWidth;
  6. txt.height = stage.stageHeight+4;
  7. txt.z = -1;
  8. txt.x = stage.stageWidth
  9. txt.rotation = 90;
  10. var count:int = 0;
  11. addEventListener(Event.ENTER_FRAME, onLoop);
  12. function onLoop(evt:Event):void{
  13.      count++;
  14.      txt.appendText(triangular(count).toString(2) + "\n");
  15.      txt.scrollV= txt.maxScrollV;
  16. }
  17. function triangular(n:int):int{
  18.        return (n * (n + 1)) / 2;
  19. }

Calculate some triangular numbers... (n * (n + 1)) / 2....

Check out the swf on wonderfl

Also posted in misc | Tagged , , | Leave a comment

Flowing Leaves (optical illusion)

By Zevan | October 19, 2009


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

CLICK HERE TO COPY
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, Vector, misc, motion, pixel manipulation | Tagged , , , | 5 Comments

Bitwise OR | and Variable Function Arguments (bitwise flags)

By Zevan | October 12, 2009
CLICK HERE TO COPY
Actionscript:
  1. const A:uint = 1;
  2. const B:uint = 2;
  3. const C:uint = 4;
  4. const D:uint = 8;
  5. const E:uint = 16;
  6.  
  7. function orArgs(args:uint):void{
  8.     if (args & A){
  9.         trace("A");
  10.     }
  11.     if (args & B){
  12.         trace("B");
  13.     }
  14.     if (args & C){
  15.         trace("C");
  16.     }
  17.     if (args & D){
  18.         trace("D");
  19.     }
  20.     if (args & E){
  21.         trace("E");
  22.     }
  23. }
  24.  
  25. // test out the function:
  26. orArgs(A | B);
  27. trace("--");
  28. orArgs(A | C | E);
  29. trace("--");
  30. orArgs(B | E | D);
  31. trace("--");
  32. orArgs(C | A);
  33.  
  34. /* outputs:
  35. A
  36. B
  37. --
  38. A
  39. C
  40. E
  41. --
  42. B
  43. D
  44. E
  45. --
  46. A
  47. C
  48. */

If you've every used Array.sort(Array.NUMERIC | Array.DESCENDING) you should have at least a vague idea about what this snippet is doing. It shows how you can pass a variable number of arguments to a function using | (bitwise OR) and & (bitwise AND). I believe the correct term for these kind of arguments is "bitwise flags". This snippet works by having a series of constant values... in this case A - E. Each constant is assigned an unsigned integer... now you may not see the significance of the values 1, 2, 4, 8 and 16 until you see them in binary... get ready this is a pretty cryptic description...

A = 00001 = 1
B = 00010 = 2
C = 00100 = 4
D = 01000 = 8
E = 10000 = 16

If we OR all these together we get: 11111... If we do:

A | E
00001 | 10000

we end up with 10001...

...we can then check which values are stored in the resulting unsigned integer by using AND:

check for A... 10001 & 00001 = 00001 = true
check for E... 10001 & 10000 = 10000 = true
check for C... 10001 & 00100 = 00000 = false

That's it... I just guessed at the way this was being done... if you have another way to do the same thing, feel free to post it in the comments....

Also posted in Operators, binary, misc | Tagged , , , | 1 Comment

Bad PI Approximation

By Zevan | October 11, 2009
CLICK HERE TO COPY
Actionscript:
  1. var inside:Number = 0
  2. var precision:Number = 1000000;
  3. for (var i:int = 0; i<precision; i++){
  4.        var xp:Number = 0.5 - Math.random();
  5.        var yp:Number = 0.5 - Math.random();
  6.        if (Math.sqrt(xp * xp + yp * yp) <0.5){
  7.                inside++;
  8.        }
  9. }
  10. trace(inside / precision * 4);
  11. // outputs : 3.143304

Someone described this bad method of a PI approximation to me the other day... figured I'd try it out... pretty funny. I always liked 22/7... but this one is definitely funnier...

Posted in Math | Tagged , , | 3 Comments